Everyone knows how an ice-skater can increase her speed by pulling her arms in. Doing so the moment of inertia decreases, and thus her angular velocity MUST increase due to the conservation of angular momentum. But work is also done in the process. My question is: Say the ice skater pulls in her arms and spins faster. If she then pulls the out again: Will she spin slower again? I think so yes, because angular momentum is conserved. I am however unable to see how she would do negative work on herself (which she MUST to lose the extra kinetic energy gained from pulling in her arms).