Failure of intuition in elementary rigid body dynamics

TL;DR

This paper demonstrates counterintuitive results in elementary rigid body dynamics, showing that maximum angular velocity is not always achieved at the extremity of a rod after a perpendicular collision, challenging common intuition.

Contribution

It provides an accessible analysis of collision outcomes in rigid body dynamics, highlighting unexpected behaviors and fostering better understanding of conservation laws.

Findings

Maximum angular velocity does not always occur at the rod's extremity.

Counterintuitive collision outcomes are explained through conservation laws.

Educational approach suitable for first-year physics or engineering students.

Abstract

Suppose a projectile collides perpendicularly with a stationary rigid rod on a smooth horizontal table. We show that, contrary to what one naturally expects, it is not always the case that the rod acquires maximum angular velocity when struck at an extremity. The treatment is intended for first year university students of Physics or Engineering, and could form the basis of a tutorial discussion of conservation laws in rigid body dynamics.