Suppose a man sits on a freely rotatable light chair holding 2 dumbbells to his chest, he then extends his hands while maintaining the height of each dumbbells (so that gravitational of the system is constant). His angular speed is reduced while his moment of inertia increases.
Where did the lost energy go?
(I do know numerical proof that energy do loss, but I wanted to know how and where did the energy go, any proofs by any formulas of physics is appreciated)
Thank you in advance