Sunday, May 8, 2016
XI - 2.1 Scalars and Vectors - Mathematics for Physics - Video Lectures
Scalars And Vectors Part 1 Physics Board video lecture By Rao IIT Academy
Rao IIT Academy
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____________
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___________
XI - 2.8 Cross product or vector product of two vectors - Video Lectures
Physics - Mechanics: Vectors (18 of 20) Product Of Vectors: Cross Product: Example 2
Michel van Biezen
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_______________
XI - 2.5 Subtraction of vectors - Video Lectures
Physics Lecture - 9 - Vector Subtraction
thenewboston
_________________
_________________
XI - 2.4 Multiplication of a vector by a number - Video Lectures
Dot Product, Cross Product, and Multiplying Vectors by Scalars
AK LECTURES
________________
________________
________________
________________
XI - 2.3 Addition of vectors - Video Lectures
Addition of vectors
Magnitude of av+bv = SQRT(a²+b²+ 2ab cos θ)
The angle of the resultant with av is α where
tanα = b sin θ/(a+b cos θ)
Interesting point to make note of:
Two vectors having equal magnitudes of a make an angle θ with each other. Find the magnitude and direction of the resultant(Resultant is output of the addition of two vectors.)
Magnitude = 2a cos θ/2
and
tan α = a sin θ/(a + a cos θ) = (2asin(θ/2)cos(θ/2))/(2acos²(θ/2))
= tan (θ/2)
Example: Two vectors are of equal magnitude of 10 units. One of them is inclined at 45° to the X-axis and the other is inclined at 75° to the X-axis. Find the magnitude and direction of the resultant with respect to X-axis.
The angle between vectors is 30°.
Hence magnitude of the resultant will be 20 cos 15°
The direction - The resultant is inclined at 60° to the X axis.
Physics Vector Addition (Algebraic)
PhysicsEH
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________________
XII - 18.3 Relation between u,v and R for spherical mirrors - Video Lectures
10 May
Ray Diagrams - Mirrors
Bozeman Science
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Relation Between Focal Length and Radius of Curvature Spherical mirror
CBSE Video Tutorials Science and Math
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Ray Diagrams - Mirrors
Bozeman Science
_______________
_______________
Relation Between Focal Length and Radius of Curvature Spherical mirror
CBSE Video Tutorials Science and Math
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XII - 18.2 Spherical mirrors - Video Lectures
10 May
Reflection by Spherical Mirrors
Educomp smartclassTab
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Concave and Convex Mirror Ray Diagrams, Chapter 17 Review
dcaulf
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Reflection by Spherical Mirrors
Educomp smartclassTab
__________________
__________________
Concave and Convex Mirror Ray Diagrams, Chapter 17 Review
dcaulf
__________________
__________________
XII - 18.1 Reflection at smooth surfaces - Video Lectures
10 May
Laws of Reflection
Byju's
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Laws of Reflection
Byju's
______________
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XII - 17. 16. Polarization of light - Video Lectures
9 May
Polarization of light, linear and circular | Light waves | Physics | Khan Academy
khanacademymedicine
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Polarization of light, linear and circular | Light waves | Physics | Khan Academy
khanacademymedicine
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Thursday, May 5, 2016
XII - 17.12. Fraunhofer Diffraction by a circular aperture - Video Lectures
_____________________
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MITOpenCourseware
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_____________________
nptelhrd
XII - 17.11. Fraunhofer Diffraction by a single slit - Video Lectures
XII - 17.11. Fraunhofer Diffraction by a single slit - Video Lectures
___________________
___________________
AK Lectures
XII - 17.10. Diffraction of light - Video Lectures
XII - 17.10. Diffraction of light - Video Lectures
____________________
____________________
ExamFearVideos
____________________
____________________
dave evans
Tuesday, May 3, 2016
XII - 17.9. coherent and incoherent sources Video Lectures
XII - 17.9. coherent and incoherent sources Video Lectures
Physics Wave Optics - Coherent & incoherent source - CBSE class 12
ExamFearVideos
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___________________________
XII - 17.8. Fresnel's Biprism -Video Lectures
XII - 17.8. Fresnel's Biprism -Video Lectures
IIT JEE Physics ( Fresnel's biprism )
Collegepedia.in
___________________
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Class 12 Physics Online Lecture | Interference | Fresnal's Biprism as a Limiting Case of YDSE
Physics Galaxy
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XII - 17.7. Interference from thin films - Video Lectures
XII - 17.7. Interference from thin films - Video Lectures
_________________
________________
Khanacadeymedicine
________________
________________
Harvard Natural Sciences Lecture Demonstrations
XII - 17.6. Optical path - Video Lectures
XII - 17.6. Optical path - Video Lectures
____________________
____________________
Jamie Althoff OD
____________________
____________________
Jumeirah College Science
Monday, May 2, 2016
XII - 17.5. Young's double slit experiment- Video Lectures
XII -
17.5. Young's double slit experiment- Video Lectures
__________________
__________________
ExamFearVideos
XI - 1.7 Order of magnitude - Video Lectures
Class XI -
1.7 Order of magnitude - Video Lectures
Order of magnitude
Convert the number into 1*10^c form.
First convert the number into a*10^b form in this case 1≤a<10 an="" and="" b="" br="" integer.="" is="">If a is less than or equal to 5 assume it is one and if a is greater than 5 assume it is 10 and convert the number into 1*10^c form.
Then c is the order of magnitude of the number.
________________
________________
Chris Doner
H.C. Verma Physics Chapter 1 Problems and Solutions
_________________
_________________
Omega Open Course
XII - 17.3. Huygen's principles - Video Lectures
____________________
____________________
MindsetLearn
http://iit-jee-physics.blogspot.com/2008/04/concept-review-ch-17-light-waves.html
Sunday, May 1, 2016
CBSE 2010 Class XI (2008-09) Syllabus
PHYSICS (Code No. 042)
Senior Secondary stage of school education is a stage of transition from general
education to discipline-based focus on curriculum. The present updated syllabus keeps
in view the rigour and depth of disciplinary approach as well as the comprehension
level of learners. Due care has also been taken that the syllabus is not heavy and is at
the same time, comparable to the international standards. Salient features of the syllabus
include:
_ Emphasis on basic conceptual understanding of the content.
_ Emphasis on use of SI units, symbols, nomenclature of physical quantities and
formulations as per international standards.
_ Providing logical sequencing of units of the subject matter and proper placement of
concepts with their linkage for better learning.
_ Reducing the curriculum load by eliminating overlapping of concepts/ content within
the discipline and other disciplines.
_ Promotion of process-skills, problem-solving abilities and applications of Physics
concepts.
Besides, the syllabus also attempts to
_ strengthen the concepts developed at the secondary stage to provide firm foundation
for further learning in the subject.
_ expose the learners to different processes used in Physics-related industrial and
technological applications.
_ develop process-skills and experimental, observational, manipulative, decision
making and investigatory skills in the learners.
_ promote problem solving abilities and creative thinking in learners.
_ develop conceptual competence in the learners and make them realize and appreciate
the interface of Physics with other disciplines.
COURSE STRUCTURE
Class XI (Theory)
One Paper Three Hours Max Marks: 70
Class XI Weightage
Unit I Physical World & Measurement 03
Unit II Kinematics 10
Unit III Laws of Motion 10
Unit IV Work, Energy & Power 06
Unit V Motion of System of particles & Rigid Body 06
Unit VI Gravitation 05
Unit VII Properties of Bulk Matter 10
Unit VIII Thermodynamics 05
Unit XI Behaviour of Perfect Gas & Kinetic Theory of gases 05
Unit X Oscillations & Waves 10
Total 70
Unit I: Physical World and Measurement (periods 10)
Physics - scope and excitement; nature of physical laws; Physics, technology and society.
Need for measurement: Units of measurement; systems of units; SI units, fundamental
and derived units. Length, mass and time measurements; accuracy and precision of
measuring instruments; errors in measurement; significant figures.
Dimensions of physical quantities, dimensional analysis and its applications.
Unit II: Kinematics (Periods 30)
Frame of reference. Motion in a straight line: Position-time graph, speed and velocity.
Uniform and non-uniform motion, average speed and instantaneous velocity.
Uniformly accelerated motion, velocity-time, position-time graphs, relations for uniformly accelerated motion (graphical treatment).
Elementary concepts of differentiation and integration for describing motion.
Scalar and vector quantities: Position and displacement vectors, general vectors and
notation, equality of vectors, multiplication of vectors by a real number; addition and
subtraction of vectors. Relative velocity.
Unit vector; Resolution of a vector in a plane - rectangular components. Motion in a
plane. Cases of uniform velocity and uniform acceleration-projectile motion. Uniform
circular motion.
Unit III: Laws of Motion (Periods 16)
Intuitive concept of force. Inertia, Newton’s first law of motion; momentum and Newton’s second law of motion; impulse; Newton’s third law of motion. Law of conservation of linear momentum and its applications.
Equilibrium of concurrent forces. Static and kinetic friction, laws of friction, rolling friction.
Dynamics of uniform circular motion: Centripetal force, examples of circular motion
(vehicle on level circular road, vehicle on banked road).
Unit IV: Work, Energy and Power (Periods 16)
Scalar product of vectors. Work done by a constant force and a variable force; kinetic
energy, work-energy theorem, power.
Notion of potential energy, potential energy of a spring, conservative forces: conservation
of mechanical energy (kinetic and potential energies); non-conservative forces: elastic
and inelastic collisions in one and two dimensions.
Unit V: Motion of System of Particles and Rigid Body (Periods 18)
Centre of mass of a two-particle system, momentum conversation and centre of mass
motion. Centre of mass of a rigid body; centre of mass of uniform rod.
Vector product of vectors; moment of a force, torque, angular momentum, conservation
of angular momentum with some examples.
Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion,
comparison of linear and rotational motions; moment of inertia, radius of gyration.
Values of moments of inertia for simple geometrical objects (no derivation). Statement of
parallel and perpendicular axes theorems and their applications.
Unit VI: Gravitation (Periods 14)
Keplar’s laws of planetary motion. The universal law of gravitation.
Acceleration due to gravity and its variation with altitude and depth.
Gravitational potential energy; gravitational potential. Escape velocity. Orbital velocity
of a satellite. Geo-stationary satellites.
Unit VII: Properties of Bulk Matter (Periods 28)
Elastic behaviour, Stress-strain relationship, Hooke’s law, Young’s modulus, bulk modulus, shear, modulus of rigidity.
Pressure due to a fluid column; Pascal’s law and its applications (hydraulic lift and hydraulic brakes). Effect of gravity on fluid pressure.
Viscosity, Stokes’ law, terminal velocity, Reynold’s number, streamline and turbulent
flow. Bernoulli’s theorem and its applications.
Surface energy and surface tension, angle of contact, application of surface tension ideas to drops, bubbles and capillary rise.
Heat, temperature, thermal expansion; specific heat - calorimetry; change of state - latent heat.
Heat transfer-conduction, convection and radiation, thermal conductivity, Newton’s law of cooling.
Unit VIII: Thermodynamics (Periods 12)
Thermal equilibrium and definition of temperature (zeroth law of thermodynamics). Heat, work and internal energy. First law of thermodynamics.
Second law of thermodynamics: reversible and irreversible processes. Heat engines and
refrigerators.
Unit IX: Behaviour of Perfect Gas and Kinetic Theory (Periods 8)
Equation of state of a perfect gas, work done on compressing a gas.
Kinetic theory of gases - assumptions, concept of pressure. Kinetic energy and temperature; rms speed of gas molecules; degrees of freedom, law of equipartition of energy (statement only) and application to specific heats of gases; concept of mean free path, Avogadro’s number.
Unit X: Oscillations and Waves (Periods 28)
Periodic motion - period, frequency, displacement as a function of time. Periodic functions.
Simple harmonic motion (S.H.M) and its equation; phase; oscillations of a spring–restoring force and force constant; energy in S.H.M.-kinetic and potential energies; simple pendulum–derivation of expression for its time period; free, forced and damped oscillations (qualitative ideas only), resonance.
Wave motion. Longitudinal and transverse waves, speed of wave motion. Displacement
relation for a progressive wave. Principle of superposition of waves, reflection of waves,
standing waves in strings and organ pipes, fundamental mode and harmonics, Beats,
Doppler effect.
Practicals
Note: Every student will perform 10 experiments (5 from each section) and 8 activities (4
from each section) during the academic year.
Two demonstration experiments must be performed by the teacher with participation of
students. The students will maintain a record of these demonstration experiments. Schools are advised to see the guidelines for evaluation in practicals for Class XII. Similar pattern may the followed for Class XI.
SECTION A
Experiments
1. Use of Vernier Callipers
(i) to measure diameter of a small spherical/cylindrical body.
(ii) to measure dimensions of a given regular body of known mass and hence find its
density.
(iii) to measure internal diameter and depth of a given beaker/calorimeter and hence
find its volume.
2. Use of screw gauge
(i) to measure diameter of a given wire, (ii) to measure thickness of a given sheet
(iii) to measure volume of an irregular lamina
3. To determine radius of curvature of a given spherical surface by a spherometer.
4. To find the weight of a given body using parallelogram law of vectors.
5. Using a simple pendulum, plot L-T and L-T2 graphs. Hence find the effective length of
second’s pendulum using appropriate graph.
6. To study the relationship between force of limiting friction and normal reaction and to find co-efficient of friction between a block and a horizontal surface.
7. To find the downward force, along an inclined plane, acting on a roller due to gravitational pull of the earth and study its relationship with the angle of inclination by plotting graph between force and sin.
Activities
1. To make a paper scale of given least count, e.g. 0.2cm, 0.5cm.
2. To determine mass of a given body using a metre scale by principle of moments.
3. To plot a graph for a given set of data, with proper choice of scales and error bars.
4. To measure the force of limiting friction for rolling of a roller on a horizontal plane.
5. To study the variation in range of a jet of water with angle of projection.
6. To study the conservation of energy of a ball rolling down on inclined plane (using a
double inclined plane).
7. To study dissipation of energy of a simple pendulum by plotting a graph between square of amplitude and time.
SECTION B
Experiments
1. To determine Young’s modulus of elasticity of the material of a given wire.
2. To find the force constant of a helical spring by plotting graph between load and extension.
3. To study the variation in volume with pressure for a sample of air at constant temperature by plotting graphs between P and V, and between P and I/V.
4. To determine the surface tension of water by capillary rise method.
5. To determine the coefficient of viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body.
6. To study the relationship between the temperature of a hot body and time by plotting a
cooling curve.
7. (i) To study the relation between frequency and length of a given wire under constant
tension using sonometer.
(ii) To study the relation between the length of a given wire and tension for constant
frequency using sonometer.
