Work-Energy theorem in rotational reference frames

TL;DR

This paper explores how the Work-Energy Theorem applies in rotating reference frames, highlighting differences from inertial frames and providing practical examples to illustrate these effects.

Contribution

It extends the Work-Energy Theorem to rotating frames of reference, an area previously less addressed, and compares it with translational motion cases.

Findings

Differences in energy calculations between rotating and inertial frames

Explicit derivation of the theorem for rotating observers

Practical examples demonstrating the effects of rotation on work and energy

Abstract

In standard textbooks of college physics, the Work Energy Theorem is usually presented for inertial frames of references and it is clear that energy is conserved when there is not net work of interaction forces. But what happens when energy and work are calculated in a non inertial frame of reference? This important issue is frequently avoided. Recently an extension of the theorem was derived for reference systems in traslational motion. Here we address the theorem for two observers in relative rotation showing explicitly the differences for them. We illustrate the problem with practical examples.