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Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
ISBN: 9781305116399

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BuyFindarrow_forward

Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
ISBN: 9781305116399
Textbook Problem

An ice skater starts a spin with her arms stretched out to the sides. She balances on the lip of one skate to mi 11 without friction. She then pulls her arms in so that her moment of inertia decreases by a factor of 2. In the process of her doing so. what happens to her kinetic energy? (a) It increases by a factor of 4. (b) It increases by a factor of 2. (c) It remains constant, (d) It decreases In a factor of 2. (e) It decreases by a factor of 4.

To determine

The kinetic energy with regard to the given situation.

Explanation

When ice skater balances on the tip of one skate to turn without friction then she pulls her arms so that her moment of inertia decreases by a factor of 2. Thus, final moment of inertia of an ice skater would be half of the initial moment of inertia.

The final moment of inertia is,

If=Ii2

Here,

If is final moment of inertia.

Ii is initial moment of inertia.

Write the expression for initial angular momentum is,

Li=Iiωi

Here,

Li is initial angular momentum.

ωi is initial angular velocity.

Write the expression for final angular momentum is,

Lf=Ifωf

Here,

Lf is final angular momentum.

ωf is final angular velocity.

According to law of conservation of momentum initial angular momentum is equal to final angular momentum.

Li=Lf (1)

Substitute Iiωi for Li and Ifωf for Lf in equation (1).

Iiωi=Ifωf (2)

Substitute ω for ωi and Ii2 for If in equation (2) to calculate ωf .

Iiω=Ii2ωfωf=2ω

Write the expression for initial rotational kinetic energy is,

KErotationali=12Iiωi2 (3)

Here,

KErotationali is initial rotational kinetic energy

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