8. To find the speed of sound in air at room temperature using a resonance tube by two resonance positions.
9. To determine specific heat of a given (i) solid (ii) liquid, by method of mixtures.
Activities
1. To observe change of state and plot a cooling curve for molten wax.
2. To observe and explain the effect of heating on a bi-metallic strip.
3. To note the change in level of liquid in a container on heating and interpret the observations.
4. To study the effect of detergent on surface tension by observing capillary rise.
5. To study the factors affecting the rate of loss of heat of a liquid.
6. To study the effect of load on depression of a suitably clamped metre scale loaded
(i) at its end (ii) in the middle.
Recommended Textbooks.
1. Physics Part-I, Textbook for Class XI, Published by NCERT
2 . Physics Part-II, Textbook for Class XI, Published by NCERT
Syllabus 2016 download
CLASS XI (THEORY)
(Total Periods: 180)
Unit I: Physical World and Measurement (Periods 10)
Physics: Scope and excitement; nature of physical laws; Physics, technology and society.
Need for measurement: Units of measurement; systems of units; SI units, fundamental and derived
units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in
measurement; significant figures.
Dimensions of physical quantities, dimensional analysis and its applications.
Unit II: Kinematics (Periods 30)
Frame of reference, Motion in a straight line: Position-time graph, speed and velocity. Uniform and
non-uniform motion, average speed and instantaneous velocity. Uniformly accelerated motion, velocitytime
and position-time graphs, relations for uniformly accelerated motion (graphical treatment).
Elementary concepts of differentiation and integration for describing motion. Scalar and vector
quantities: Position and displacement vectors, general vectors and notation, equality of vectors, multiplication
of vectors by a real number; addition and subtraction of vectors. Relative velocity.
Unit vectors. Resolution of a vector in a plane – rectangular components.
Scalar and Vector products of Vectors. Motion in a plane. Cases of uniform velocity and uniform
acceleration – projectile motion. Uniform circular motion.
Unit III: Laws of Motion (Periods 16)
Intuitive concept of force. Inertia, Newton’s first law of motion; momentum and Newton’s second
law of motion; impulse; Newton’s third law of motion. Law of conservation of linear momentum and its
applications.
Equilibrium of concurrent forces. Static and kinetic friction, laws of friction, rolling friction, lubrication.
Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on
level circular road, vehicle on banked road).
Unit IV: Work, Energy and Power (Periods 16)
Work done by a constant force and a variable force; kinetic energy, work-energy theorem, power.
Notion of potential energy, potential energy of a spring, conservative forces; conservation of mechanical
energy (kinetic and potential energies); non-conservative forces; motion in a vertical circle, elastic and
inelastic collisions in one and two dimensions.
Unit V: Motion of System of Particles and Rigid Body (Periods 18)
Centre of mass of a two-particle system, momentum conservation and centre of mass motion. Centre
of mass of a rigid body; centre of mass of uniform rod.
Moment of a force, torque, angular momentum, conservation of angular momentum with some
examples.
4
Equilibrium of rigid bodies, rigid body rotation and equation of rotational motion, comparison of linear
and rotational motions; moment of inertia, radius of gyration. Values of M.I. for simple geometrical objects
(no derivation). Statement of parallel and perpendicular axes theorems and their applications.
Unit VI: Gravitation (Periods 14)
Kepler’s laws of planetary motion. The universal law of gravitation. Acceleration due to gravity and its
variation with altitude and depth.
Gravitational potential energy; gravitational potential. Escape velocity, orbital velocity of a satellite.
Geostationary satellites.
Unit VII: Properties of Bulk Matter (Periods 28)
Elastic behaviour, Stress-strain relationship, Hooke’s law, Young’s modulus, bulk modulus, shear,
modulus of rigidity, poisson’s ratio; elastic energy.
Pressure due to a fluid column; Pascal’s law and its applications (hydraulic lift and hydraulic brakes).
Effect of gravity on fluid pressure.
Viscosity, Stokes’ law, terminal velocity, Reynold’s number, streamline and turbulent flow. Critical
velocity, Bernoulli’s theorem and its applications.
Surface energy and surface tension, angle of contact, excess of pressure, application of surface tension
ideas to drops, bubbles and capillary rise.
Heat, temperature, thermal expansion; thermal expansion of solids, liquids, and gases. Anomalous
expansion. Specific heat capacity: Cp
, Cv
– calorimetry; change of state – latent heat.
Heat transfer – conduction and thermal conductivity, convection and radiation. Qualitative ideas of
Black Body Radiation, Wein’s displacement law, and Green House effect.
Newton’s law of cooling and Stefan’s law.
Unit VIII: Thermodynamics (Periods 12)
Thermal equilibrium and definition of temperature (zeroth law of Thermodynamics). Heat, work and
internal energy. First law of thermodynamics. Isothermal and adiabatic processes.
Second law of thermodynamics: Reversible and irreversible processes. Heat engines and refrigerators.
Unit IX: Behaviour of Perfect Gas and Kinetic Theory (Periods 8)
Equation of state of a perfect gas, work done on compressing a gas.
Kinetic theory of gases: Assumptions, concept of pressure. Kinetic energy and temperature; rms
speed of gas molecules; degrees of freedom, law of equipartition of energy (statement only) and application
to specific heat capacities of gases; concept of mean free path, Avogadro’s number.
Unit X: Oscillations and Waves (Periods 28)
Periodic motion – period, frequency, displacement as a function of time. Periodic functions. Simple
harmonic motion (SHM) and its equation; phase; oscillations of a spring – restoring force and force constant;
energy in SHM – kinetic and potential energies; simple pendulum – derivation of expression for its time
period; free, forced and damped oscillations (qualitative ideas only), resonance.
Wave motion. Longitudinal and transverse waves, speed of wave motion. Displacement relation for a
progressive wave. Principle of superposition of waves, reflection of waves, standing waves in strings and
organ pipes, fundamental mode and harmonics. Beats. Doppler effect.
5
PRACTICALS
Total Periods 60
Section A
Experiments
1. To measure diameter of a small spherical/cylindrical body using Vernier callipers.
2. To measure internal diameter and depth of a given beaker/calorimeter using Vernier callipers and
hence find its volume.
3. To measure diameter of a given wire using screw gauge.
4. To measure thickness of a given sheet using screw gauge.
5. To measure volume of an irregular lamina using screw gauge.
6. To determine radius of curvature of a given spherical surface by a spherometer.
7. To determine the mass of two different objects using a beam balance.
8. To find the weight of a given body using parallelogram law of vectors.
9. Using a simple pendulum, plot L-T and L-T2
graphs. Hence find the effective length of a second’s
pendulum using appropriate graph.
10. To study the relationship between force of limiting friction and normal reaction and to find the
coefficient of friction between a block and a horizontal surface.
11. To find the downward force, along an inclined plane, acting on a roller due to gravitational pull of
the earth and study its relationship with the angle of inclination (θ) by plotting graph between force
and sin θ.
Activities
1. To make a paper scale of given least count, e.g. 0.2 cm, 0.5 cm.
2. To determine mass of a given body using a metre scale by principle of moments.
3. To plot a graph for a given set of data, with proper choice of scales and error bars.
4. To measure the force of limiting friction for rolling of a roller on a horizontal plane.
5. To study the variation in the range of a jet of water with the angle of projection.
6. To study the conservation of energy of a ball rolling down on inclined plane (using a double
inclined plane).
7. To study dissipation of energy of a simple pendulum by plotting a graph between square of
amplitude and time.
Senior Secondary stage of school education is a stage of transition from general
education to discipline-based focus on curriculum. The present updated syllabus keeps
in view the rigour and depth of disciplinary approach as well as the comprehension
level of learners. Due care has also been taken that the syllabus is not heavy and is at
the same time, comparable to the international standards. Salient features of the syllabus
include:
_ Emphasis on basic conceptual understanding of the content.
_ Emphasis on use of SI units, symbols, nomenclature of physical quantities and
formulations as per international standards.
_ Providing logical sequencing of units of the subject matter and proper placement of
concepts with their linkage for better learning.
_ Reducing the curriculum load by eliminating overlapping of concepts/ content within
the discipline and other disciplines.
_ Promotion of process-skills, problem-solving abilities and applications of Physics
concepts.
Besides, the syllabus also attempts to
_ strengthen the concepts developed at the secondary stage to provide firm foundation
for further learning in the subject.
_ expose the learners to different processes used in Physics-related industrial and
technological applications.
_ develop process-skills and experimental, observational, manipulative, decision
making and investigatory skills in the learners.
_ promote problem solving abilities and creative thinking in learners.
_ develop conceptual competence in the learners and make them realize and appreciate
the interface of Physics with other disciplines.
COURSE STRUCTURE
Class XI (Theory)
One Paper Three Hours Max Marks: 70
Class XI Weightage
Unit I Physical World & Measurement 03
Unit II Kinematics 10
Unit III Laws of Motion 10
Unit IV Work, Energy & Power 06
Unit V Motion of System of particles & Rigid Body 06
Unit VI Gravitation 05
Unit VII Properties of Bulk Matter 10
Unit VIII Thermodynamics 05
Unit XI Behaviour of Perfect Gas & Kinetic Theory of gases 05
Unit X Oscillations & Waves 10
Total 70
Unit I: Physical World and Measurement (periods 10)
Physics - scope and excitement; nature of physical laws; Physics, technology and society.
Need for measurement: Units of measurement; systems of units; SI units, fundamental
and derived units. Length, mass and time measurements; accuracy and precision of
measuring instruments; errors in measurement; significant figures.
Dimensions of physical quantities, dimensional analysis and its applications.
Unit II: Kinematics (Periods 30)
Frame of reference. Motion in a straight line: Position-time graph, speed and velocity.
Uniform and non-uniform motion, average speed and instantaneous velocity.
Uniformly accelerated motion, velocity-time, position-time graphs, relations for uniformly accelerated motion (graphical treatment).
Elementary concepts of differentiation and integration for describing motion.
Scalar and vector quantities: Position and displacement vectors, general vectors and
notation, equality of vectors, multiplication of vectors by a real number; addition and
subtraction of vectors. Relative velocity.
Unit vector; Resolution of a vector in a plane - rectangular components. Motion in a
plane. Cases of uniform velocity and uniform acceleration-projectile motion. Uniform
circular motion.
Unit III: Laws of Motion (Periods 16)
Intuitive concept of force. Inertia, Newton’s first law of motion; momentum and Newton’s second law of motion; impulse; Newton’s third law of motion. Law of conservation of linear momentum and its applications.
Equilibrium of concurrent forces. Static and kinetic friction, laws of friction, rolling friction.
Dynamics of uniform circular motion: Centripetal force, examples of circular motion
(vehicle on level circular road, vehicle on banked road).
Unit IV: Work, Energy and Power (Periods 16)
Scalar product of vectors. Work done by a constant force and a variable force; kinetic
energy, work-energy theorem, power.
Notion of potential energy, potential energy of a spring, conservative forces: conservation
of mechanical energy (kinetic and potential energies); non-conservative forces: elastic
and inelastic collisions in one and two dimensions.
Unit V: Motion of System of Particles and Rigid Body (Periods 18)
Centre of mass of a two-particle system, momentum conversation and centre of mass
motion. Centre of mass of a rigid body; centre of mass of uniform rod.
Vector product of vectors; moment of a force, torque, angular momentum, conservation
of angular momentum with some examples.
Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion,
comparison of linear and rotational motions; moment of inertia, radius of gyration.
Values of moments of inertia for simple geometrical objects (no derivation). Statement of
parallel and perpendicular axes theorems and their applications.
Unit VI: Gravitation (Periods 14)
Keplar’s laws of planetary motion. The universal law of gravitation.
Acceleration due to gravity and its variation with altitude and depth.
Gravitational potential energy; gravitational potential. Escape velocity. Orbital velocity
of a satellite. Geo-stationary satellites.
Unit VII: Properties of Bulk Matter (Periods 28)
Elastic behaviour, Stress-strain relationship, Hooke’s law, Young’s modulus, bulk modulus, shear, modulus of rigidity.
Pressure due to a fluid column; Pascal’s law and its applications (hydraulic lift and hydraulic brakes). Effect of gravity on fluid pressure.
Viscosity, Stokes’ law, terminal velocity, Reynold’s number, streamline and turbulent
flow. Bernoulli’s theorem and its applications.
Surface energy and surface tension, angle of contact, application of surface tension ideas to drops, bubbles and capillary rise.
Heat, temperature, thermal expansion; specific heat - calorimetry; change of state - latent heat.
Heat transfer-conduction, convection and radiation, thermal conductivity, Newton’s law of cooling.
Unit VIII: Thermodynamics (Periods 12)
Thermal equilibrium and definition of temperature (zeroth law of thermodynamics). Heat, work and internal energy. First law of thermodynamics.
Second law of thermodynamics: reversible and irreversible processes. Heat engines and
refrigerators.
Unit IX: Behaviour of Perfect Gas and Kinetic Theory (Periods 8)
Equation of state of a perfect gas, work done on compressing a gas.
Kinetic theory of gases - assumptions, concept of pressure. Kinetic energy and temperature; rms speed of gas molecules; degrees of freedom, law of equipartition of energy (statement only) and application to specific heats of gases; concept of mean free path, Avogadro’s number.
Unit X: Oscillations and Waves (Periods 28)
Periodic motion - period, frequency, displacement as a function of time. Periodic functions.
Simple harmonic motion (S.H.M) and its equation; phase; oscillations of a spring–restoring force and force constant; energy in S.H.M.-kinetic and potential energies; simple pendulum–derivation of expression for its time period; free, forced and damped oscillations (qualitative ideas only), resonance.
Wave motion. Longitudinal and transverse waves, speed of wave motion. Displacement
relation for a progressive wave. Principle of superposition of waves, reflection of waves,
standing waves in strings and organ pipes, fundamental mode and harmonics, Beats,
Doppler effect.
Practicals
Note: Every student will perform 10 experiments (5 from each section) and 8 activities (4
from each section) during the academic year.
Two demonstration experiments must be performed by the teacher with participation of
students. The students will maintain a record of these demonstration experiments. Schools are advised to see the guidelines for evaluation in practicals for Class XII. Similar pattern may the followed for Class XI.
SECTION A
Experiments
1. Use of Vernier Callipers
(i) to measure diameter of a small spherical/cylindrical body.
(ii) to measure dimensions of a given regular body of known mass and hence find its
density.
(iii) to measure internal diameter and depth of a given beaker/calorimeter and hence
find its volume.
2. Use of screw gauge
(i) to measure diameter of a given wire, (ii) to measure thickness of a given sheet
(iii) to measure volume of an irregular lamina
3. To determine radius of curvature of a given spherical surface by a spherometer.
4. To find the weight of a given body using parallelogram law of vectors.
5. Using a simple pendulum, plot L-T and L-T2 graphs. Hence find the effective length of
second’s pendulum using appropriate graph.
6. To study the relationship between force of limiting friction and normal reaction and to find co-efficient of friction between a block and a horizontal surface.
