The falling pencil: a "Divertimento" in four movements

TL;DR

This paper investigates the physics of a pencil falling on a rough surface, providing exact results on sliding angles and friction coefficients, serving as a pedagogic case study with simplified models.

Contribution

It offers new analytical insights into the dynamics of a falling pencil on a rough surface, including critical static friction and sliding angles, through simplified movement models.

Findings

Exact results on sliding angles

Critical static friction coefficient identified

Simplified models elucidate pencil dynamics

Abstract

The dynamics of a simple pencil with a tip laid on a rough table and set free to fall under the action of gravity is scrutinized as a pedagogic case study. The full inquiry is anticipated by a review of three other simplified movements foreshadowing its main features. A few exact and general results about the sliding angles and the critical static coefficient of friction are established.