Speeding to a stop: the finite-time singularity of a spinning disk

The final stages of a coin spinning on a flat surface have recently been proposed [H.K. Moffatt, Nature (London) 404, 833 (2000)] as an example of a finite-time singularity, wherein the precession rate of the symmetry axis of the coin diverges as it comes to a stop. We report measurements by high-speed video imaging of the rolling motion of disks and rings on a variety of surfaces. We find that the precession rate, Omega, diverges as a power law in time: Omega(t) proportional, variant (t-t(o))(-1/n), where t(o) is the instant the motion ceases. The exponent n varies between 2.7 and 3.2 under different experimental conditions. The value of n, as well as the systematic dependence of precession rate on coefficients of friction, establishes that the primary mechanism of energy dissipation is rolling friction rather than air drag, as previously suggested.