7. To find the downward force, along an inclined plane, acting on a roller due to gravitational pull of the earth and study its relationship with the angle of inclination by plotting graph between force and sin.
Activities
1. To make a paper scale of given least count, e.g. 0.2cm, 0.5cm.
2. To determine mass of a given body using a metre scale by principle of moments.
3. To plot a graph for a given set of data, with proper choice of scales and error bars.
4. To measure the force of limiting friction for rolling of a roller on a horizontal plane.
5. To study the variation in range of a jet of water with angle of projection.
6. To study the conservation of energy of a ball rolling down on inclined plane (using a
double inclined plane).
7. To study dissipation of energy of a simple pendulum by plotting a graph between square of amplitude and time.
SECTION B
Experiments
1. To determine Young’s modulus of elasticity of the material of a given wire.
2. To find the force constant of a helical spring by plotting graph between load and extension.
3. To study the variation in volume with pressure for a sample of air at constant temperature by plotting graphs between P and V, and between P and I/V.
4. To determine the surface tension of water by capillary rise method.
5. To determine the coefficient of viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body.
6. To study the relationship between the temperature of a hot body and time by plotting a
cooling curve.
7. (i) To study the relation between frequency and length of a given wire under constant
tension using sonometer.
(ii) To study the relation between the length of a given wire and tension for constant
frequency using sonometer.
8. To find the speed of sound in air at room temperature using a resonance tube by two resonance positions.
9. To determine specific heat of a given (i) solid (ii) liquid, by method of mixtures.
Activities
1. To observe change of state and plot a cooling curve for molten wax.
2. To observe and explain the effect of heating on a bi-metallic strip.
3. To note the change in level of liquid in a container on heating and interpret the observations.
4. To study the effect of detergent on surface tension by observing capillary rise.
5. To study the factors affecting the rate of loss of heat of a liquid.
6. To study the effect of load on depression of a suitably clamped metre scale loaded
(i) at its end (ii) in the middle.
Recommended Textbooks.
1. Physics Part-I, Textbook for Class XI, Published by NCERT
2 . Physics Part-II, Textbook for Class XI, Published by NCERT
Syllabus 2016 download
CLASS XI (THEORY)
(Total Periods: 180)
Unit I: Physical World and Measurement (Periods 10)
Physics: Scope and excitement; nature of physical laws; Physics, technology and society.
Need for measurement: Units of measurement; systems of units; SI units, fundamental and derived
units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in
measurement; significant figures.
Dimensions of physical quantities, dimensional analysis and its applications.
Unit II: Kinematics (Periods 30)
Frame of reference, Motion in a straight line: Position-time graph, speed and velocity. Uniform and
non-uniform motion, average speed and instantaneous velocity. Uniformly accelerated motion, velocitytime
and position-time graphs, relations for uniformly accelerated motion (graphical treatment).
Elementary concepts of differentiation and integration for describing motion. Scalar and vector
quantities: Position and displacement vectors, general vectors and notation, equality of vectors, multiplication
of vectors by a real number; addition and subtraction of vectors. Relative velocity.
Unit vectors. Resolution of a vector in a plane – rectangular components.
Scalar and Vector products of Vectors. Motion in a plane. Cases of uniform velocity and uniform
acceleration – projectile motion. Uniform circular motion.
Unit III: Laws of Motion (Periods 16)
Intuitive concept of force. Inertia, Newton’s first law of motion; momentum and Newton’s second
law of motion; impulse; Newton’s third law of motion. Law of conservation of linear momentum and its
applications.
Equilibrium of concurrent forces. Static and kinetic friction, laws of friction, rolling friction, lubrication.
Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on
level circular road, vehicle on banked road).
Unit IV: Work, Energy and Power (Periods 16)
Work done by a constant force and a variable force; kinetic energy, work-energy theorem, power.
Notion of potential energy, potential energy of a spring, conservative forces; conservation of mechanical
energy (kinetic and potential energies); non-conservative forces; motion in a vertical circle, elastic and
inelastic collisions in one and two dimensions.
Unit V: Motion of System of Particles and Rigid Body (Periods 18)
Centre of mass of a two-particle system, momentum conservation and centre of mass motion. Centre
of mass of a rigid body; centre of mass of uniform rod.
Moment of a force, torque, angular momentum, conservation of angular momentum with some
examples.
4
Equilibrium of rigid bodies, rigid body rotation and equation of rotational motion, comparison of linear
and rotational motions; moment of inertia, radius of gyration. Values of M.I. for simple geometrical objects
(no derivation). Statement of parallel and perpendicular axes theorems and their applications.
Unit VI: Gravitation (Periods 14)
Kepler’s laws of planetary motion. The universal law of gravitation. Acceleration due to gravity and its
variation with altitude and depth.
Gravitational potential energy; gravitational potential. Escape velocity, orbital velocity of a satellite.
Geostationary satellites.
Unit VII: Properties of Bulk Matter (Periods 28)
Elastic behaviour, Stress-strain relationship, Hooke’s law, Young’s modulus, bulk modulus, shear,
modulus of rigidity, poisson’s ratio; elastic energy.
Pressure due to a fluid column; Pascal’s law and its applications (hydraulic lift and hydraulic brakes).
Effect of gravity on fluid pressure.
Viscosity, Stokes’ law, terminal velocity, Reynold’s number, streamline and turbulent flow. Critical
velocity, Bernoulli’s theorem and its applications.
Surface energy and surface tension, angle of contact, excess of pressure, application of surface tension
ideas to drops, bubbles and capillary rise.
Heat, temperature, thermal expansion; thermal expansion of solids, liquids, and gases. Anomalous
expansion. Specific heat capacity: Cp
, Cv
– calorimetry; change of state – latent heat.
Heat transfer – conduction and thermal conductivity, convection and radiation. Qualitative ideas of
Black Body Radiation, Wein’s displacement law, and Green House effect.
Newton’s law of cooling and Stefan’s law.
Unit VIII: Thermodynamics (Periods 12)
Thermal equilibrium and definition of temperature (zeroth law of Thermodynamics). Heat, work and
internal energy. First law of thermodynamics. Isothermal and adiabatic processes.
Second law of thermodynamics: Reversible and irreversible processes. Heat engines and refrigerators.
Unit IX: Behaviour of Perfect Gas and Kinetic Theory (Periods 8)
Equation of state of a perfect gas, work done on compressing a gas.
Kinetic theory of gases: Assumptions, concept of pressure. Kinetic energy and temperature; rms
speed of gas molecules; degrees of freedom, law of equipartition of energy (statement only) and application
to specific heat capacities of gases; concept of mean free path, Avogadro’s number.
Unit X: Oscillations and Waves (Periods 28)
Periodic motion – period, frequency, displacement as a function of time. Periodic functions. Simple
harmonic motion (SHM) and its equation; phase; oscillations of a spring – restoring force and force constant;
energy in SHM – kinetic and potential energies; simple pendulum – derivation of expression for its time
period; free, forced and damped oscillations (qualitative ideas only), resonance.
Wave motion. Longitudinal and transverse waves, speed of wave motion. Displacement relation for a
progressive wave. Principle of superposition of waves, reflection of waves, standing waves in strings and
organ pipes, fundamental mode and harmonics. Beats. Doppler effect.
5
PRACTICALS
Total Periods 60
Section A
Experiments
1. To measure diameter of a small spherical/cylindrical body using Vernier callipers.
2. To measure internal diameter and depth of a given beaker/calorimeter using Vernier callipers and
hence find its volume.
3. To measure diameter of a given wire using screw gauge.
4. To measure thickness of a given sheet using screw gauge.
5. To measure volume of an irregular lamina using screw gauge.
6. To determine radius of curvature of a given spherical surface by a spherometer.
7. To determine the mass of two different objects using a beam balance.
8. To find the weight of a given body using parallelogram law of vectors.
9. Using a simple pendulum, plot L-T and L-T2
graphs. Hence find the effective length of a second’s
pendulum using appropriate graph.
10. To study the relationship between force of limiting friction and normal reaction and to find the
coefficient of friction between a block and a horizontal surface.
11. To find the downward force, along an inclined plane, acting on a roller due to gravitational pull of
the earth and study its relationship with the angle of inclination (θ) by plotting graph between force
and sin θ.
Activities
1. To make a paper scale of given least count, e.g. 0.2 cm, 0.5 cm.
2. To determine mass of a given body using a metre scale by principle of moments.
3. To plot a graph for a given set of data, with proper choice of scales and error bars.
4. To measure the force of limiting friction for rolling of a roller on a horizontal plane.
5. To study the variation in the range of a jet of water with the angle of projection.
6. To study the conservation of energy of a ball rolling down on inclined plane (using a double
inclined plane).
7. To study dissipation of energy of a simple pendulum by plotting a graph between square of
amplitude and time.
CBSE Syllabus Physics - Class 12
Unit I Electrostatics
Unit II Current Electricity
Unit III Magnetic effect of current & Magnetism
Unit IV Electromagnetic Induction and Alternating current
Unit V Electromagnetic Waves
Unit VI Optics
Unit VII Dual Nature of Matter
Unit VIII Atoms and Nuclei
Unit IX Electronic Devices
Unit X Communication Systems
Unit I: Electrostatics (Periods 25)
Electric Charges; Conservation of charge, Coulomb’s law-force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution.
Electric field, electric field due to a point charge, electric field lines; electric dipole, electric field due to a dipole; torque on a dipole in uniform electric field.
Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside).
Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field.
Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor. Van de Graaff generator.
Unit II: Current Electricity (Periods 22)
Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current; Ohm’s law, electrical resistance, V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity. Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance.
Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel.
Kirchhoff’s laws and simple applications. Wheatstone bridge, metre bridge.
Potentiometer - principle and its applications to measure potential difference and for comparing emf of two cells; measurement of internal resistance of a cell.
Unit III: Magnetic Effects of Current and Magnetism (Periods 25)
Concept of magnetic field, Oersted’s experiment.
Biot - Savart law and its application to current carrying circular loop.
Ampere’s law and its applications to infinitely long straight wire, straight and toroidal solenoids.
Force on a moving charge in uniform magnetic and electric fields. Cyclotron.
Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel current-carrying conductors-definition of ampere. Torque experienced by a current loop in uniform magnetic field; moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter.
Current loop as a magnetic dipole and its magnetic dipole moment. Magnetic dipole moment of a revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements.
Para-, dia- and ferro - magnetic substances, with examples. Electromagnets and factors affecting their strengths. Permanent magnets.
Unit IV: Electromagnetic Induction and Alternating Currents (Periods 20)
Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents.
Self and mutual inductance.
Need for displacement current.
Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance;
LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless current.
AC generator and transformer.
Unit V: Electromagnetic waves (Periods 4)
Displacement current, Electromagnetic waves and their characteristics (qualitative ideas only).
Transverse nature of electromagnetic waves.
Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses.
Unit VI: Optics (Periods 30)
Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lensmaker’s formula. Magnification, power of a lens, combination of thin lenses in contact. Refraction and dispersion of light through a prism.
Scattering of light - blue colour of the sky and reddish appearance of the sun at sunrise and sunset.
Optical instruments: Human eye, image formation and accommodation, correction of eye defects (myopia, hypermetropia, presbyopia and astigmatism) using lenses. Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.
Wave optics: wave front and Huygens’ principle, reflection and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygens’ principle.
Interference, Young’s double slit experiment and expression for fringe width, coherent sources and sustained interference of light. Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical telescopes. Polarisation, plane polarised light; Brewster’s law, uses of plane polarised light and Polaroids.
Unit VII: Dual Nature of Matter and Radiation (Periods 8)
Dual nature of radiation. Photoelectric effect, Hertz and Lenard’s observations; Einstein’s
photoelectric equation-particle nature of light.
Matter waves-wave nature of particles, de Broglie relation. Davisson-Germer experiment.
Unit VIII: Atoms & Nuclei (Periods 18)
Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum.
Composition and size of nucleus, atomic masses, isotopes, isobars; isotones. Radioactivityalpha, beta and gamma particles/rays and their properties; radioactive decay law.
Mass-energy relation, mass defect; binding energy per nucleon and its variation with
mass number; nuclear fission, nuclear reactor, nuclear fusion.
Unit IX: Electronic Devices (Periods 18)
Semiconductors; semiconductor diode – I-V characteristics in forward and reverse bias, diode as a rectifier; I-V characteristics of LED, photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor; transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch.
Unit X: Communication Systems (Periods 10)
Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated wave.
Practicals
Every student will perform 10 experiments (5 from each section) & 8 activities (4 from each section) during the academic year. Two demonstration experiments must be performed by the teacher with participation of students. The students will maintain a record of these demonstration experiments.
SECTION A
Experiments
1. To determine resistance per cm of a given wire by plotting a graph of potential difference versus current.
2. To find resistance of a given wire using metre bridge and hence determine the specific
resistance of its material.
3. To verify the laws of combination (series/parallel) of resistances using a metre bridge.
4. To compare the emf of two given primary cells using potentiometer.
5. To determine the internal resistance of given primary cell using potentiometer.
6. To determine resistance of a galvanometer by half-deflection method and to find its figure of merit.
7. To convert the given galvanometer (of known resistance and figure of merit) into an ammeter and voltmeter of desired range and to verify the same.
8. To find the frequency of the a.c. mains with a sonometer.
Activities
1. To measure the resistance and impedance of an inductor with or without iron core.
2. To measure resistance, voltage (AC/DC), current (AC) and check continuity of a given
circuit using multimeter.
3. To assemble a household circuit comprising three bulbs, three (on/off) switches, a fuse
and a power source.
4. To assemble the components of a given electrical circuit.
5. To study the variation in potential drop with length of a wire for a steady current.
6. To draw the diagram of a given open circuit comprising at least a battery, resistor/rheostat, key, ammeter and voltmeter. Mark the components that are not connected in proper order and correct the circuit and also the circuit diagram.
SECTION B
Experiments
1. To find the value of v for different values of u in case of a concave mirror and to find the focal length.
2. To find the focal length of a convex lens by plotting graphs between u and v or between l/u and l/v.
3. To find the focal length of a convex mirror, using a convex lens.
4. To find the focal length of a concave lens, using a convex lens.
5. To determine angle of minimum deviation for a given prism by plotting a graph between angle of incidence and angle of deviation.
6. To determine refractive index of a glass slab using a travelling microscope.
7. To find refractive index of a liquid by using (i) concave mirror, (ii) convex lens and plane mirror.
8. To draw the I-V characteristic curve of a p-n junction in forward bias and reverse bias.
9. To draw the characteristic curve of a zener diode and to determine its reverse break
down voltage.
10. To study the characteristics of a common - emitter npn or pnp transistor and to find
out the values of current and voltage gains.
Activities
1. To study effect of intensity of light (by varying distance of the source) on an L.D.R.
2. To identify a diode, an LED, a transistor, and IC, a resistor and a capacitor from mixed
collection of such items.
