Physics I / Angular Momentum and Conservation

Practice question · Multiple choice

A spinning figure skater pulls her arms in and speeds up (angular momentum is conserved). What happens to her rotational kinetic energy?

Hints

Write $KE = \frac{L^{2}}{2I}$ . With $L$ fixed, what does shrinking $I$ do?
Pulling her arms in means dragging mass inward against the centrifugal tendency, that takes muscular work, and work changes energy.

Show the answer

C. It increases, her muscles do work pulling her arms inward

Why

With $L = I\omega$ constant, $KE = L^{2}/2I$ rises as $I$ falls. Conservation of one quantity does not imply conservation of another: the extra energy is supplied by the skater’s muscles.

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