Cycloidal paths are ubiquitous in physics. Here, we show that representative cycloidal paths in physics can be described as superpositions of translations and rotations of a point through space. Using this unifying principle, the parametric equations of the path of a point on a rolling disk are derived for rolling without slipping, rolling with frictionless slipping, and when kinetic solid-on-solid friction is present during rolling with slipping. In a similar way, the parametric equations versus time for the orbit with respect to a star of a moon in a circular orbit about a planet that is in a circular orbit about a star are derived, where the orbits are coplanar. The parametric equations versus time for the path of the magnetization vector during undamped electron-spin resonance are found using the same principle, which show that cycloidal paths can occur under specified conditions.
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October 2019
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October 01 2019
Cycloidal paths in physics as superpositions of translational and rotational motions Available to Purchase
David C. Johnston
David C. Johnston
Ames Laboratory and Department of Physics and Astronomy, Iowa State University
, Ames, Iowa 50011
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David C. Johnston
Ames Laboratory and Department of Physics and Astronomy, Iowa State University
, Ames, Iowa 50011Am. J. Phys. 87, 802–814 (2019)
Article history
Received:
September 07 2018
Accepted:
June 15 2019
Citation
David C. Johnston; Cycloidal paths in physics as superpositions of translational and rotational motions. Am. J. Phys. 1 October 2019; 87 (10): 802–814. https://doi.org/10.1119/1.5115340
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