3. Use of multimeter to (i) identify base of transistor. (ii) distinguish between npn and pnp type transistors. (iii) see the unidirectional flow of current in case of a diode and an LED.
(iv) check whether a given electronic component (e.g. diode, transistor or I C) is in working order.
4. To observe refraction and lateral deviation of a beam of light incident obliquely on a glass slab.
5. To observe polarization of light using two Polaroids.
6. To observe diffraction of light due to a thin slit.
7. To study the nature and size of the image formed by (i) convex lens (ii) concave mirror, on
a screen by using a candle and a screen (for different distances of the candle from the lens/mirror).
8. To obtain a lens combination with the specified focal length by using two lenses from the given set of lenses.
B. Evaluation Scheme for Practical Examination:
_ One experiment from any one section 8 Marks
_ Two activities (one from each section) (4+4) 8 Marks
_ Practical record (experiments & activities) 6 Marks
_ Record of demonstration experiments & Viva based on these experiments 3 Marks
_ Viva on experiments & activities 5 Marks
Total 30 Marks
Recommended Textbooks.
1. Physics Part-I, Textbook for XII, Published by NCERT
2. Physics Part-II, Textbook for XII, Published by NCERT
Source: http://www.cbse.nic.in/welcome.htm
Downloaded 1 May 2016
CLASS XII (THEORY)
(Total Periods: 180)
Unit I: Electrostatics (Periods 25)
Electric charges and their conservation. Coulomb’s law – force between two point charges, forces
between multiple charges; superposition principle and continuous charge distribution.
Electric field, electric field due to a point charge, electric field lines; electric dipole, electric field due to
a dipole; torque on a dipole in a uniform electric field.
Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long
straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside
and outside).
7
Electric potential, potential difference, electric potential due to a point charge, a dipole and system of
charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric
dipoles in an electrostatic field.
Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric
polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance
of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a
capacitor, Van de Graaff generator.
Unit II: Current Electricity (Periods 22)
Electric current, flow of electric charges in a metallic conductor, drift velocity and mobility, and their
relation with electric current; Ohm’s law, electrical resistance, V-I characteristics (linear and non-linear),
electrical energy and power, electrical resistivity and conductivity.
Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors;
temperature dependence of resistance.
Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in
parallel.
Kirchhoff ’s laws and simple applications. Wheatstone bridge, metre bridge.
Potentiometer – principle and applications to measure potential difference, and for comparing emf of
two cells; measurement of internal resistance of a cell.
Unit III: Magnetic Effects of Current and Magnetism (Periods 25)
Concept of magnetic field, Oersted’s experiment. Biot - Savart law and its application to current
carrying circular loop.
Ampere’s law and its applications to infinitely long straight wire, straight and toroidal solenoids. Force
on a moving charge in uniform magnetic and electric fields. Cyclotron.
Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel currentcarrying
conductors – definition of ampere. Torque experienced by a current loop in a magnetic field;
moving coil galvanometer – its current sensitivity and conversion to ammeter and voltmeter.
Current loop as a magnetic dipole and its magnetic dipole moment. Magnetic dipole moment of a
revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and
perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet
as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements.
Para-, dia- and ferro - magnetic substances, with examples.
Electromagnets and factors affecting their strengths. Permanent magnets.
Unit IV: Electromagnetic Induction and Alternating Currents
(Periods 20)
Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents. Self
and mutual inductance.
Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance; LC
oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless
current.
AC generator and transformer.
8
Unit V: Electromagnetic Waves (Periods 4)
Need for displacement current.
Electromagnetic waves and their characteristics (qualitative ideas only). Transverse nature of
electromagnetic waves.
Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma
rays) including elementary facts about their uses.
Unit VI: Optics (Periods 30)
Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and its
applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens-maker’s formula.
Magnification, power of a lens, combination of thin lenses in contact combination of a lens and a mirror.
Refraction and dispersion of light through a prism.
Scattering of light – blue colour of the sky and reddish appearance of the sun at sunrise and sunset.
Optical instruments: Human eye, image formation and accommodation, correction of eye defects
(myopia and hypermetropia) using lenses.
Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.
Wave optics: Wavefront and Huygens’ principle, reflection and refraction of plane wave at a plane
surface using wavefronts.
Proof of laws of reflection and refraction using Huygens’ principle.
Interference, Young’s double hole experiment and expression for fringe width, coherent sources and
sustained interference of light.
Diffraction due to a single slit, width of central maximum.
Resolving power of microscopes and astronomical telescopes. Polarisation, plane polarised light;
Brewster’s law, uses of plane polarised light and Polaroids.
Unit VII: Dual Nature of Matter and Radiation (Periods 8)
Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation – particle
nature of light.
Matter waves – wave nature of particles, de Broglie relation. Davisson-Germer experiment
(experimental details should be omitted; only conclusion should be explained.)
Unit VIII: Atoms and Nuclei (Periods 18)
Alpha - particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels,
hydrogen spectrum. Composition and size of nucleus, atomic masses, isotopes, isobars; isotones.
Radioactivity – alpha, beta and gamma particles/rays and their properties; radioactive decay law.
Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear
fission and fusion.
Unit IX: Electronic Devices (Periods 18)
Energy bands in solids (qualitative ideas only), conductors, insulators and semiconductors;
semiconductor diode – I-V characteristics in forward and reverse bias, diode as a rectifier; I-V characteristics
of LED, photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator. Junction transistor,
9
transistor action, characteristics of a transistor; transistor as an amplifier (common emitter configuration)
and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch.
Unit X: Communication Systems (Periods 10)
Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and
digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere,
sky and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated
wave.
Practicals
Total Periods 60
Section A
Experiments
1. To find resistance of a given wire using metre bridge and hence determine the specific resistance
of its material.
2. To determine resistance per cm of a given wire by plotting a graph of potential difference versus
current.
3. To verify the laws of combination (series/parallel) of resistances using a metre bridge.
4. To compare the emf ’s of two given primary cells using potentiometer.
5. To determine the internal resistance of given primary cell using potentiometer.
6. To determine resistance of a galvanometer by half-deflection method and to find its figure of
merit.
7. To convert the given galvanometer (of known resistance of figure of merit) into an ammeter and
voltmeter of desired range and to verify the same.
8. To find the frequency of the ac mains with a sonometer.
Activities
1. To measure the resistance and impedance of an inductor with or without iron core.
2. To measure resistance, voltage (ac/dc), current (ac) and check continuity of a given circuit using
multimeter.
3. To assemble a household circuit comprising three bulbs, three (on/off) switches, a fuse and a
power source.
4. To assemble the components of a given electrical circuit.
5. To study the variation in potential drop with length of a wire for a steady current.
6. To draw the diagram of a given open circuit comprising at least a battery, resistor/rheostat, key,
ammeter and voltmeter. Mark the components that are not connected in proper order and correct
the circuit and also the circuit diagram.
10
Section B
Experiments
1. To find the value of v for different values of u in case of a concave mirror and to find the focal
length.
2. To find the focal length of a convex mirror, using a convex lens.
3. To find the focal length of a convex lens by plotting graphs between u and v or between 1/u and
1/v.
4. To find the focal length of a concave lens, using a convex lens.
5. To determine angle of minimum deviation for a given prism by plotting a graph between the angle
of incidence and the angle of deviation.
6. To determine refractive index of a glass slab using a travelling microscope.
7. To find refractive index of a liquid by using (i) concave mirror, (ii) convex lens and plane mirror.
8. To draw the I-V characteristics curves of a p-n junction in forward bias and reverse bias.
9. To draw the characteristics curve of a zener diode and to determine its reverse break down
voltage.
10. To study the characteristics of a common-emitter npn or pnp transistor and to find out the values
of current and voltage gains.
Activities
1. To identify a diode, an LED, a transistor, and IC, a resistor and a capacitor from mixed collection
of such items.
2. Use of multimeter to (i) identify base of transistor, (ii) distinguish between npn and pnp type
transistors, (iii) see the unidirectional flow of current in case of a diode and an LED, (iv) check
whether a given electronic component (e.g. diode, transistor or IC) is in working order.
3. To study effect of intensity of light (by varying distance of the source) on an LDR.
4. To observe refraction and lateral deviation of a beam of light incident obliquely on a glass slab.
5. To observe polarization of light using two polaroids.
6. To observe diffraction of light due to a thin slit.
7. To study the nature and size of the image formed by (i) convex lens (ii) concave mirror, on a
screen by using a candle and a screen (for different distances of the candle from the lens/mirror).
8. To obtain a lens combination with the specified focal length by using two lenses from the given set
of lenses.
Unit II Current Electricity
Unit III Magnetic effect of current & Magnetism
Unit IV Electromagnetic Induction and Alternating current
Unit V Electromagnetic Waves
Unit VI Optics
Unit VII Dual Nature of Matter
Unit VIII Atoms and Nuclei
Unit IX Electronic Devices
Unit X Communication Systems
Unit I: Electrostatics (Periods 25)
Electric Charges; Conservation of charge, Coulomb’s law-force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution.
Electric field, electric field due to a point charge, electric field lines; electric dipole, electric field due to a dipole; torque on a dipole in uniform electric field.
Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside).
Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field.
Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor. Van de Graaff generator.
Unit II: Current Electricity (Periods 22)
Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current; Ohm’s law, electrical resistance, V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity. Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance.
Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel.
Kirchhoff’s laws and simple applications. Wheatstone bridge, metre bridge.
Potentiometer - principle and its applications to measure potential difference and for comparing emf of two cells; measurement of internal resistance of a cell.
Unit III: Magnetic Effects of Current and Magnetism (Periods 25)
Concept of magnetic field, Oersted’s experiment.
Biot - Savart law and its application to current carrying circular loop.
Ampere’s law and its applications to infinitely long straight wire, straight and toroidal solenoids.
Force on a moving charge in uniform magnetic and electric fields. Cyclotron.
Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel current-carrying conductors-definition of ampere. Torque experienced by a current loop in uniform magnetic field; moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter.
Current loop as a magnetic dipole and its magnetic dipole moment. Magnetic dipole moment of a revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements.
Para-, dia- and ferro - magnetic substances, with examples. Electromagnets and factors affecting their strengths. Permanent magnets.
Unit IV: Electromagnetic Induction and Alternating Currents (Periods 20)
Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents.
Self and mutual inductance.
Need for displacement current.
Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance;
LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless current.
AC generator and transformer.
Unit V: Electromagnetic waves (Periods 4)
Displacement current, Electromagnetic waves and their characteristics (qualitative ideas only).
Transverse nature of electromagnetic waves.
Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses.
Unit VI: Optics (Periods 30)
Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lensmaker’s formula. Magnification, power of a lens, combination of thin lenses in contact. Refraction and dispersion of light through a prism.
Scattering of light - blue colour of the sky and reddish appearance of the sun at sunrise and sunset.
Optical instruments: Human eye, image formation and accommodation, correction of eye defects (myopia, hypermetropia, presbyopia and astigmatism) using lenses. Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.
Wave optics: wave front and Huygens’ principle, reflection and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygens’ principle.
Interference, Young’s double slit experiment and expression for fringe width, coherent sources and sustained interference of light. Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical telescopes. Polarisation, plane polarised light; Brewster’s law, uses of plane polarised light and Polaroids.
Unit VII: Dual Nature of Matter and Radiation (Periods 8)
Dual nature of radiation. Photoelectric effect, Hertz and Lenard’s observations; Einstein’s
photoelectric equation-particle nature of light.
Matter waves-wave nature of particles, de Broglie relation. Davisson-Germer experiment.
Unit VIII: Atoms & Nuclei (Periods 18)
Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum.
Composition and size of nucleus, atomic masses, isotopes, isobars; isotones. Radioactivityalpha, beta and gamma particles/rays and their properties; radioactive decay law.
Mass-energy relation, mass defect; binding energy per nucleon and its variation with
mass number; nuclear fission, nuclear reactor, nuclear fusion.
Unit IX: Electronic Devices (Periods 18)
Semiconductors; semiconductor diode – I-V characteristics in forward and reverse bias, diode as a rectifier; I-V characteristics of LED, photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor; transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch.
Unit X: Communication Systems (Periods 10)
Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated wave.
Practicals
Every student will perform 10 experiments (5 from each section) & 8 activities (4 from each section) during the academic year. Two demonstration experiments must be performed by the teacher with participation of students. The students will maintain a record of these demonstration experiments.
SECTION A
Experiments
1. To determine resistance per cm of a given wire by plotting a graph of potential difference versus current.
2. To find resistance of a given wire using metre bridge and hence determine the specific
resistance of its material.
3. To verify the laws of combination (series/parallel) of resistances using a metre bridge.
4. To compare the emf of two given primary cells using potentiometer.
5. To determine the internal resistance of given primary cell using potentiometer.
6. To determine resistance of a galvanometer by half-deflection method and to find its figure of merit.
7. To convert the given galvanometer (of known resistance and figure of merit) into an ammeter and voltmeter of desired range and to verify the same.
8. To find the frequency of the a.c. mains with a sonometer.
Activities
1. To measure the resistance and impedance of an inductor with or without iron core.
2. To measure resistance, voltage (AC/DC), current (AC) and check continuity of a given
circuit using multimeter.
3. To assemble a household circuit comprising three bulbs, three (on/off) switches, a fuse
and a power source.
4. To assemble the components of a given electrical circuit.
5. To study the variation in potential drop with length of a wire for a steady current.
6. To draw the diagram of a given open circuit comprising at least a battery, resistor/rheostat, key, ammeter and voltmeter. Mark the components that are not connected in proper order and correct the circuit and also the circuit diagram.
SECTION B
Experiments
1. To find the value of v for different values of u in case of a concave mirror and to find the focal length.
2. To find the focal length of a convex lens by plotting graphs between u and v or between l/u and l/v.
3. To find the focal length of a convex mirror, using a convex lens.
4. To find the focal length of a concave lens, using a convex lens.
5. To determine angle of minimum deviation for a given prism by plotting a graph between angle of incidence and angle of deviation.
6. To determine refractive index of a glass slab using a travelling microscope.
7. To find refractive index of a liquid by using (i) concave mirror, (ii) convex lens and plane mirror.
8. To draw the I-V characteristic curve of a p-n junction in forward bias and reverse bias.
9. To draw the characteristic curve of a zener diode and to determine its reverse break
down voltage.
10. To study the characteristics of a common - emitter npn or pnp transistor and to find
out the values of current and voltage gains.
Activities
1. To study effect of intensity of light (by varying distance of the source) on an L.D.R.
2. To identify a diode, an LED, a transistor, and IC, a resistor and a capacitor from mixed
collection of such items.
3. Use of multimeter to (i) identify base of transistor. (ii) distinguish between npn and pnp type transistors. (iii) see the unidirectional flow of current in case of a diode and an LED.
