Euler's disk

Example

Euler's disk is a heavy metal disc spun on its edge on a flat, smooth mirror. It rolls on its rim around a circle, with the disc tilted at an angle $\alpha$ to the table. As it loses energy, $\alpha$ decreases, and the point of contact runs around faster and faster. The motion stops abruptly after a finite time, with a whirring sound of rising pitch.

The motion before the end is close to rolling without slipping: the material point of the disc at the contact is nearly at rest. For such a rolling disc, the rate of precession of the contact point around the vertical grows without bound as $\alpha$ tends to $0$. So the energy loss, though small, drives the disc towards a singular end of the motion in finite time.