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Physics For Scientists & Engineers
Found in: Page 354
Physics For Scientists & Engineers

Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

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Short Answer

Two ponies of equal mass are initially at diametrically opposite points on the rim of a large horizontal turn table that is turning freely on a frictionless, vertical axle through its centre. The ponies simultaneously start walking toward each other across the turntable.

(i) As they walk, what happens to the angular speed of the turn table?

(a) It increases.

(b) It decreases.

(c) It stays constant.

Consider the ponies’ turntable system in this process and answer yes or no for the following questions.

(ii) Is the mechanical energy of the system conserved?

(iii) Is the momentum of the system conserved?

(iv) Is the angular momentum of the system conserved?

(i) Hence, option (a) “It increases” is the right answer.

(ii) No, the mechanical energy of the system does not get conserved

(iii) Yes, the turntable has a fixed centre of mass.

(iv) Yes, the angular momentum of the system gets conserved.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Angular momentum

Angular momentum is the rotational analogy of the linear momentum and it is an important quantity in physics.

Step 2: Angular speed of the turntable

(i)

The ponies decrease the moment of inertia of the system with respect to the axis by walking towards the centre.

As there is no eternal torque to the system, the angular gets conserved.

When angular momentum gets conserved, gets decreased and the angular velocity will increase.

Hence, option (a) is the right answer.

Step 3: Mechanical energy of the system

(ii)

No, the mechanical energy of the system does not get conserved as the ponies are using the muscles to convert stored chemical energy into kinetic energy.

Step 4: Momentum of the system

(iii)

Yes, the turntable has a fixed centre of mass.

As it has fixed mass, it would never have any linear momentum.

Their linear momentum cancel out as the velocities of the ponies are always equal and opposite.

Hence, the system has zero total linear momentum always.

Step 5: Angular momentum of the system

(iv)

Yes, the angular momentum of the system gets conserved.

As the axle is frictionless, there is no external torque to the system.

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