Moments to remember—The conditions for equating torque and rate of change of angular momentum

Abstract

It is a well-known but frequently forgotten fact that the net external torque on a system of particles is equal to the rate of change of angular momentum only if the point about which moments are taken satisfies certain stringent conditions: The point must have zero acceleration, or it must be the center of mass, or its instantaneous acceleration must be directly toward or away from the center of mass. A simple problem in rigid-body mechanics has been solved by Crawford, taking moments about the center of mass. It is shown here that the problem may also be solved using a point that does not satisfy any of these conditions, in which case a more general equation is required. An external fixed point may also be used for calculating moments. When carefully executed, all correct approaches yield the same solution.