All Physics Faculty Publications

Document Type

Article

Journal/Book Title/Conference

American Journal of Physics

Volume

89

Issue

9

Publisher

AIP Publishing LLC

Publication Date

8-19-2021

Award Number

NSF, Division of Chemistry (CHE) 1808225

Funder

NSF, Division of Chemistry (CHE)

First Page

830

Last Page

842

Abstract

We explore the forces and conservation laws that govern the motion of a hockey puck that slides without friction on a smooth, rotating, self-gravitating spheroid. The earth's oblate spheroidal shape (apart from small-scale surface features) is determined by balancing the gravitational forces that hold it together against the centrifugal forces that try to tear it apart. The earth achieves this shape when the apparent gravitational force on the puck, defined as the vector sum of the gravitational and centrifugal forces, is perpendicular to the earth's surface at every point on the surface. Thus, the earth's spheroidal deformations neutralize the centrifugal and gravitational forces on the puck, leaving only the Coriolis force to govern its motion. Motion on the spheroid therefore differs profoundly from motion on a rotating sphere, for which the centrifugal force plays a key role. Kinetic energy conservation reflects this difference: On a stably rotating spheroid, the kinetic energy is conserved in the rotating frame, whereas on a rotating sphere, it is conserved in the inertial frame. We derive these results and illustrate them using CorioVis software for visualizing the motion of a puck on the earth's spheroidal surface.

Comments

Reproduced from Am.J. Phys. 89, 830-842 (2021), with the permission of the American Association of Physics Teachers.

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