Brief Communication | Published:

Euler's disk and its finite-time singularity

Nature volume 404, pages 833834 (20 April 2000) | Download Citation

Subjects

Abstract

It is a fact of common experience that if a circular disk (for example, a penny) is spun upon a table, then ultimately it comes to rest quite abruptly, the final stage of motion being characterized by a shudder and a whirring sound of rapidly increasing frequency. As the disk rolls on its rim, the point P of rolling contact describes a circle with angular velocity Ω. In the classical (non-dissipative) theory1, Ω is constant and the motion persists forever, in stark conflict with observation. Here I show that viscous dissipation in the thin layer of air between the disk and the table is sufficient to account for the observed abruptness of the settling process, during which, paradoxically, Ω increases without limit. I analyse the nature of this ‘finite-time singularity’, and show how it must be resolved.

Air viscosity makes the rolling speed of a disk go up as its energy goes down.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    Treatise on Analytical Dynamics (Heinemann, London, 1965).

  2. 2.

    Theoria Motus Corporum Solidorum Seu Rigidorum (Greifswald, 1765).

Download references

Author information

Corresponding author

Correspondence to H. K. Moffatt.

About this article

Publication history

Published

DOI

https://doi.org/10.1038/35009017

Authors

  1. Search for H. K. Moffatt in:

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.