Kinetic energy of rolling motion from the contact point

We make use of the fact that the instantaneous velocity field of a body in a planar, pure rolling motion is identical to that of a rigid rotation about the contact point. As a consequence, the total kinetic energy can be written with respect to that point. For bodies with circular symmetry, the usual Koenig decomposition into translational and rotational contributions is immediately recovered, and remains valid for any radially symmetric mass distribution.