(iv) check whether a given electronic component (e.g. diode, transistor or I C) is in working order.
4. To observe refraction and lateral deviation of a beam of light incident obliquely on a glass slab.
5. To observe polarization of light using two Polaroids.
6. To observe diffraction of light due to a thin slit.
7. To study the nature and size of the image formed by (i) convex lens (ii) concave mirror, on
a screen by using a candle and a screen (for different distances of the candle from the lens/mirror).
8. To obtain a lens combination with the specified focal length by using two lenses from the given set of lenses.
B. Evaluation Scheme for Practical Examination:
_ One experiment from any one section 8 Marks
_ Two activities (one from each section) (4+4) 8 Marks
_ Practical record (experiments & activities) 6 Marks
_ Record of demonstration experiments & Viva based on these experiments 3 Marks
_ Viva on experiments & activities 5 Marks
Total 30 Marks
Recommended Textbooks.
1. Physics Part-I, Textbook for XII, Published by NCERT
2. Physics Part-II, Textbook for XII, Published by NCERT
Source: http://www.cbse.nic.in/welcome.htm
Downloaded 1 May 2016
CLASS XII (THEORY)
(Total Periods: 180)
Unit I: Electrostatics (Periods 25)
Electric charges and their conservation. Coulomb’s law – force between two point charges, forces
between multiple charges; superposition principle and continuous charge distribution.
Electric field, electric field due to a point charge, electric field lines; electric dipole, electric field due to
a dipole; torque on a dipole in a uniform electric field.
Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long
straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside
and outside).
7
Electric potential, potential difference, electric potential due to a point charge, a dipole and system of
charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric
dipoles in an electrostatic field.
Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric
polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance
of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a
capacitor, Van de Graaff generator.
Unit II: Current Electricity (Periods 22)
Electric current, flow of electric charges in a metallic conductor, drift velocity and mobility, and their
relation with electric current; Ohm’s law, electrical resistance, V-I characteristics (linear and non-linear),
electrical energy and power, electrical resistivity and conductivity.
Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors;
temperature dependence of resistance.
Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in
parallel.
Kirchhoff ’s laws and simple applications. Wheatstone bridge, metre bridge.
Potentiometer – principle and applications to measure potential difference, and for comparing emf of
two cells; measurement of internal resistance of a cell.
Unit III: Magnetic Effects of Current and Magnetism (Periods 25)
Concept of magnetic field, Oersted’s experiment. Biot - Savart law and its application to current
carrying circular loop.
Ampere’s law and its applications to infinitely long straight wire, straight and toroidal solenoids. Force
on a moving charge in uniform magnetic and electric fields. Cyclotron.
Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel currentcarrying
conductors – definition of ampere. Torque experienced by a current loop in a magnetic field;
moving coil galvanometer – its current sensitivity and conversion to ammeter and voltmeter.
Current loop as a magnetic dipole and its magnetic dipole moment. Magnetic dipole moment of a
revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and
perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet
as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements.
Para-, dia- and ferro - magnetic substances, with examples.
Electromagnets and factors affecting their strengths. Permanent magnets.
Unit IV: Electromagnetic Induction and Alternating Currents
(Periods 20)
Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents. Self
and mutual inductance.
Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance; LC
oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless
current.
AC generator and transformer.
8
Unit V: Electromagnetic Waves (Periods 4)
Need for displacement current.
Electromagnetic waves and their characteristics (qualitative ideas only). Transverse nature of
electromagnetic waves.
Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma
rays) including elementary facts about their uses.
Unit VI: Optics (Periods 30)
Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and its
applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens-maker’s formula.
Magnification, power of a lens, combination of thin lenses in contact combination of a lens and a mirror.
Refraction and dispersion of light through a prism.
Scattering of light – blue colour of the sky and reddish appearance of the sun at sunrise and sunset.
Optical instruments: Human eye, image formation and accommodation, correction of eye defects
(myopia and hypermetropia) using lenses.
Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.
Wave optics: Wavefront and Huygens’ principle, reflection and refraction of plane wave at a plane
surface using wavefronts.
Proof of laws of reflection and refraction using Huygens’ principle.
Interference, Young’s double hole experiment and expression for fringe width, coherent sources and
sustained interference of light.
Diffraction due to a single slit, width of central maximum.
Resolving power of microscopes and astronomical telescopes. Polarisation, plane polarised light;
Brewster’s law, uses of plane polarised light and Polaroids.
Unit VII: Dual Nature of Matter and Radiation (Periods 8)
Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation – particle
nature of light.
Matter waves – wave nature of particles, de Broglie relation. Davisson-Germer experiment
(experimental details should be omitted; only conclusion should be explained.)
Unit VIII: Atoms and Nuclei (Periods 18)
Alpha - particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels,
hydrogen spectrum. Composition and size of nucleus, atomic masses, isotopes, isobars; isotones.
Radioactivity – alpha, beta and gamma particles/rays and their properties; radioactive decay law.
Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear
fission and fusion.
Unit IX: Electronic Devices (Periods 18)
Energy bands in solids (qualitative ideas only), conductors, insulators and semiconductors;
semiconductor diode – I-V characteristics in forward and reverse bias, diode as a rectifier; I-V characteristics
of LED, photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator. Junction transistor,
9
transistor action, characteristics of a transistor; transistor as an amplifier (common emitter configuration)
and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch.
Unit X: Communication Systems (Periods 10)
Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and
digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere,
sky and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated
wave.
Practicals
Total Periods 60
Section A
Experiments
1. To find resistance of a given wire using metre bridge and hence determine the specific resistance
of its material.
2. To determine resistance per cm of a given wire by plotting a graph of potential difference versus
current.
3. To verify the laws of combination (series/parallel) of resistances using a metre bridge.
4. To compare the emf ’s of two given primary cells using potentiometer.
5. To determine the internal resistance of given primary cell using potentiometer.
6. To determine resistance of a galvanometer by half-deflection method and to find its figure of
merit.
7. To convert the given galvanometer (of known resistance of figure of merit) into an ammeter and
voltmeter of desired range and to verify the same.
8. To find the frequency of the ac mains with a sonometer.
Activities
1. To measure the resistance and impedance of an inductor with or without iron core.
2. To measure resistance, voltage (ac/dc), current (ac) and check continuity of a given circuit using
multimeter.
3. To assemble a household circuit comprising three bulbs, three (on/off) switches, a fuse and a
power source.
4. To assemble the components of a given electrical circuit.
5. To study the variation in potential drop with length of a wire for a steady current.
6. To draw the diagram of a given open circuit comprising at least a battery, resistor/rheostat, key,
ammeter and voltmeter. Mark the components that are not connected in proper order and correct
the circuit and also the circuit diagram.
10
Section B
Experiments
1. To find the value of v for different values of u in case of a concave mirror and to find the focal
length.
2. To find the focal length of a convex mirror, using a convex lens.
3. To find the focal length of a convex lens by plotting graphs between u and v or between 1/u and
1/v.
4. To find the focal length of a concave lens, using a convex lens.
5. To determine angle of minimum deviation for a given prism by plotting a graph between the angle
of incidence and the angle of deviation.
6. To determine refractive index of a glass slab using a travelling microscope.
7. To find refractive index of a liquid by using (i) concave mirror, (ii) convex lens and plane mirror.
8. To draw the I-V characteristics curves of a p-n junction in forward bias and reverse bias.
9. To draw the characteristics curve of a zener diode and to determine its reverse break down
voltage.
10. To study the characteristics of a common-emitter npn or pnp transistor and to find out the values
of current and voltage gains.
Activities
1. To identify a diode, an LED, a transistor, and IC, a resistor and a capacitor from mixed collection
of such items.
2. Use of multimeter to (i) identify base of transistor, (ii) distinguish between npn and pnp type
transistors, (iii) see the unidirectional flow of current in case of a diode and an LED, (iv) check
whether a given electronic component (e.g. diode, transistor or IC) is in working order.
3. To study effect of intensity of light (by varying distance of the source) on an LDR.
4. To observe refraction and lateral deviation of a beam of light incident obliquely on a glass slab.
5. To observe polarization of light using two polaroids.
6. To observe diffraction of light due to a thin slit.
7. To study the nature and size of the image formed by (i) convex lens (ii) concave mirror, on a
screen by using a candle and a screen (for different distances of the candle from the lens/mirror).
8. To obtain a lens combination with the specified focal length by using two lenses from the given set
of lenses.
Study guide H C Verma JEE Physics Ch. 18 GEOMETRICAL OPTICS
JEE syllabus
Optics: Rectilinear propagation of light; Reflection and refraction at plane and spherical surfaces; Total internal reflection; Deviation and dispersion of light by a prism; Thin lenses; Combinations of mirrors and thin lenses; Magnification.
----------
1. Reflection at smooth surfaces
5. Refraction at plane surfaces
6. Critical angle
8. Prism
9. Refraction at spherical surfaces;
10. refraction through thin lenses
-----------
Sections in Chapter 18 of HV Verma - Geometrical Optics
18.1 reflection at smooth surfaces
18.2 Spherical mirrors
18.3 Relation between u,v and R for spherical mirrors
18.4 extended objects and magnification
18.5 Refraction at plane surfaces
18.6 Critical angle
18.7 Optical fibre
18.8 Prism
18.9 Refraction at spherical surfaces
18.10 extended objects - laterial magnification
18.11 Refraction through thin lenses
18.12 Lens maker's formula and lens formula
18.13 Extended objects: Lateral magninification
18.14 Power of a lens
18.15 thin lenses in contact
18.16 two thin lenses separated by a distance
18.17 defects of images
Study Plan
Day 1
18.1 Reflection at smooth surfaces
18.2 Spherical mirrors
18.3 Relation between u,v and R for spherical mirrors
Example 18.1
Day 2
18.4 extended objects and magnification
18.5 Refraction at plane surfaces
18.6 Critical angle
Examples 18. 2,18.3, 18.4
Day 3
18.7 Optical fibre
18.8 Prism
18.9 Refraction at spherical surfaces
Examples 18.5 to 8
Exercises
1-5
Day 4
18.10 extended objects - laterial magnification
18.11 Refraction through thin lenses
Examples 18.9 to 12
Exercises
6-10
Day 5
18.12 Lens maker's formula and lens formula
18.13 Extended objects: Lateral magninification
18.14 Power of a lens
Examples 18.13 to 16
Exercises
11-15
Day 5
18.15 thin lenses in contact
18.16 two thin lenses separated by a distance
18.17 defects of images
Examples 18.17 to 20
Exercises
16-20
Day 6
Examples 18.17 to 28
Exercises 16-25
Day 7
Exercises 26-45
Day 8
Exercises
46-55
Day 9
Exercises 56 to 65
Day 10
Exercises 66 to 70
Day 11
Exercises 71 to 75
Day 12
Exercises 76 to 79
Day 13
Objective I 1 to 18
Day 14
Objective II 1 to 7
Day 15
Questions for short answer 1 to 19
----------------------
Audiovisual lectures
Lesson 48: Reflection and Refraction
www.curriki.org/nroc/Introductory_Physics_2/lesson48/Container.html
Lesson 49: Mirrorswww.curriki.org/nroc/Introductory_Physics_2/lesson49/Container.html
Lesson 50: Lenses
www.curriki.org/nroc/Introductory_Physics_2/lesson50/Container.html
JEE Question 2007 Paper I
In an experiment to determine the focal length (f) of a concave mirror by the u–v method, a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,
(A) x < f (B) f < x < 2f (C) x = 2f (D) x > 2f
Sol: Ans [B]
Image is between object and eye. So object is within focus of mirror.
---------------------------------
JEE Question 2007 Paper I
STATEMENT-1
The formula connecting u, v and f for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
because
STATEMENT-2
Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
Correct choice: C
Laws of reflection are valid for any kind of reflecting surface.
--------------------
JEE 2006
A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm. If the plane surface is silvered, the image will form at
(A) 60 cm left of AB (B) 30 cm left of AB
(C) 12 cm left of AB (D) 60 cm right of AB
Answer: C
----------------------------------
JEE 2006
A biconvex lens of focal length f forms a circular image of sun of radius r in focal plane. Then
(A) πr² α f
(B) πr² α f²
(C) if lower half part is covered by black sheet, then area of the image is equal to πr²/2
(D) if f is doubled, intensity will increase
Answer: B
------------------------------
Updated 1 May 2016, 23 Oct 2007
Optics: Rectilinear propagation of light; Reflection and refraction at plane and spherical surfaces; Total internal reflection; Deviation and dispersion of light by a prism; Thin lenses; Combinations of mirrors and thin lenses; Magnification.
----------
1. Reflection at smooth surfaces
5. Refraction at plane surfaces
6. Critical angle
8. Prism
9. Refraction at spherical surfaces;
10. refraction through thin lenses
-----------
Sections in Chapter 18 of HV Verma - Geometrical Optics
18.1 reflection at smooth surfaces
18.2 Spherical mirrors
18.3 Relation between u,v and R for spherical mirrors
18.4 extended objects and magnification
18.5 Refraction at plane surfaces
18.6 Critical angle
18.7 Optical fibre
18.8 Prism
18.9 Refraction at spherical surfaces
18.10 extended objects - laterial magnification
18.11 Refraction through thin lenses
18.12 Lens maker's formula and lens formula
18.13 Extended objects: Lateral magninification
18.14 Power of a lens
18.15 thin lenses in contact
18.16 two thin lenses separated by a distance
18.17 defects of images
Study Plan
Day 1
18.1 Reflection at smooth surfaces
18.2 Spherical mirrors
18.3 Relation between u,v and R for spherical mirrors
Example 18.1
Day 2
18.4 extended objects and magnification
18.5 Refraction at plane surfaces
18.6 Critical angle
Examples 18. 2,18.3, 18.4
Day 3
18.7 Optical fibre
18.8 Prism
18.9 Refraction at spherical surfaces
Examples 18.5 to 8
Exercises
1-5
Day 4
18.10 extended objects - laterial magnification
18.11 Refraction through thin lenses
Examples 18.9 to 12
Exercises
6-10
Day 5
18.12 Lens maker's formula and lens formula
18.13 Extended objects: Lateral magninification
18.14 Power of a lens
Examples 18.13 to 16
Exercises
11-15
Day 5
18.15 thin lenses in contact
18.16 two thin lenses separated by a distance
18.17 defects of images
Examples 18.17 to 20
Exercises
16-20
Day 6
Examples 18.17 to 28
Exercises 16-25
Day 7
Exercises 26-45
Day 8
Exercises
46-55
Day 9
Exercises 56 to 65
Day 10
Exercises 66 to 70
Day 11
Exercises 71 to 75
Day 12
Exercises 76 to 79
Day 13
Objective I 1 to 18
Day 14
Objective II 1 to 7
Day 15
Questions for short answer 1 to 19
----------------------
Audiovisual lectures
Lesson 48: Reflection and Refraction
www.curriki.org/nroc/Introductory_Physics_2/lesson48/Container.html
Lesson 49: Mirrorswww.curriki.org/nroc/Introductory_Physics_2/lesson49/Container.html
Lesson 50: Lenses
www.curriki.org/nroc/Introductory_Physics_2/lesson50/Container.html
JEE Question 2007 Paper I
In an experiment to determine the focal length (f) of a concave mirror by the u–v method, a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,
(A) x < f (B) f < x < 2f (C) x = 2f (D) x > 2f
Sol: Ans [B]
Image is between object and eye. So object is within focus of mirror.
