TY - JOUR

T1 - Rotating and rolling rigid bodies and the "hairy ball" theorem

AU - Bormashenko, Edward

AU - Kazachkov, Alexander

N1 - Publisher Copyright:
© 2017 American Association of Physics Teachers.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85019348157&partnerID=8YFLogxK

U2 - 10.1119/1.4979343

DO - 10.1119/1.4979343

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AN - SCOPUS:85019348157

SN - 0002-9505

VL - 85

SP - 447

EP - 453

JO - American Journal of Physics

JF - American Journal of Physics

IS - 6

ER -