The famous example of acrobats shrinking their bodies to increase their rotation speed is well known. Where does the energy to increase the speed of their rotation comes from?
1 Answer
The energy comes from the work involved to bring in that mass into a tight ball. If a spinning body is completely relaxed then all the limbs would flail outwards due to centrifugal force. Bringing all those parts radially inward means doing work by resisting that force. This results in reducing the moment of inertia but because of the conservation of angular momentum, there must be a corresponding increase in angular velocity(or rotational spin) in order to keep the angular momentum constant.
So the short answer is that the energy comes from your muscles.