Showing posts with label Physics-Mathematics. Show all posts
Showing posts with label Physics-Mathematics. Show all posts
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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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
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XI - 2.4 Multiplication of a vector by a number - Video Lectures
Dot Product, Cross Product, and Multiplying Vectors by Scalars
AK LECTURES
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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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Wednesday, May 20, 2015
Concept Review - Chapter 2 Physics and Mathematics
Scalars
Vectors
Equality of vectors
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.
Subtraction of vectors
Multiplication of vector by a number
2.6 Resolution of vectors
2.7 Dot product or scalar of two vectors
2.8 Cross product or vector product of two vectors
Zero vector
2.9 Differential Calculus
Concepts form Calculus
dy/dx as rate measure
2.10 Maxima and minima
2.11 Integral Calculus
2.12 Significant digits
2.14 Errors in measurement
In recording measurements in experiments, several errors can occur. The equipment can be set in a faulty manner, and experimenter can make errors. These errors can be corrected by supervisors and trainers. But still some errors are committed due to random noncontrollable causes.
As random errors are sometime positive and sometimes negative, average is considered as true value. But sigma or standard deviation of the measurements can be calculated and 1.96 sigma limits and 3 sigma limits can be determined to specify confidence limits for true value. But at least 8 measurements are to be taken to get a good statistical estimate for average and standard deviation.
Update 20 May 2015
Earlier update 7 May 2008
Vectors
Equality of vectors
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.
Subtraction of vectors
Multiplication of vector by a number
2.6 Resolution of vectors
2.7 Dot product or scalar of two vectors
2.8 Cross product or vector product of two vectors
Zero vector
2.9 Differential Calculus
Concepts form Calculus
dy/dx as rate measure
2.10 Maxima and minima
2.11 Integral Calculus
2.12 Significant digits
2.14 Errors in measurement
In recording measurements in experiments, several errors can occur. The equipment can be set in a faulty manner, and experimenter can make errors. These errors can be corrected by supervisors and trainers. But still some errors are committed due to random noncontrollable causes.
As random errors are sometime positive and sometimes negative, average is considered as true value. But sigma or standard deviation of the measurements can be calculated and 1.96 sigma limits and 3 sigma limits can be determined to specify confidence limits for true value. But at least 8 measurements are to be taken to get a good statistical estimate for average and standard deviation.
Update 20 May 2015
Earlier update 7 May 2008
Friday, November 7, 2008
2. Physics and Mathematics - Revision Facilitator
2. Physics and mathematics
Sections
2.1 Vectors and scalars
2.2 Equality of vectors
2.3 Addition of vectors
2.4 Multiplication of a vector by a number
2.5 Subtraction of vectors
2.6 Resolution of vectors
2.7 DCT product or scalar product of two vectors
2.8 Cross product or vector product of two vectors
2.9 Differential calculus: dy/dx as rate measure
2.10 Maxima and Minima
2.11 Integral calculus
2.12 Significant digits
2.13 Significant digits in calculations
2.14 Errors in measurements
Sections
2.1 Vectors and scalars
2.2 Equality of vectors
2.3 Addition of vectors
2.4 Multiplication of a vector by a number
2.5 Subtraction of vectors
2.6 Resolution of vectors
2.7 DCT product or scalar product of two vectors
2.8 Cross product or vector product of two vectors
2.9 Differential calculus: dy/dx as rate measure
2.10 Maxima and Minima
2.11 Integral calculus
2.12 Significant digits
2.13 Significant digits in calculations
2.14 Errors in measurements
Tuesday, October 23, 2007
Study guide H C Verma JEE Physics Ch. 2 PHYSICS AND MATHEMATICS
HCV Chapter Sections
2.1 Vectors and scalars
2.2 Equality of vectors
2.3 Addition of vectors
2.4 Multiplication of a vector by a number
2.5 Subtraction of vectors
2.6 Resolution of vectors
2.7 DCT product or scalar product of two vectors
2.8 Cross product or vector product of two vectors
2.9 Differential calculus: dy/dx as rate measure
2.10 Maxima and Minima
2.11 Integral calculus
2.12 Significant digits
2.13 Significant digits in calculations
2.14 Errors in measurements
Study Plan
Day 1
2.1 Vectors and scalars
2.2 Equality of vectors
2.3 Addition of vectors
Example 2.1
2.4 Multiplication of a vector by a number
2.5 Subtraction of vectors
Example 2.2
Day 2
2.6 Resolution of vectors
Example 2.3
2.7 DOT product or scalar product of two vectors
Example 2.4
Worked out examples 1 to 4
Day 3
2.8 Cross product or vector product of two vectors
Example 2.5
Worked out example 5 to 10.
