Question

A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms. Which of the following statements are true about the skater during this process? (There could be more than one correct choice.)
Her kinetic energy remains constant.
Her moment of inertia remains constant.
Her angular momentum remains constant.
She is subject to a constant non-zero torque.

Answer 1

Answer:

Correct -> Her angular momentum remains constant.

Explanation:

If the skater pulls her arms, her radius changes, so her moment of inertia changes.

By definition, moment of inertia is the resistance to rotation. So, if her moment of inertia decreases, her angular velocity increases, because if there is no external torque (in this question there is none), angular momentum is conserved.

$L = I\omega$

$K = \frac{1}{2}I\omega^2$

If the moment of inertia decreases by half, the angular velocity doubles. In that case kinetic energy also increases, because the square of the angular velocity affects the kinetic energy more than the decrease of the moment of inertia.