There is similar question on this but I have a specific issue that needs clarification. For the classic example of the ballerina spinning, on extension angular speed decreases, and on retraction angular speed increases because of conservation of angular momentum (no net torque). Lets take the case where angular speed increases due to retraction. Now it also the case rotational KE changes. I am told that work is done by the ballerina in moving her legs/hands inward.
My issue is the last part about the work done by the ballerina. I thought that to change rotational KE we must have torque applied over an angle. Is this wrong? If any kind of nonconservative force acts over a distance/angle then KE, whether it be rotational or translational, will change? I'm confused about how the relationships between torque x angle, force x distance, and, KE rotational and translational.