---------------------------------
JEE Question 2007 Paper I
STATEMENT-1
The formula connecting u, v and f for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
because
STATEMENT-2
Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
Correct choice: C
Laws of reflection are valid for any kind of reflecting surface.
--------------------
JEE 2006
A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm. If the plane surface is silvered, the image will form at
(A) 60 cm left of AB (B) 30 cm left of AB
(C) 12 cm left of AB (D) 60 cm right of AB
Answer: C
----------------------------------
JEE 2006
A biconvex lens of focal length f forms a circular image of sun of radius r in focal plane. Then
(A) πr² α f
(B) πr² α f²
(C) if lower half part is covered by black sheet, then area of the image is equal to πr²/2
(D) if f is doubled, intensity will increase
Answer: B
------------------------------
Updated 1 May 2016, 23 Oct 2007
Study guide H C Verma JEE Physics Ch. 17 LIGHT WAVES
JEE Syllabus
Wave nature of light:
Huygen’s principle,
interference limited to Young’s double-slit experiment.
----------
1. Waves or Particles
2. The nature of light waves
3. Huygen's principles
4. Young's double hole experiment
5. Young's double slit experiment
6. Optical path
7. Interference from thin films
Fresnel's Biprism
9. coherent and incoherent sources
10. Diffreaction of light
11. Fraunhofer Diffraction by a single slit
12.Fraunhofer Diffraction by a circular aperture
13.Fresnel diffraction at a straight edge
14.Limit of resolution
15.scattering of light
16. Polarization of light
-----------
Study Plan
Day 1
1. Waves or Particles
2. The nature of light waves
Day 2
3. Huygen's principles
Worked out examples 1,2
Day 3
4. Young's double hole experiment
5. Young's double slit experiment
Day 4
6. Optical path
7. Interference from thin films
8. Fresnel's Biprism
9. coherent and incoherent sources
Day 5
WOE 3 to 7
Exerciese 1 to 5
Day 6
10. Diffraction of light
11. Fraunhofer Diffraction by a single slit
12.Fraunhofer Diffraction by a circular aperture
Day 7
13.Fresnel diffraction at a straight edge
14.Limit of resolution
15.scattering of light
Day 8
WoE 8 to 11
Exercises 6 to 10
Day 9
16. Polarization of light
Exercises 11 to 25
Day 10
Exercises 26 to 35
Day 11
Exercises 36 to 41
Day 12
Objective I 1 to 17
Day 13
Objective II 1 to 10
Day 14
Questions for short answer 1 to 11
Concept review - Formula review
--------------
Concepts covered
2. The nature of light waves
In a wave motion, there is some quantity which changes its value with time and space.
That quantity is the electric field existing in space where light travels.
The electric field is transverse to to the direction of propagation of light.
The equation of such light wave may be written as
E - E0 sin ω(t-x/v)
Light of single wavelength is called monochromatic light.
Huygen's principle
Various points of an arbitrary surface, when reached by a wave front, become secondary sources of light emitting secondary wavelets. The disturbance beyond the surface results from the superposition of these secondary wavelets.
Updated 1 May 2016, 23 Oct 2007
Wave nature of light:
Huygen’s principle,
interference limited to Young’s double-slit experiment.
----------
1. Waves or Particles
2. The nature of light waves
3. Huygen's principles
4. Young's double hole experiment
5. Young's double slit experiment
6. Optical path
7. Interference from thin films
Fresnel's Biprism
9. coherent and incoherent sources
10. Diffreaction of light
11. Fraunhofer Diffraction by a single slit
12.Fraunhofer Diffraction by a circular aperture
13.Fresnel diffraction at a straight edge
14.Limit of resolution
15.scattering of light
16. Polarization of light
-----------
Study Plan
Day 1
1. Waves or Particles
2. The nature of light waves
Day 2
3. Huygen's principles
Worked out examples 1,2
Day 3
4. Young's double hole experiment
5. Young's double slit experiment
Day 4
6. Optical path
7. Interference from thin films
8. Fresnel's Biprism
9. coherent and incoherent sources
Day 5
WOE 3 to 7
Exerciese 1 to 5
Day 6
10. Diffraction of light
11. Fraunhofer Diffraction by a single slit
12.Fraunhofer Diffraction by a circular aperture
Day 7
13.Fresnel diffraction at a straight edge
14.Limit of resolution
15.scattering of light
Day 8
WoE 8 to 11
Exercises 6 to 10
Day 9
16. Polarization of light
Exercises 11 to 25
Day 10
Exercises 26 to 35
Day 11
Exercises 36 to 41
Day 12
Objective I 1 to 17
Day 13
Objective II 1 to 10
Day 14
Questions for short answer 1 to 11
Concept review - Formula review
--------------
Concepts covered
2. The nature of light waves
In a wave motion, there is some quantity which changes its value with time and space.
That quantity is the electric field existing in space where light travels.
The electric field is transverse to to the direction of propagation of light.
The equation of such light wave may be written as
E - E0 sin ω(t-x/v)
Light of single wavelength is called monochromatic light.
Huygen's principle
Various points of an arbitrary surface, when reached by a wave front, become secondary sources of light emitting secondary wavelets. The disturbance beyond the surface results from the superposition of these secondary wavelets.
Updated 1 May 2016, 23 Oct 2007
Saturday, April 9, 2016
Video Lectures 15.2 Wave pulse on a string
Video Lectures 15.2 Wave pulse on a string
Propagation of a pulse in a string
Fernando Dall'Agnol
________________
________________
waves on a string
Zachary Tourville
________________
_________________
Video Lectures 15.1 Wave motion
Video Lectures 15.1 Wave motion
_______________
_______________
TutorVista
Characteristics of Waves
Study guide H C Verma JEE Physics Ch. 15 WAVE MOTION AND WAVES ON A STRING
JEE Syllabus
Wave motion (plane waves only) 15.1,
longitudinal and transverse waves 15.13, 15.14,
superposition of waves; 15.6
Progressive and stationary waves(15.9 ,10);
Vibration of strings 15.11, 12, 13
-----------
Sections of the chapter
15.1 Wave motion
15.2 Wave pulse on a string
15.3 Sine wave travelling on a string
15.4 Velocity of a wave on a string
15.5 Power transmitted along the string by a sine wave
15.6 Interference and the Principle of Superposition
15.7 Interference of waves going in same direction
15.8 reflection and tramission of waves
15.9 Standing waves
15.10 Standing waves on a string fixed at both ends
15.11 analytic treatment of vibration of string fixed at both ends
15.12 Vibration of string fixed at both ends
15.13 Laws of Transverse vibrations of a string; Sonometer
15.14 Transverse and Longitudinal waves
15.15 Polarisation of waves
-------------
Study Plan
Day 1
Concept review Ch.15 Wave Motion and Waves on a String
Study sections
15.1 and 15.2
Video Lectures 15.1 Wave motion
Video Lectures 15.2 Wave pulse on a string
Day 2
Study sections
15.3 and 15.4
Study sections
15.5 and 15.6
Day 3
Study sections
15.5 and 15.6
Do worked out examples 1,2,3
Day 4
Study sections
15.7 Interference of waves going the same direction
and
15.8 Reflection and transmission of waves
Read example 15.5
Study worked out examples 4 and 5
Day 5
Study sections
15.9 and 15.10
Day 6
Study sections
15.11 and 15.12
15,11 Analytical treatment of vibration of a string fixed at both end.
15.12 Vibration of a string fixed at one end
Study worked out examples 6 and 7
Day 7
Study 15.13 and 15.14
15.13 Laws of Transverse Vibrations of a string: Sonometer
15.14 Transverse and Longitudinal waves
Study example 15.8
Study worked out examples 7,8,9
Do exercise problems 1,2,3
Day 8
Study 15.15 Polarization of waves
Study worked out examples 10
Do exercise problems 4 to 10
Day 9
Revision
Concept review Ch.15 Wave Motion and Waves on a String
Wave Motion - Waves on a String - Laws
Formula Revision 15. Wave motion and waves on a string
Do exercise problems 11 to 20
Day 10
Do exercise problems 21 to 30
Day 11
Do exercise problems 31 - 35
Day 12
Do exercise problems 36 - 40
Day 13
Do exercise problems 41 - 45
Day 14
Do exercise problems 46 - 50
Day 15
Do exercise problems 51 - 55
Day 16
Do exercise problems 56 - 57
Day 17
Objective I 1 to 12
Day 18
Objective I 13 to 22
Day 19
Objective II
Day 20
Questions for short answer 1 to 8
Concepts covered
Wave motion
Way of transporting energy from part of space to the other without any bulk motion of material together with it is wave motion. Sound is transmitted in air in this manner.
Waves that require a medium to travel are called mechanical waves and those which do not require a medium are called nonmechanical waves.
Travelling wave or progressive wave
---------------
Audiovisual lectures
Lesson 42: Wave Basics
www.curriki.org/nroc/Introductory_Physics_2/lesson42/Container.html
Lesson 43: Properties of Traveling Waves
www.curriki.org/nroc/Introductory_Physics_2/lesson43/Container.html
Lesson 44: Properties of Standing Waves
www.curriki.org/nroc/Introductory_Physics_2/lesson44/Container.html
Web sites
http://physics.pdx.edu/~larosaa/Ph-223/larosa_lecture_3.pdfnte
Wave motion (plane waves only) 15.1,
longitudinal and transverse waves 15.13, 15.14,
superposition of waves; 15.6
Progressive and stationary waves(15.9 ,10);
Vibration of strings 15.11, 12, 13
-----------
Sections of the chapter
15.1 Wave motion
15.2 Wave pulse on a string
15.3 Sine wave travelling on a string
15.4 Velocity of a wave on a string
15.5 Power transmitted along the string by a sine wave
15.6 Interference and the Principle of Superposition
15.7 Interference of waves going in same direction
15.8 reflection and tramission of waves
15.9 Standing waves
15.10 Standing waves on a string fixed at both ends
15.11 analytic treatment of vibration of string fixed at both ends
15.12 Vibration of string fixed at both ends
15.13 Laws of Transverse vibrations of a string; Sonometer
15.14 Transverse and Longitudinal waves
15.15 Polarisation of waves
-------------
Study Plan
Day 1
Concept review Ch.15 Wave Motion and Waves on a String
Study sections
15.1 and 15.2
Video Lectures 15.1 Wave motion
Video Lectures 15.2 Wave pulse on a string
Day 2
Study sections
15.3 and 15.4
Study sections
15.5 and 15.6
Day 3
Study sections
15.5 and 15.6
Do worked out examples 1,2,3
Day 4
Study sections
15.7 Interference of waves going the same direction
and
15.8 Reflection and transmission of waves
Read example 15.5
Study worked out examples 4 and 5
Day 5
Study sections
15.9 and 15.10
Day 6
Study sections
15.11 and 15.12
15,11 Analytical treatment of vibration of a string fixed at both end.
15.12 Vibration of a string fixed at one end
Study worked out examples 6 and 7
Day 7
Study 15.13 and 15.14
15.13 Laws of Transverse Vibrations of a string: Sonometer
15.14 Transverse and Longitudinal waves
Study example 15.8
Study worked out examples 7,8,9
Do exercise problems 1,2,3
Day 8
Study 15.15 Polarization of waves
Study worked out examples 10
Do exercise problems 4 to 10
Day 9
Revision
Concept review Ch.15 Wave Motion and Waves on a String
Wave Motion - Waves on a String - Laws
Formula Revision 15. Wave motion and waves on a string
Do exercise problems 11 to 20
Day 10
Do exercise problems 21 to 30
Day 11
Do exercise problems 31 - 35
Day 12
Do exercise problems 36 - 40
Day 13
Do exercise problems 41 - 45
Day 14
Do exercise problems 46 - 50
Day 15
Do exercise problems 51 - 55
Day 16
Do exercise problems 56 - 57
Day 17
Objective I 1 to 12
Day 18
Objective I 13 to 22
Day 19
Objective II
Day 20
Questions for short answer 1 to 8
Concepts covered
Wave motion
Way of transporting energy from part of space to the other without any bulk motion of material together with it is wave motion. Sound is transmitted in air in this manner.
Waves that require a medium to travel are called mechanical waves and those which do not require a medium are called nonmechanical waves.
