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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PAPERS| October 01 2019
Cycloidal paths in physics as superpositions of translational and rotational motions
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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