A man spinning in free space changes the shape of his body by spreading his arms or curling up. By doing this he can change his

Weight of the man does not produce any moment about its centre of mass. So net external torque acting on the man is zero and hence its angular momentum L remains conserved. In the process of spreading of arms or curling up, The man can change his moment of inertia I. Since L = Iω angular velocity ω changes. Since rotational kinetic energy K=L22I, rotational kinetic energy also changes.