Conservation of angular momentum - change of inertia

[Asgrrr]

Recently I was searching the internet and books for the connection between conservation of angular momentum and conservation of rotational energy and found nothing. Let's say an ice skater rotates and draws the arms in - the rotation speeds up. The rotational energy must increase because the linear velocity of every particle is increased.

I think I managed to prove that the work required to draw in the arms is equal to the increase in rotational energy. Could this be correct?

 

[Vanadium 50]

Sure - work has to come from somewhere. In this case it's the skater's muscles.