A skater spinning with arms outstretched pulls the arms inwards. The result is that

Explanation

With no external torque the angular momentum, the product of moment of inertia and angular speed, stays constant, so reducing the moment of inertia must raise the angular speed. The skater's rotational kinetic energy actually increases, and the extra energy comes from the muscular work done pulling the arms in against the outward tendency. The same principle explains the spin of a collapsing star.