## Tuesday, October 23, 2007

### Study guide H C Verma JEE Physics Ch. 7 CIRCULAR MOTION

JEE Syllabus

Uniform Circular motion;

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Sections of the chapter

7.1 Angular variables
7.2 Unit vectors along the radius and the tangent
7.3 Acceleration in circular motion
7.4 Dynamics of circular motion
7.5 Circular turnings and banking of roads
7.6 Centrifugal force
7.7 Effect of earth's rotation on apprarent weight

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Study Plan

Day 1

7.1 Angular variables
Ex. 7.1, 7.2
7.2 Unit vectors along the radius and the tangent

Day 2
7.3 Acceleration in circular motion
Ex. 7.3,7.4
7.4 Dynamics of circular motion
Ex. 7.5
W.O.E. 3,4,5,7

Day 3
7.5 Circular turnings and banking of roads
Ex. 7.6
W.O.E. 1 and 2

Day 4

7.6 Centrifugal force
w.O.E. 7, 8,9,10,

Day 5

7.7 Effect of earth's rotation on apprarent weight
Ex. 7.7
w.O.E. 11 to 13

Day 6
Chapter 7
Objective I

Day 7
Chapter 7
Objective II

Day 8
Chapter 7
Exercises 1 to 5

Day 9
Chapter 7
Exercises 6 to 10

Day 10
Chapter 7
Exercises 11 to 15

Revision period
Chapter 7 Revision
Day 11
Chapter 7 Revision
Exercises: 16 to 18

Day 12
Chapter 7 Revision
Exercises: 19 to 21

Day 13
Chapter 7 Revision
Exercises: 22 to 24

Day 14
Chapter 7 Revision
Exercises: 25 to 27

Day 15
Chapter 7 Revision
Exercises: 28 to 30

Day 16
Chapter 7 Revision
Short answer questions: 1 to 10

Day 17
Chapter 7 Revision
Try some past JEE questions

Day 18
Chapter 7 Revision
Try some past JEE questions

Day 19
Chapter 7 Revision
Try some past JEE questions

Day 20
Chapter 7 Revision
Try some past JEE questions

Concepts covered

7.1 Angular variables

Angular position
angular velocity
Angular acceleration

Linear speed
Rate of change of speed
Tangential accelaration

7.2 Unit vectors along the radius and the tangent

Tangential unit vector

7.3 Acceleration in circular motion

Uniform circular motion
Centripetal acceleration

radial component of acceleration
Tangential component of acceleration

7.4 Dynamics of circular motion

Centripetal force

7.5 Circular turnings and banking of roads

When vehicles go through turnings, they travel along a nearly circular arc. That means there is centrepetal accelaration. What forces cause this acceleration? Friction fs can act towards the centre. However this may not be sufficient and the vehicle may skid.

To take care of it, the roads are banked t the turn so that outer part of the road is somewhat lifted up as compared to the inner part. therefore the normal force makes an angle θ wit hte vertical. The horizontal component of the normal force helps in providing the accelaration required.

The θ required for a speed of the vehicle of v is given by

tanθ = v²/rg

7.6 Centrifugal force

What psuedo force is required if the frame of reference rotates at a constant angular velocity ω with respect to an inertial frame?

Cetrifugal force
Coriolis force

Note: It is a common minsconception among the beginners that centrifugal force acts on a particle because the particle goes on a circle. Centrigual force acts (or is assumed to act) becasue we describe the particle from a rotating frame which is noninertial and still use Newton's laws.

7.7 Effect of earth's rotation on apprarent weight

A plumb line stays in a direction which is different from true vertical to earth at that point. The walls of building are built by making them parallel to the plumb line and not to the true vertical.

The weight of a body is mg' and not mg and g' is less than g.
g' = g only at the poles as the poles themselved do not rotate and hence the effect of earth's rotation is not felt there.

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JEE Question 2007 Paper I

Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I respectively about the common axis. Disc A is imparted an initial angular velocity 2w using the entire potential energy of a spring compressed by a distance x-1 . Disc B is imparted an angular velocity by a spring having the same spring constant and compressed by a distance x-2 . Both the discs rotate in the
clockwise direction

1. The ratio x-1 /x-2 is
(A) 2
(B)1/2
(C) SQRT(2)
(D)1/SQRT(2)

2. When disc B is brought in contact with disc A, they acquire a common angular velocity in time t.The average frictional torque on one disc by the other during this period is

3.The loss of kinetic energy during the above process is

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JEE question 2007 Paper II

A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of 3v^2/4g with respect to the initial position. The object is

(A) ring
(B) solid sphere
(C) hollow sphere
(D) Disc

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JEE Question Paper II 2007

Statement - 1

If there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant.

Because

Statement - 2

The linear momentum of an isolated system remains constant.

(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

Right choice; D
S1 is incorrect. without external torque but with external force the centre can move.
S2 is correct.
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JEE 2006

A solid sphere of mass M, radius R and having moment of inertia about an axis passing through the centre of mass as I, is recast into a disc of thickness t, whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains I. Then, radius of the disc will be

(A) 2R/SQRT(15)

(B) R*(SQRT(2/15)
(C) 4R/SQRT(15)
(D) R/4