Everyone has seen a figure skater spin, where the skater draws her arms and a leg in and speeds up tremendously. This is the result of conservation of angular momentum. As the skater reduces her rotational inertia by pulling her arms and leg in, her rotation speed must increase to maintain constant angular momentum. Angular momentum conservation plays a VERY important role in all figure skating routines. See for yourself:
Angular momentum applies to a body rotating around a fixed object. The amount of angular momentum, say, a spinning skater depends on both the speed of rotation, and the weight and distribution of mass around the center. So once her arms and leg came into her body, the mass is much closer to her center of gravity, spinning her much faster then if they were spinning with the mass of their arms and leg away from the body. (Dependent upon radius).