Euler's Disk finite-time singularity

Partly settled. Some of it is understood, some is still argued about.

A spun coin or disk settling on a table produces a distinctive whirring sound that rises in pitch right up to an abrupt stop, and in 2000 Keith Moffatt proposed in Nature that viscous dissipation in the thin air layer trapped between disk and table was sufficient to explain this finite-time singularity. His explanation was disputed almost immediately by van den Engh, Nelson and Roach, who ran the experiment in a near-vacuum and found the disk still stopped abruptly, implicating rolling and slipping friction rather than air viscosity as the dominant mechanism. Subsequent experimental studies in the 2000s generally supported the friction-dominated picture, though refinements to the precise combination of effects (contact-line friction, air, elastic deformation) have continued, so the problem is better described as substantially clarified but not fully closed on every quantitative detail.

A spinning coin winding down to a stop turns out to hide a genuine mathematical singularity - infinite spin rate in finite time - that sparked a public scientific dispute over whether air or friction is really to blame.

Explanations that circulated

• Moffatt's original claim that viscous dissipation in the thin air layer between disk and table alone explains the abrupt stop was directly contradicted by vacuum experiments (van den Engh, Nelson & Roach, 2000) showing air makes little difference.
• Treating the 'finite-time singularity' as evidence of some exotic physics is misleading - later work (Easwar et al. 2002; Caps et al. 2004, per secondary sources) attributes the abrupt stop mainly to ordinary rolling and slipping (Coulomb) friction at the contact line.

References

• Euler's disk and its finite-time singularity, H. K. Moffatt, Nature, 2000