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arXiv · 2603.14520

Air Drag Controls the Finite-Time Singularity of Euler's Disk

Benjamin G. Thorne·Ahmad Zareei·Kausalya Mahadevan·Shmuel M. Rubinstein·Ariel Amir
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Abstract

The motion of a disk spinning to rest after being tipped on its side is a classic example of a finite-time singularity, yet the dominant dissipation mechanism governing this process remains debated. Using stereoscopic high-speed imaging, we study the dynamics of disks with varying mass and radius on different surfaces. We show that the late-time motion near the singularity is governed by viscous air-drag arising from shear in the boundary layer beneath the disk, as evidenced by the mass dependence of the dynamics, measurements in a partial vacuum, and a geometric control using a steel ring. At earlier times, dissipation is dominated by rolling friction, which on glass exhibits an unexpected sublinear scaling with disk mass, suggesting an adhesion-based rolling resistance. These results clarify the dissipation mechanisms underlying the singularity of Euler's disk and have broader implications for rolling-contact systems operating under low loads on smooth surfaces.

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Benjamin G. Thorne, Ahmad Zareei, Kausalya Mahadevan, Shmuel M. Rubinstein, Ariel Amir. 2026-03-15. Air Drag Controls the Finite-Time Singularity of Euler's Disk. https://arxiv.org/abs/2603.14520

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