Report
Cycloidal Paths in Physics
| العنوان: | Cycloidal Paths in Physics |
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| المؤلفون: | Johnston, David C. |
| المصدر: | Am. J. Phys. 87, 802-814 (2019) |
| سنة النشر: | 2018 |
| المجموعة: | Physics (Other) |
| مصطلحات موضوعية: | Physics - Popular Physics |
| الوصف: | A popular classroom demonstration is to draw a cycloid on a blackboard with a piece of chalk inserted through a hole at a point P with radius r = R from the center of a wood disk of radius R that is rolling without slipping along the chalk tray of the blackboard. Here the parametric equations versus time are derived for the path of P from the superposition of the translational motion of the center of mass (cm) of the disk and the rotational motion of P about this cm for r = R (cycloid), r < R (curtate cycloid) and r > R (prolate cycloid). It is further shown that the path of P is still a cycloidal function for rolling with frictionless slipping, but where the time dependence of the sinusoidal Cartesian coordinates of the position of P is modified. 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. Finally, the general parametric equations versus time for the path of the magnetization vector during undamped electron-spin resonance are found, which show that cycloidal paths can occur under certain conditions. Comment: 9 pages, 10 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1119/1.5115340 |
| URL الوصول: | http://arxiv.org/abs/1809.03871 |
| رقم الانضمام: | edsarx.1809.03871 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1119/1.5115340 |
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