Euler's Disk - Physics

Physics

A spinning/rolling disk ultimately comes to rest; and it does so quite abruptly, the final stage of motion being accompanied by a whirring sound of rapidly increasing frequency. As the disk rolls, the point P of rolling contact describes a circle that oscillates with a constant angular velocity . If the motion is non-dissipative, is constant and the motion persists forever, contrary to observation (since is not constant in real life situations). In fact, precession rate of the axis of symmetry approaches a finite-time singularity modeled by a power law with exponent approximately −1/3 (depending on specific conditions).

There are two conspicuous dissipative effects: rolling friction when the coin slips along the surface, and air drag from the resistance of air. Experiments show that rolling friction is mainly responsible for the dissipation and behavior – experiments in a vacuum show that the absence of air affects behavior only slightly, while the behavior (precession rate) depends systematically on coefficient of friction. In the limit of small angle (i.e., immediately before the coin stops spinning), air drag (specifically, viscous dissipation) is the dominant factor, but prior to this rolling friction is the dominant effect.