Work and energy in inertial and non inertial reference frames

TL;DR

This paper investigates how work and energy transform between inertial and non-inertial reference frames, confirming invariance under Galilean transformations and analyzing fictitious work effects with illustrative examples.

Contribution

It provides a detailed analysis of work and energy transformations under reference frame changes, including non-inertial systems, which is less explored in existing literature.

Findings

Work and energy are invariant under Galilean transformations.

Total fictitious work in the center of mass frame vanishes.

Examples illustrate subtleties in energy transformation formalism.

Abstract

It is usual in introductory courses of mechanics to develop the work and energy formalism from Newton's laws. On the other hand, literature analyzes the way in which forces transform under a change of reference frame. Notwithstanding, no analogous study is done for the way in which work and energy transform under those changes of reference frames. We analyze the behavior of energy and work under such transformations and show explicitly the expected invariance of the formalism under Galilean transformations for one particle and a system of particles. The case of non inertial systems is also analyzed and the fictitious works are characterized. In particular, we show that the total fictitious work in the center of mass system vanishes even if the center of mass defines a non inertial frame. Finally, some subtleties that arise from the formalism are illustrated by examples.