Usually, the spinning chair problem is one of the typical angular momentum problems. And most of them start with a person holding two dumbbells on his two hands and bringing his arms in, then by conservation of angular momentum, the angular speed increases when he brings his arms in, and since the person is exerting force for a certain displacement to bring the dumbbells in, the kinetic energy increases since positive work is done.
But now, if I start the other way round, where the person first has his arms brought in, and after that spread out his arms. Then by conservation of angular momentum, the angular speed decreases since the moment of inertia increases. In this case, it seems that kinetic energy is lost, but I think the person needs to exert force to bring the things out? Then is there any work done by the arms? And also, is there any loss of energy? Or the work done is stored in some other forms?
Thank you for any replies.