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
a) Moment of inertia
b) Angular momentum

The moment of inertia can be increased or angular velocity can be decreased by stretching hands outside. Also, smaller the moment of inertia means less resistance to rotation (some rapid corrections have to made to achieve rotational equilibrium), hence change in moment of inertia leads the change in rotational kinetic energy. While angular momentum remains conserved.