Torques without Rotation: the Right-Angle Lever

TL;DR

This paper clarifies the right-angle lever paradox by analyzing how an extended body's torque can appear nonzero in different inertial frames without causing rotation, resolving longstanding controversy.

Contribution

It provides a clear explanation of the paradox through a proper treatment of angular momentum and simultaneity in special relativity.

Findings

Nonzero torque in one frame does not imply rotation in another

Proper angular momentum treatment resolves the paradox

Clarifies the role of simultaneity in relativistic torque analysis

Abstract

An extended body subject to external forces which exert zero net force and zero total torque in the rest frame, may experience a nonzero torque in another inertial frame, and nonetheless does not rotate. Long known as the Trouton-Noble or right-angle lever paradox, there has been extensive discussion and indeed controversy, but a clear understanding comes from a suitable treatment of angular momentum and simultaneity.