# Ice skater increase of energy

This may be a very basic question but I am not seeing how it works. Consider the standard example of an ice skate rotating about his/her center of mass and pulling in his/her arms. The torque is zero so we have conservation of angular momentum. This implies that $\omega$ increases to keep $I\omega$ constant, but then $K_{rot}=\frac{1}{2}I\omega^2$ doesn't stay constant, it increases. This implies that there is work done, but what force is doing this work?

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The energy comes from the ice-skater's muscles; they have to work to pull their arms in.

There is no external work done on the skater - the energy is converted from the chemical potential energy stored in the skater's body to kinetic energy.

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This is best seen if the system is defined to be just the skater. Then we see a change in internal energy. –  user11266 Dec 3 '12 at 2:02
@JoeH "Best" is subjective, but I agree that this is a valuable point of view. I wrote about it extensively on this question: physics.stackexchange.com/a/3675/74 –  Mark Eichenlaub Dec 3 '12 at 3:13