Work and energy in rotating systems

TL;DR

This paper extends the work and energy theorem to rotating systems, clarifying the role of fictitious forces and analyzing the effects of system acceleration and rotation.

Contribution

It demonstrates that the work and energy theorem applies in rotating systems when fictitious forces are properly included, clarifying misconceptions about work contributions of these forces.

Findings

Fictitious forces' work must be included for energy analysis.

Coriolis force does not contribute to work.

Real forces can do work differently in rotating frames.

Abstract

Literature analyzes the way in which Newton's second law can be used when non-inertial rotating systems are used. However, the treatment of the work and energy theorem in rotating systems is not considered in textbooks. In this paper, we show that the work and energy theorem can still be applied to a closed system of particles in a rotating system, as long as the work of fictitious forces is properly included in the formalism. The coriolis force does not contribute to the work coming from fictitious forces. It worths remarking that real forces that do not do work in an inertial reference frame can do work in the rotating reference frame and viceversa. The combined effects of acceleration of the origin and rotation of the non-inertial system are also studied.