Travelling wave or progressive wave
---------------
Audiovisual lectures
Lesson 42: Wave Basics
www.curriki.org/nroc/Introductory_Physics_2/lesson42/Container.html
Lesson 43: Properties of Traveling Waves
www.curriki.org/nroc/Introductory_Physics_2/lesson43/Container.html
Lesson 44: Properties of Standing Waves
www.curriki.org/nroc/Introductory_Physics_2/lesson44/Container.html
Web sites
http://physics.pdx.edu/~larosaa/Ph-223/larosa_lecture_3.pdfnte
Thursday, February 11, 2016
CBSE - JEE - Chapters from H C Verma - Study Guides, Revision Notes, Revision Questions and Problems, Lecture Videos
Concepts of Physics Part I by H C Verma
Chapters
1. Introduction to physics
2. Physics and mathematics
3. Rest and motion :kinematics
4. The forces
5. Newtons law of motion
6. Friction
7. Circular motion
8. Work and energy
9. Centre of mass,linear momentum,collision
10. Rotational mechanics
11. Gravitation
12. Simple harmonic motion
13. Fluid mechanics
14. Some mechanical properties of matter
15. Wave motion and waves on a string
16. Sound waves
17. Light waves
18. Geometrical optics
19. Optical instruments
20. Dispersion and spectra
21. Speed of light
22. Photometry
23. Heat and Temperature
24. Kinetic theory of Gases
25. Calorimetry
26. Laws of Thermodynamics
27. Specific Heat of Capacities of Gases
28. Heat transfer
29. Electric Field and Potential
30. Gauss's Law
31. Capacitors
32. Electric Current in Conductors
32. Thermal and Chemical effects of Electric Current
33. Thermal and Chemical Effects of Electric Current
34. Magentic Field
35. Magnetic field due to a Current
36. Permanent Magnets
37. Magnetic Properties of Matter
38. Electro Magentic Induction
39. Alternating current
40. electromagentic Waves
41. Electric Current through Gases
42. Photoelectric Effect and Waveparticle Duality
43. Bohr's Model and Physics of Atom
44. X-Rays
45. SemiConductors and Semiconductor Devices
46. Nucleus
47. The Special Theory of Relativity
H C Verma Book Chapters - Study Guides
1. Introduction to physics
2. Physics and mathematics
3. Rest and motion :kinematics
4. The forces
5. Newtons law of motion
6. Friction
7. Circular motion
8. Work and energy
9. Centre of mass,linear momentum,collision
10. Rotational mechanics
11. Gravitation
12. Simple harmonic motion
13. Fluid mechanics
14. Some mechanical properties of matter
15. Wave motion and waves on a string
16. Sound waves
17. Light waves
18. Geometrical optics
19. Optical instruments
20. Dispersion and spectra
21. Speed of light
22. Photometry
23. Heat and Temperature
24. Kinetic theory of Gases
25. Calorimetry
26. Laws of Thermodynamics
27. Specific Heat of Capacities of Gases
28. Heat transfer
29. Electric Field and Potential
30. Gauss's Law
31. Capacitors
32. Electric Current in Conductors
32. Thermal and Chemical effects of Electric Current
33. Thermal and Chemical Effects of Electric Current
34. Magentic Field
35. Magnetic field due to a Current
36. Permanent Magnets
37. Magnetic Properties of Matter
38. Electro Magentic Induction
39. Alternating current
40. electromagentic Waves
41. Electric Current through Gases
42. Photoelectric Effect and Waveparticle Duality
43. Bohr's Model and Physics of Atom
44. X-Rays
45. SemiConductors and Semiconductor Devices
46. Nucleus
47. The Special Theory of Relativity
Chapters
1. Introduction to physics
2. Physics and mathematics
3. Rest and motion :kinematics
4. The forces
5. Newtons law of motion
6. Friction
7. Circular motion
8. Work and energy
9. Centre of mass,linear momentum,collision
10. Rotational mechanics
11. Gravitation
12. Simple harmonic motion
13. Fluid mechanics
14. Some mechanical properties of matter
15. Wave motion and waves on a string
16. Sound waves
17. Light waves
18. Geometrical optics
19. Optical instruments
20. Dispersion and spectra
21. Speed of light
22. Photometry
23. Heat and Temperature
24. Kinetic theory of Gases
25. Calorimetry
26. Laws of Thermodynamics
27. Specific Heat of Capacities of Gases
28. Heat transfer
29. Electric Field and Potential
30. Gauss's Law
31. Capacitors
32. Electric Current in Conductors
32. Thermal and Chemical effects of Electric Current
33. Thermal and Chemical Effects of Electric Current
34. Magentic Field
35. Magnetic field due to a Current
36. Permanent Magnets
37. Magnetic Properties of Matter
38. Electro Magentic Induction
39. Alternating current
40. electromagentic Waves
41. Electric Current through Gases
42. Photoelectric Effect and Waveparticle Duality
43. Bohr's Model and Physics of Atom
44. X-Rays
45. SemiConductors and Semiconductor Devices
46. Nucleus
47. The Special Theory of Relativity
Chapters
1. Introduction to physics
2. Physics and mathematics
3. Rest and motion :kinematics
4. The forces
5. Newtons law of motion
6. Friction
7. Circular motion
8. Work and energy
9. Centre of mass,linear momentum,collision
10. Rotational mechanics
11. Gravitation
12. Simple harmonic motion
13. Fluid mechanics
14. Some mechanical properties of matter
15. Wave motion and waves on a string
16. Sound waves
17. Light waves
18. Geometrical optics
19. Optical instruments
20. Dispersion and spectra
21. Speed of light
22. Photometry
23. Heat and Temperature
24. Kinetic theory of Gases
25. Calorimetry
26. Laws of Thermodynamics
27. Specific Heat of Capacities of Gases
28. Heat transfer
29. Electric Field and Potential
30. Gauss's Law
31. Capacitors
32. Electric Current in Conductors
32. Thermal and Chemical effects of Electric Current
33. Thermal and Chemical Effects of Electric Current
34. Magentic Field
35. Magnetic field due to a Current
36. Permanent Magnets
37. Magnetic Properties of Matter
38. Electro Magentic Induction
39. Alternating current
40. electromagentic Waves
41. Electric Current through Gases
42. Photoelectric Effect and Waveparticle Duality
43. Bohr's Model and Physics of Atom
44. X-Rays
45. SemiConductors and Semiconductor Devices
46. Nucleus
47. The Special Theory of Relativity
Updated 11 Feb 2016, 16 May 2007
Chapters
1. Introduction to physics
2. Physics and mathematics
3. Rest and motion :kinematics
4. The forces
5. Newtons law of motion
6. Friction
7. Circular motion
8. Work and energy
9. Centre of mass,linear momentum,collision
10. Rotational mechanics
11. Gravitation
12. Simple harmonic motion
13. Fluid mechanics
14. Some mechanical properties of matter
15. Wave motion and waves on a string
16. Sound waves
17. Light waves
18. Geometrical optics
19. Optical instruments
20. Dispersion and spectra
21. Speed of light
22. Photometry
23. Heat and Temperature
24. Kinetic theory of Gases
25. Calorimetry
26. Laws of Thermodynamics
27. Specific Heat of Capacities of Gases
28. Heat transfer
29. Electric Field and Potential
30. Gauss's Law
31. Capacitors
32. Electric Current in Conductors
32. Thermal and Chemical effects of Electric Current
33. Thermal and Chemical Effects of Electric Current
34. Magentic Field
35. Magnetic field due to a Current
36. Permanent Magnets
37. Magnetic Properties of Matter
38. Electro Magentic Induction
39. Alternating current
40. electromagentic Waves
41. Electric Current through Gases
42. Photoelectric Effect and Waveparticle Duality
43. Bohr's Model and Physics of Atom
44. X-Rays
45. SemiConductors and Semiconductor Devices
46. Nucleus
47. The Special Theory of Relativity
H C Verma Book Chapters - Study Guides
1. Introduction to physics
2. Physics and mathematics
3. Rest and motion :kinematics
4. The forces
5. Newtons law of motion
6. Friction
7. Circular motion
8. Work and energy
9. Centre of mass,linear momentum,collision
10. Rotational mechanics
11. Gravitation
12. Simple harmonic motion
13. Fluid mechanics
14. Some mechanical properties of matter
15. Wave motion and waves on a string
16. Sound waves
17. Light waves
18. Geometrical optics
19. Optical instruments
20. Dispersion and spectra
21. Speed of light
22. Photometry
23. Heat and Temperature
24. Kinetic theory of Gases
25. Calorimetry
26. Laws of Thermodynamics
27. Specific Heat of Capacities of Gases
28. Heat transfer
29. Electric Field and Potential
30. Gauss's Law
31. Capacitors
32. Electric Current in Conductors
32. Thermal and Chemical effects of Electric Current
33. Thermal and Chemical Effects of Electric Current
34. Magentic Field
35. Magnetic field due to a Current
36. Permanent Magnets
37. Magnetic Properties of Matter
38. Electro Magentic Induction
39. Alternating current
40. electromagentic Waves
41. Electric Current through Gases
42. Photoelectric Effect and Waveparticle Duality
43. Bohr's Model and Physics of Atom
44. X-Rays
45. SemiConductors and Semiconductor Devices
46. Nucleus
47. The Special Theory of Relativity
Chapters
1. Introduction to physics
2. Physics and mathematics
3. Rest and motion :kinematics
4. The forces
5. Newtons law of motion
6. Friction
7. Circular motion
8. Work and energy
9. Centre of mass,linear momentum,collision
10. Rotational mechanics
11. Gravitation
12. Simple harmonic motion
13. Fluid mechanics
14. Some mechanical properties of matter
15. Wave motion and waves on a string
16. Sound waves
17. Light waves
18. Geometrical optics
19. Optical instruments
20. Dispersion and spectra
21. Speed of light
22. Photometry
23. Heat and Temperature
24. Kinetic theory of Gases
25. Calorimetry
26. Laws of Thermodynamics
27. Specific Heat of Capacities of Gases
28. Heat transfer
29. Electric Field and Potential
30. Gauss's Law
31. Capacitors
32. Electric Current in Conductors
32. Thermal and Chemical effects of Electric Current
33. Thermal and Chemical Effects of Electric Current
34. Magentic Field
35. Magnetic field due to a Current
36. Permanent Magnets
37. Magnetic Properties of Matter
38. Electro Magentic Induction
39. Alternating current
40. electromagentic Waves
41. Electric Current through Gases
42. Photoelectric Effect and Waveparticle Duality
43. Bohr's Model and Physics of Atom
44. X-Rays
45. SemiConductors and Semiconductor Devices
46. Nucleus
47. The Special Theory of Relativity
Chapters
1. Introduction to physics
2. Physics and mathematics
3. Rest and motion :kinematics
4. The forces
5. Newtons law of motion
6. Friction
7. Circular motion
8. Work and energy
9. Centre of mass,linear momentum,collision
10. Rotational mechanics
11. Gravitation
12. Simple harmonic motion
13. Fluid mechanics
14. Some mechanical properties of matter
15. Wave motion and waves on a string
16. Sound waves
17. Light waves
18. Geometrical optics
19. Optical instruments
20. Dispersion and spectra
21. Speed of light
22. Photometry
23. Heat and Temperature
24. Kinetic theory of Gases
25. Calorimetry
26. Laws of Thermodynamics
27. Specific Heat of Capacities of Gases
28. Heat transfer
29. Electric Field and Potential
30. Gauss's Law
31. Capacitors
32. Electric Current in Conductors
32. Thermal and Chemical effects of Electric Current
33. Thermal and Chemical Effects of Electric Current
34. Magentic Field
35. Magnetic field due to a Current
36. Permanent Magnets
37. Magnetic Properties of Matter
38. Electro Magentic Induction
39. Alternating current
40. electromagentic Waves
41. Electric Current through Gases
42. Photoelectric Effect and Waveparticle Duality
43. Bohr's Model and Physics of Atom
44. X-Rays
45. SemiConductors and Semiconductor Devices
46. Nucleus
47. The Special Theory of Relativity
Updated 11 Feb 2016, 16 May 2007
General Theory of Relativity in Hindi
जनरल थ्योरी ऑफ रिलेटिविटी - अल्बर्ट आइन्स्टीन (Albert Einstein)
कल्पना कीजिए एक बिन्दु में विस्फोट होता है और वह कई भागों में बंट जाता है और भाग एक दूसरे से दूर जाने लगेंगे। और इसके लिये ये जगह को भी खुद से पैदा करेंगे। सभी भाग विस्फोट हुए बिन्दु से बाहर की ओर सीढ़ी रेखा में चलते जायेंगे। किन्तु अगर ये भाग एक दूसरे को परस्पर किसी कमजोर बल द्वारा आकर्षित करें ? तो इनकी गति सीढ़ी रेखा में नहीं रह जायेगी। अगर इन बिन्दुओं के समूह को आकाश माना जाये तो यह आकाश सीधा न होकर वक्र (curve) होगा
http://blog.scientificworld.in/2016/02/general-theory-of-relativity-in-hindi.html
कल्पना कीजिए एक बिन्दु में विस्फोट होता है और वह कई भागों में बंट जाता है और भाग एक दूसरे से दूर जाने लगेंगे। और इसके लिये ये जगह को भी खुद से पैदा करेंगे। सभी भाग विस्फोट हुए बिन्दु से बाहर की ओर सीढ़ी रेखा में चलते जायेंगे। किन्तु अगर ये भाग एक दूसरे को परस्पर किसी कमजोर बल द्वारा आकर्षित करें ? तो इनकी गति सीढ़ी रेखा में नहीं रह जायेगी। अगर इन बिन्दुओं के समूह को आकाश माना जाये तो यह आकाश सीधा न होकर वक्र (curve) होगा
http://blog.scientificworld.in/2016/02/general-theory-of-relativity-in-hindi.html
Sunday, January 31, 2016
JEE - CBSE - Physics Ch. 1 INTRODUCTION TO PHYSICS - Revision Questions
This blog was started along with my blog. Still being updated.
http://physicsgoeasy.blogspot.in/
Test on all chapters
http://www.mtel.nesinc.com/pdfs/ma_fld011_practice_test.pdf
http://www.topperlearning.com/study/cbse/class-11/physics/multiple-choice-questions/units-and-measurement/b101c3s4e23ch121#begin-test
Sunday, January 10, 2016
Concept Review - Chapter 9 Centre of Mass, Collision
Centre of mass
Definition
Centre of mass of several groups of particles
Centre of mass of continuous bodies
Motion of centre of mass
Linear momentum
Principle of conservation of linear momentum
Collision
Elastic collision
Inelastic collision
Coefficient of restitution
Impulse
Impulse force
Centre of mass - Linear momentum - Videos
Updated 10 Jan 2016, 7 May 2008
Definition
Centre of mass of several groups of particles
Centre of mass of continuous bodies
Motion of centre of mass
Linear momentum
Principle of conservation of linear momentum
Collision
Elastic collision
Inelastic collision
Coefficient of restitution
Impulse
Impulse force
Centre of mass - Linear momentum - Videos
Updated 10 Jan 2016, 7 May 2008
Concept Review - Chapter 10 Rotational Mechanics
Rotation of a rigid body
Kinematics of rotation of rigid body
Torque of a force about the axis of rotation
Angular momentum
Conservation of angular momentum
Work done by a torque
Power delivered by a torque
Moment of inertia
Moment of inertia theorems
Theorem of parallel axes
Theorem of perpendicular axes
Combined rotation and translation
Rolling
If each particle of a rigid body moves in a circle, with centres of all the circles on a straight line and with planes of the circles perpendicular to this line we say that the body is rotating about this line. The straight line is called the axis of rotation. (Particle makes circular motion. Rigid body makes rotation.)
Kinematics of rotation of rigid body
For a rigid body let the axis of rotation be Z-axis.
At time t =0, let particle P be at P0.
Perpendicular to axis of rotation from P0 be PQ. (Q is on the axis)
If at time t Particle P moves P1 and angle P0Q P1 = θ.
Hence the particle has rotated through θ.
All particles have rotated through θ.
We can say the whole rigid body has rotated through angle θ.
The angular position of the body at time t is θ.
If P has made a complete revolution its circular path, every particle will do so and hence rigid body has done so. We can say rigid body made a complete revolution and it has rotated through an angle of 2 π radians.
Hence, rotation of a rigid body is measured by the rotation of a line PQ (P is a particle on the rigid body and Q is a point on the axis of rotation and PQ is perpendicular from P to the axis of rotation).
As the rotation of rigid body is defined in terms of the circular motion of a particle on the rigid body, kinematics of circular motion of particle becomes applicable to rotation.
Angular variables
θ = angular position of the particle
ω = angular velocity = d θ/dt = lim∆t→0 ∆θ/∆t
α = angular acceleration = d ω/dt = d²θ/dt²
If the angular acceleration is constant, formulas similar in form to linear formulas can be used to find the angular variables:
θ = ω0t + ½ αt²
ω = ω0 + αt
ω² = ω0² + 2 α θ
Where
ω0 is velocity at time t = 0.
