Air Drag Controls the Finite-Time Singularity of Euler's Disk
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911518226907136 |
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| author | Thorne, Benjamin G. Zareei, Ahmad Mahadevan, Kausalya Rubinstein, Shmuel M. Amir, Ariel |
| author_facet | Thorne, Benjamin G. Zareei, Ahmad Mahadevan, Kausalya Rubinstein, Shmuel M. Amir, Ariel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14520 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Air Drag Controls the Finite-Time Singularity of Euler's Disk Thorne, Benjamin G. Zareei, Ahmad Mahadevan, Kausalya Rubinstein, Shmuel M. Amir, Ariel Soft Condensed Matter Classical Physics Fluid Dynamics 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. |
| title | Air Drag Controls the Finite-Time Singularity of Euler's Disk |
| topic | Soft Condensed Matter Classical Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2603.14520 |