Rotating and rolling rigid bodies and the "hairy ball" theorem

Edward Bormashenko, Alexander Kazachkov

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Rotating and rolling rigid bodies exemplify a fascinating theorem of topology, jokingly called the "hairy ball" theorem, which demands that any continuous tangent vector field on the sphere has at least one point where the field is zero. We demonstrate via a gedanken experiment how drilling through a rotating ball, thereby converting it into a torus, leads to the elimination of zero-velocity points on the ball surface. Using the same reasoning, zero-velocity points can be removed from the surface of a drilled spinning top. We discuss the location of zero-velocity points on the surfaces of rigid bodies rolling with no slip and with slip. Observations made from different reference frames identify various zero-velocity points. Illustrative experiments visualizing zero-velocity points are presented.

Original languageEnglish
Pages (from-to)447-453
Number of pages7
JournalAmerican Journal of Physics
Volume85
Issue number6
DOIs
StatePublished - 1 Jun 2017

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