Center of Mass, The Action of the Force

The Action of the Force

Assume a force field is applied to an object, proportional to the density at every point, and everywhere parallel. This occurs when a small object is attracted to a distant object by gravity. Fix a coordinate system with the origin at the center of mass. Any change in rotation occurs because of a net torque about 0. Yet computing torque is equivalent to computing the center of mass. The net torque is 0 and there is no change in rotation. The object acts as though all its mass were concentrated at a point, namely its center of mass. If the object is supported at that point, it remains motionless, as described in the previous section.