Spinning Ice Skater
A spinning ice skater is a common example of conservation of angular momentum. When the skater starts spinning with hands outstretched, the angular velocity is low, but the spinning becomes very fast as the hands are pulled in. What happens is that as the moment of inertia decreases, the angular velocity increases, so that the angular momentum is conserved.
The moment of inertia provides a measure of the difficulty of changing the rotational motion of a body.
The conservation of angular momentum establishes that
where and are the initial and final moments of inertia and and are the corresponding angular velocities.
The skater's arms are treated as a dumbbell, approximated as the moment of inertia of a mass at the end of a rod:
where r is the distance from the axis of rotation to the center of mass of the ends of the dumbbell; then
See P. J. Nolan, Fundamentals of College Physics, 2nd ed., Dubuque, IA: Wm. C. Brown, 1995.