## 09 August 2012

### Euler's Disk spins for a long time

The toy consists of a heavy, thick chrome plated steel disk, a slightly concave, mirrored base, and holographic magnetic stickers which can be placed on the disk. The disk, when spun on the mirror, exhibits a spinning/rolling motion (or spolling, a blend of "spin" and "roll"), slowly moving through different rates and types of motion before coming to rest – for example, the precession rate of the axis of symmetry accelerates as the disk spins down. Euler’s Disk has an optimized aspect ratio and a precision polished, slightly rounded edge to maximize the spinning/rolling time. A coin spun on a table, as with any disk spun on a relatively flat surface, exhibits essentially the same type of motion, but is normally more constrained in the length of time before stopping. The Disk provides a more effective demonstration of the phenomenon than more commonly found items.

...the total spinning time is
$t_0=\left(\frac{\alpha_0^3}{2\pi}\right)\frac{M}{\mu a}$
where $\alpha_0$ is the initial inclination of the disk.
M is the mass of the disk, and mu is the dynamic viscosity of air.  More at Wikipedia.