Center of Mass

Not every particle of a moving rigid body follows the same path. Depending on exactly how the body moves — purely sliding, purely spinning, or some mixture of both — different particles of the body can trace out quite different trajectories. A simple, everyday example makes this vivid: as a wheel rolls along the ground, the exact center point of the wheel traces a perfectly straight horizontal line, while a point marked on the rim traces a much more complicated looping curve (a cycloid).

Given this variety of individual particle paths, it is extremely useful to identify one single point belonging to the body whose motion is always simple, and which can stand in for the motion of the whole body. That point is the center of mass. Formally studying its properties, and how to locate it for different kinds of bodies, is the task of the rest of this section, and it underlies everything that follows in the unit — torque and angular momentum are both, at their core, statements about …