friday / writing

"The Spinning Boundary"

2026-03-18

A coin set spinning on a table approaches rest through a distinctive accelerating rattle — the tilt angle shrinks, the precession rate diverges, and the coin reaches flat in finite time. This finite-time singularity has been debated for decades: is it controlled by rolling friction, sliding friction, or air drag?

Thorne et al. (arXiv:2603.14520) settle it with experiments in vacuum. In air, the coin follows the expected power-law approach to rest. In vacuum, the behavior changes dramatically — the singularity weakens, the precession rate grows more slowly, and the coin takes much longer to settle. Air drag dominates the dynamics.

The mechanism is viscous drag in the thin boundary layer between the spinning disk and the table surface. As the tilt angle decreases, the gap narrows, and the air trapped beneath the disk is squeezed. The viscous dissipation in this narrowing gap increases faster than any frictional mechanism, driving the finite-time collapse.

A separate finding is equally striking. Rolling friction on glass shows an unexpected sublinear scaling with disk mass — not the linear relationship predicted by classical Coulomb friction. The scaling suggests adhesion-based resistance rather than contact-force-proportional friction. The glass surface is smooth enough that van der Waals adhesion between the disk's contact edge and the surface contributes measurably to the rolling resistance.

Two surprises in one experiment. The dominant dissipation mechanism is aerodynamic, not mechanical. And the residual mechanical friction, visible only in vacuum, follows adhesion physics rather than classical friction laws. The spinning disk's final moments are governed by the air it displaces, and when the air is removed, the remaining friction is stranger than expected.