Rolling/Slipping Motion of Euler's Disk

TL;DR

This experimental study investigates the dynamics of a spinning disk on a table, analyzing how inclination, angular velocity, and precession evolve, with a focus on energy dissipation due to slipping and the influence of mass and friction.

Contribution

The paper provides detailed experimental measurements of Euler's disk motion, including divergence of precession rate and power-law decay of inclination and angular velocity, highlighting slipping as the main energy loss.

Findings

Inclination angle and angular velocity decrease following a power law.

Precession rate diverges as the disk comes to rest.

Slipping is identified as the primary energy dissipation mechanism.

Abstract

We present an experimental study of the motion of a circular disk spun onto a table. With the help of a high speed video system, the temporal evolutions of (i) the inclination angle $\alpha$, (ii) the angular velocity $\omega$ and (iii) the precession rate $\Omega$ are studied. The influence of the mass of the disk and the friction between the disk and the supporting surface are considered. %The motions of disks with different masses and over different surfaces are studied. The inclination angle $\alpha$ and the angular velocity are observed to decrease according to a power law. We also show that the precession rate $\Omega$ diverges as the disk stops. Exponents are measured very near the collapse as well as on long range times. Collapsing times have been also measured. The results are compared with previous theoretical and experimental works. The major source of energy dissipation is found to be the slipping of the disk on the plane.