Now we can calculate the kinetic energy of a rolling wheel. One way is to use the fact that the kinetic energy is the sum of the center of mass kinetic energy and the rotational energy:
but from rolling motion, , so
So this says that the kinetic energy is increased by the moment of inertia of the wheel.
Another way of getting the kinetic energy is to use the fact that the wheel appears to be instantaneously pivoted about the bottom. So
But is the moment of inertia of the wheel when rotated about an axis passing through the rim. By the parallel axis theorem we can relate this to the moment of inertia about the center of mass:
Giving the same result as above.