The falling pencil: a "Divertimento" in four movements
Nicola Cufaro Petroni

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.
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Taxonomy
TopicsExperimental and Theoretical Physics Studies · Mathematics and Applications · Sports Dynamics and Biomechanics
