The kinetic energy of an object moving from one point to another is found by using the equation 1/2mv2 . To determine the kinetic energy of an object rotating about an axis, the object is broken down into small-mass objects that are treated as point masses. The sum of the contributions of each small-mass object provides the kinetic energy of the rotating object. As this is done, a new quantity called the moment of inertia is introduced, which acts similar to mass.

First, consider a point mass m that is orbiting in a circular path of radius r around some fixed point. Its kinetic energy is given by 1/2mv2 , where v is the magnitude of its velocity vector. Because the point mass repeats its motion each time it makes one complete orbit, its energy can be expressed in terms of an...