A spinning figure skater is an excellent example of angular momentum conservation. The skater starts spinning with her arms outstretched, and has a a rotational inertia of I_i and an initial angular velocity of ω_i. 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:

L_i = L_f

I_i ω_i = I_f ω_f

In this process, what happens to the skater's kinetic energy?

1. the kinetic energy decreases
2. the kinetic energy stays the same
3. the kinetic energy increases

In this case the kinetic energy actually increases.

K_i = ½ I_i ω_i² = ½ (I_i ω_i) ω_i

K_f = ½ I_f ω_f² = ½ (I_f ω_f) ω_f

The figure skater does work on her arms and hands as she brings them closer to her body - that's where the extra energy comes from.