An ice skater spins with her arms extended and then pulls...

An ice skater spins with her arms extended and then pulls her arms in and spins faster. Which statement is correct? a) Her kinetic energy of rotation does not change because, by conservation of angular momentum, the fraction by which her angular velocity increases is the same as the fraction by which her rotational inertia decreases. b) Her kinetic energy of rotation increases because of the work she does to pull her arms in. c) Her kinetic energy of rotation decreases because of the decrease in her rotational inertia; she loses energy because she gradually gets tired.

An ice skater spins with her arms extended and then pulls her arms in and spins faster. Which statement is correct?
a) Her kinetic energy of rotation does not change because, by conservation of angular momentum, the fraction by which her angular velocity increases is the same as the fraction by which her rotational inertia decreases.
b) Her kinetic energy of rotation increases because of the work she does to pull her arms in.
c) Her kinetic energy of rotation decreases because of the decrease in her rotational inertia; she loses energy because she gradually gets tired.

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Key Concepts

Rotational Kinetic Energy

Rotational kinetic energy is given by the formula K = (1/2)I?². Even though angular momentum is conserved, a decrease in the moment of inertia leads to an increased angular velocity which causes the rotational kinetic energy to increase, since kinetic energy depends on the square of angular velocity.

Conservation of Angular Momentum

In a closed system with no external torques, angular momentum remains constant. For a spinning skater, this means that if the skater pulls in her arms (reducing her moment of inertia), her angular velocity must increase proportionally to conserve angular momentum.

Moment of Inertia

Moment of inertia is a measure of how mass is distributed relative to an axis of rotation. It plays a crucial role in rotational dynamics; a decrease in the moment of inertia, such as when a skater pulls in her arms, causes an increase in angular velocity if angular momentum is conserved.

Work and Energy in Rotational Systems

When the skater pulls her arms in, she is not only relying on conservation laws, but also doing work on her body. The act of pulling the arms inward does work against centrifugal forces, which adds energy to the system, leading to an increase in rotational kinetic energy.

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