Work and energy in inertial and noninertial reference frames

Abstract

It is usual in introductory courses of mechanics to develop the work and energy formalism from Newton’s laws. It has been shown how forces transform under a change of reference frame. No analogous study is usually done for the way in which work and energy transform under a change of reference frames. We analyze the behavior of energy and work under such transformations and explicitly show the expected invariance of the formalism under Galilean transformations for one particle and a system of particles. The case of noninertial systems is also analyzed and the fictitious work is characterized. In particular, we showed that the total fictitious work in the center of mass system vanishes even if the center of mass defines a noninertial frame. Some subtleties that arise from the formalism are illustrated by examples.