Given the axis of rotation, the body can rotate in two directions – clockwise or anticlockwise. One of the directions has to be defined as positive direction according to the convenience of the problem.
The SI unit for angular velocity is radian/sec (rad/s).
One revolution/sec = 2 π radian/sec
Similar to the circular motion of the particle, in rotation for a particle P
s = Linear distance traveled by the particle in circular motion
∆s = Linear distance traveled by the particle in circular motion in time ∆t
∆s = r∆θ
Where
r = radius of the circle over which the particle is moving
∆θ = angular displacement in time ∆t
∆s/∆t = r∆θ/∆t
v = r ω
where
v = linear speed of the particle
at = rate of change of speed of the particle in circular motion
at = dv/dt = rdω/dt = r α
Rotational dynamics
In rotation of a body the resultant force due to external forces is zero, but the resultant of
Torque produced by the external forces is nonzero and this torque produces rotation motion.
Torque of a force about the axis of rotation
First we define torque a force about a point.
For a force F acting on a particle P, to find torque about a point O, define the position vector of P with respect to O. Let this position vector be r.
Torque of force F about O = Γ = F × r.
This is vector product of two vectors hence a vector quantity, as per the rules of vector product, the direction of Γ will be perpendicular to to F and r.
When the torque about an axis of rotation is to be determined, select a point on the axis of the rotation and find the torque of the force acting on a particle about this point. Find the angle between the axis and the line joining the point on axis (about which the torque is calculated) and the particle (one which the force is acting). Let the angle be θ.
Torque about the axis due to a force is the component along the axis, of the torque of the force about a point on the axis.
Magnitude of the torque = | F × r | cos θ
The torque about the axis is same, even if different points are chosen along the axis for determining the torque of the force about those points.
Some special cases of relation between force and the axis of rotation.
1. Force is parallel to the axis of rotation.
Torque along the axis is zero.
2. F and r are collinear. The torque about O is zero and the torque about axis is zero.
3. Force and axis are perpendicular but they do not intersect. In three dimensions, two lines may be perpendicular without intersecting. Example: A vertical line on
a wall and a horizontal line on the opposite wall.
In this case torque about the axis is equal to Force multiplied by the perpendicular to axis from the force direction (line along which the force is acting).
Torque produced by forces on a particle
A particle having circular motion will have two forces acting on it.
One force produces tangential acceleration dv/dt in it. Hence the force named tangential force is 'ma' = mdv/dt = mrα
This force creates a torque of mr²α
the other force creates radial acceleration or centripetal acceleration ω²r. Hence the force named radial force is mω²r
As intersects the axis of rotation, the torque produced by it is zero.
Hence total torque produced by a rigid body consisting of n particles is
Г(total) = Σmiri²α
= αΣmiri² as α is same for all particles
Let I = Σmiri²
Г(total) = Iα
Quantity I is called moment of inertia of the body about the axis of rotation.
I = Σmiri²
where
mi = mass of the ith particle
ri = perpendicular distance of ith particle from the axis of rotation.
Angular momentum
Conservation of angular momentum
Work done by a torque
Power delivered by a torque
Moment of inertia
Moment of Inertia
Torque created by external forces in rotating motion
When a particle is rotating it has tangential acceleration and radial acceleration.
Radial acceleration = ω²r
Hence radial force acting on it = m ω²r
Tangential acceleration = dv/dt = rdω/dt = r α
ω = angular velocity
α = angular acceleration
Tangential force = mrα
Torque created by radial force is zero as the force intersects the axis of rotation.
Tangential force and axis are skew (they do not intersect) and they are perpendicular. Thus the resultant torque is Force*radius = mr²α
In the case of a body having ‘n’ particles and rotating, the total torque is equal to torque acting on each of the particles
Total torque on the body = Γ(total) = Σ miri²α
Σ miri² is called as moment of inertia.
Moment of inertia can be calculated using the above formula for collection of discrete particles.
If the body is a continuous, the technique of integration needs to be used. We consider a small element of the body with mass dm and having a perpendicular distance from the axis or line about which moment of inertial is to be calculated.
We find ∫ r²dm under proper limits to get the moment of inertia of the body.
r²dm is the moment of inertia of the small element.
Determination of moment of inertia of representative bodies.
1. Uniform rod about a perpendicular
M = total mass of the body
l = length of the body
I = Ml²/12
I is obtained by taking a small element dx at a distance x from the centre of the rod.
Mass dm of the element = (M/l)*dx (M/l give mass per unit length)
dI = (M/l)*dx*x²
I = ∫(M/l)*dx*x² (limits are from –l/2 to l/2: these limits cover the entire rod).
= M/l[x³/3] from –l/2 to l/2
= M/3l[l³/8 + l³/8] = M/3l(l³/40) = Ml²/12
2. Moment of inertia of uniform rectangular plate about a line parallel to an edge and passing through the centre.
M = total mass of the body
Plate measurements l,b
Axis or line is parallel to b
I = Ml²/12
If the axis of line is parallel to l
I = Mb²/12
3. Circular ring
M = total mass of the body
R = radius
I = MR²
4. Uniform circular plate
M = total mass of the body
R = radius
I = MR²/2
5. Hollow cylinder about its axis
M = total mass of the body
R = radius
I = MR²
6. Uniform solid cylinder about its axis.
M = total mass of the body
R = radius
I = MR²/2
7. Hollow sphere about a diameter
M = total mass of the body
R = radius
I =(2/3) MR²
8. Uniform solid sphere about a diameter
M = total mass of the body
R = radius
I = (2/5) MR²
Moment of inertia theorems
Theorem of parallel axes
Thoerem of perpendicular axes
Combined rotation and translation
Rolling
Rotational kinematics
Angular variables
θ = angular position of the particle
ω = angular velocity = dθ/dt = lim∆t→0 ∆θ/∆t
α = angular acceleration = dω/dt = d²θ/dt²
If the angular acceleration is constant, formulas similar in form to linear formulas can be used to find the angular variables:
θ = ω0t + ½ αt²
ω = ω0 + αt
ω² = ω0² + 2 α θ
where
ω0 = angular velocity at the beginning
Relation between the linear motion of a particle of a rigid body and rotation of the rigid body
v = r ω
where
v = linear speed of the particle
at = rate of change of speed of the particle in circular motion
at = dv/dt = rdω/dt = r α (These relations are from the chapter of circular motion)
Updated 10 Jan 2016, 7 May 2008
Kinematics of rotation of rigid body
Torque of a force about the axis of rotation
Angular momentum
Conservation of angular momentum
Work done by a torque
Power delivered by a torque
Moment of inertia
Moment of inertia theorems
Theorem of parallel axes
Theorem of perpendicular axes
Combined rotation and translation
Rolling
Rotation of a rigid body
If each particle of a rigid body moves in a circle, with centres of all the circles on a straight line and with planes of the circles perpendicular to this line we say that the body is rotating about this line. The straight line is called the axis of rotation. (Particle makes circular motion. Rigid body makes rotation.)
Kinematics of rotation of rigid body
For a rigid body let the axis of rotation be Z-axis.
At time t =0, let particle P be at P0.
Perpendicular to axis of rotation from P0 be PQ. (Q is on the axis)
If at time t Particle P moves P1 and angle P0Q P1 = θ.
Hence the particle has rotated through θ.
All particles have rotated through θ.
We can say the whole rigid body has rotated through angle θ.
The angular position of the body at time t is θ.
If P has made a complete revolution its circular path, every particle will do so and hence rigid body has done so. We can say rigid body made a complete revolution and it has rotated through an angle of 2 π radians.
Hence, rotation of a rigid body is measured by the rotation of a line PQ (P is a particle on the rigid body and Q is a point on the axis of rotation and PQ is perpendicular from P to the axis of rotation).
As the rotation of rigid body is defined in terms of the circular motion of a particle on the rigid body, kinematics of circular motion of particle becomes applicable to rotation.
Angular variables
θ = angular position of the particle
ω = angular velocity = d θ/dt = lim∆t→0 ∆θ/∆t
α = angular acceleration = d ω/dt = d²θ/dt²
If the angular acceleration is constant, formulas similar in form to linear formulas can be used to find the angular variables:
θ = ω0t + ½ αt²
ω = ω0 + αt
ω² = ω0² + 2 α θ
Where
ω0 is velocity at time t = 0.
Given the axis of rotation, the body can rotate in two directions – clockwise or anticlockwise. One of the directions has to be defined as positive direction according to the convenience of the problem.
The SI unit for angular velocity is radian/sec (rad/s).
One revolution/sec = 2 π radian/sec
Similar to the circular motion of the particle, in rotation for a particle P
s = Linear distance traveled by the particle in circular motion
∆s = Linear distance traveled by the particle in circular motion in time ∆t
∆s = r∆θ
Where
r = radius of the circle over which the particle is moving
∆θ = angular displacement in time ∆t
∆s/∆t = r∆θ/∆t
v = r ω
where
v = linear speed of the particle
at = rate of change of speed of the particle in circular motion
at = dv/dt = rdω/dt = r α
Rotational dynamics
In rotation of a body the resultant force due to external forces is zero, but the resultant of
Torque produced by the external forces is nonzero and this torque produces rotation motion.
Torque of a force about the axis of rotation
First we define torque a force about a point.
For a force F acting on a particle P, to find torque about a point O, define the position vector of P with respect to O. Let this position vector be r.
Torque of force F about O = Γ = F × r.
This is vector product of two vectors hence a vector quantity, as per the rules of vector product, the direction of Γ will be perpendicular to to F and r.
When the torque about an axis of rotation is to be determined, select a point on the axis of the rotation and find the torque of the force acting on a particle about this point. Find the angle between the axis and the line joining the point on axis (about which the torque is calculated) and the particle (one which the force is acting). Let the angle be θ.
Torque about the axis due to a force is the component along the axis, of the torque of the force about a point on the axis.
Magnitude of the torque = | F × r | cos θ
The torque about the axis is same, even if different points are chosen along the axis for determining the torque of the force about those points.
Some special cases of relation between force and the axis of rotation.
1. Force is parallel to the axis of rotation.
Torque along the axis is zero.
2. F and r are collinear. The torque about O is zero and the torque about axis is zero.
3. Force and axis are perpendicular but they do not intersect. In three dimensions, two lines may be perpendicular without intersecting. Example: A vertical line on
a wall and a horizontal line on the opposite wall.
In this case torque about the axis is equal to Force multiplied by the perpendicular to axis from the force direction (line along which the force is acting).
Torque produced by forces on a particle
A particle having circular motion will have two forces acting on it.
One force produces tangential acceleration dv/dt in it. Hence the force named tangential force is 'ma' = mdv/dt = mrα
This force creates a torque of mr²α
the other force creates radial acceleration or centripetal acceleration ω²r. Hence the force named radial force is mω²r
As intersects the axis of rotation, the torque produced by it is zero.
Hence total torque produced by a rigid body consisting of n particles is
Г(total) = Σmiri²α
= αΣmiri² as α is same for all particles
Let I = Σmiri²
Г(total) = Iα
Quantity I is called moment of inertia of the body about the axis of rotation.
I = Σmiri²
where
mi = mass of the ith particle
ri = perpendicular distance of ith particle from the axis of rotation.
Angular momentum
Conservation of angular momentum
Work done by a torque
Power delivered by a torque
Moment of inertia
Moment of Inertia
Torque created by external forces in rotating motion
When a particle is rotating it has tangential acceleration and radial acceleration.
Radial acceleration = ω²r
Hence radial force acting on it = m ω²r
Tangential acceleration = dv/dt = rdω/dt = r α
ω = angular velocity
α = angular acceleration
Tangential force = mrα
Torque created by radial force is zero as the force intersects the axis of rotation.
Tangential force and axis are skew (they do not intersect) and they are perpendicular. Thus the resultant torque is Force*radius = mr²α
In the case of a body having ‘n’ particles and rotating, the total torque is equal to torque acting on each of the particles
Total torque on the body = Γ(total) = Σ miri²α
Σ miri² is called as moment of inertia.
Moment of inertia can be calculated using the above formula for collection of discrete particles.
If the body is a continuous, the technique of integration needs to be used. We consider a small element of the body with mass dm and having a perpendicular distance from the axis or line about which moment of inertial is to be calculated.
We find ∫ r²dm under proper limits to get the moment of inertia of the body.
r²dm is the moment of inertia of the small element.
Determination of moment of inertia of representative bodies.
1. Uniform rod about a perpendicular
M = total mass of the body
l = length of the body
I = Ml²/12
I is obtained by taking a small element dx at a distance x from the centre of the rod.
Mass dm of the element = (M/l)*dx (M/l give mass per unit length)
dI = (M/l)*dx*x²
I = ∫(M/l)*dx*x² (limits are from –l/2 to l/2: these limits cover the entire rod).
= M/l[x³/3] from –l/2 to l/2
= M/3l[l³/8 + l³/8] = M/3l(l³/40) = Ml²/12
2. Moment of inertia of uniform rectangular plate about a line parallel to an edge and passing through the centre.
M = total mass of the body
Plate measurements l,b
Axis or line is parallel to b
I = Ml²/12
If the axis of line is parallel to l
I = Mb²/12
3. Circular ring
M = total mass of the body
R = radius
I = MR²
4. Uniform circular plate
M = total mass of the body
R = radius
I = MR²/2
5. Hollow cylinder about its axis
M = total mass of the body
R = radius
I = MR²
6. Uniform solid cylinder about its axis.
M = total mass of the body
R = radius
I = MR²/2
7. Hollow sphere about a diameter
M = total mass of the body
R = radius
I =(2/3) MR²
8. Uniform solid sphere about a diameter
M = total mass of the body
R = radius
I = (2/5) MR²
Moment of inertia theorems
Theorem of parallel axes
Thoerem of perpendicular axes
Combined rotation and translation
Rolling
Formula Sheet – Rotational Mechanics
Rotational kinematics
Angular variables
θ = angular position of the particle
ω = angular velocity = dθ/dt = lim∆t→0 ∆θ/∆t
α = angular acceleration = dω/dt = d²θ/dt²
If the angular acceleration is constant, formulas similar in form to linear formulas can be used to find the angular variables:
θ = ω0t + ½ αt²
ω = ω0 + αt
ω² = ω0² + 2 α θ
where
ω0 = angular velocity at the beginning
Relation between the linear motion of a particle of a rigid body and rotation of the rigid body
v = r ω
where
v = linear speed of the particle
at = rate of change of speed of the particle in circular motion
at = dv/dt = rdω/dt = r α (These relations are from the chapter of circular motion)
Updated 10 Jan 2016, 7 May 2008
Saturday, January 9, 2016
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Updated 9 Jan 2016, 7 May 2008
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