A spinning figure skater is an excellent example of angular momentum conservation. The skater starts spinning with her arms outstretched, and has a rotational inertia of Ii and an initial angular velocity of wi. When she moves her arms close to her body, she spins faster. Her moment of inertia decreases, so her angular velocity must increase to keep the angular momentum constant.
Conserving angular momentum:
Li = Lf
Ii wi = If wf
In this process, what happens to the skater's kinetic energy?