The Rolling Motion of a Disk on a Horizontal Plane

TL;DR

This paper investigates the dynamics of a rolling disk on a horizontal plane, emphasizing energy dissipation mechanisms and experimental validation of the relationship between angular velocity and power loss.

Contribution

It provides a detailed review of the equations of motion and experimental evidence showing dissipation proportional to the square of angular velocity.

Findings

Dissipative power loss is proportional to Omega^2.

Experimental results confirm theoretical predictions.

Analysis enhances understanding of energy loss in rolling motion.

Abstract

Recent interest in the old problem of the motion of a coin spinning on a tabletop has focused on mechanisms of dissipation of energy as the angle alpha of the coin to the table decreases, while the angular velocity Omega of the point of contact increases. Following a review of the general equations of motion of a thin disk rolling without slipping on a horizontal surface, we present results of simple experiment on the time dependence of the motion that indicate the dominant dissipative power loss to be proportional to the Omega^2 up to and including the last observable cycle.