Day 4
2.9 Differential calculus: dy/dx as rate measure
Ex. 2.6, 2.7
2.10 Maxima and Minima
Ex.2.8
Day 5
2.11 Integral calculus
Ex. 2.9
Worked out examples 11 to 13
Day 6
2.12 Significant digits
2.13 Significant digits in calculations
Ex. 2.10 to 2.12
Worked out examples 14 to 17
Day 7
2.14 Errors in measurements
Ex. 2.13
Worked example 18
Exercise Problems: 1 to 4
Day 8
Objective I
Exercise Problems 5 to 8
Day 9
Objective II
Exercise Problems 9 to 12
Day 10
Exercise Problems 13 to 20
Day 11 Your are entering into revision 10 days
Exercise problems 21,22
Day 12
Exercise problems 23,24
Day 13
Exercise problems 25,26
Day 14
Exercise problems 27,28
Day 15
Exercise problems 29,30
Day 16
Exercise problems 31,32
Day 17
Exercise problems 33,34
Day 18
Exercise problems 35
Day 19
Attempt Questions for short answer 1 to 7
Day 20
Exercise problems
Attempt Questions for short answer 8 to 14
Web sites
lecture notes - Vectors
http://plasma4.sr.unh.edu/ng/phys407/phys407-6-16-05.pdf
2.1 Vectors and scalars
2.2 Equality of vectors
2.3 Addition of vectors
2.4 Multiplication of a vector by a number
2.5 Subtraction of vectors
2.6 Resolution of vectors
2.7 DCT product or scalar product of two vectors
2.8 Cross product or vector product of two vectors
2.9 Differential calculus: dy/dx as rate measure
2.10 Maxima and Minima
2.11 Integral calculus
2.12 Significant digits
2.13 Significant digits in calculations
2.14 Errors in measurements
Study Plan
Day 1
2.1 Vectors and scalars
2.2 Equality of vectors
2.3 Addition of vectors
Example 2.1
2.4 Multiplication of a vector by a number
2.5 Subtraction of vectors
Example 2.2
Day 2
2.6 Resolution of vectors
Example 2.3
2.7 DOT product or scalar product of two vectors
Example 2.4
Worked out examples 1 to 4
Day 3
2.8 Cross product or vector product of two vectors
Example 2.5
Worked out example 5 to 10.
Day 4
2.9 Differential calculus: dy/dx as rate measure
Ex. 2.6, 2.7
2.10 Maxima and Minima
Ex.2.8
Day 5
2.11 Integral calculus
Ex. 2.9
Worked out examples 11 to 13
Day 6
2.12 Significant digits
2.13 Significant digits in calculations
Ex. 2.10 to 2.12
Worked out examples 14 to 17
Day 7
2.14 Errors in measurements
Ex. 2.13
Worked example 18
Exercise Problems: 1 to 4
Day 8
Objective I
Exercise Problems 5 to 8
Day 9
Objective II
Exercise Problems 9 to 12
Day 10
Exercise Problems 13 to 20
Day 11 Your are entering into revision 10 days
Exercise problems 21,22
Day 12
Exercise problems 23,24
Day 13
Exercise problems 25,26
Day 14
Exercise problems 27,28
Day 15
Exercise problems 29,30
Day 16
Exercise problems 31,32
Day 17
Exercise problems 33,34
Day 18
Exercise problems 35
Day 19
Attempt Questions for short answer 1 to 7
Day 20
Exercise problems
Attempt Questions for short answer 8 to 14
Web sites
lecture notes - Vectors
http://plasma4.sr.unh.edu/ng/phys407/phys407-6-16-05.pdf
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