Analyzing the motion of a mass sliding on a sphere with friction
- 1 October 2021
- journal article
- research article
- Published by American Association of Physics Teachers (AAPT) in American Journal of Physics
- Vol. 89 (10), 921-926
- https://doi.org/10.1119/10.0005071
Abstract
A well-known problem in classical mechanics that is often presented for pedagogical purposes involves a small mass that slides without friction under a gravitational force on the surface of a sphere. Commonly, students are asked to find the angular position where a mass with no azimuthal motion leaves the spherical surface, and this question is easily within the reach of most intermediate physics students. However, a complete solution for more general motion of the mass on the spherical surface (including friction) may be suitable for many advanced undergraduates. Without friction, the problem including azimuthal motion is really an inverted version of an ideal spherical pendulum. This problem is also useful for extending discussion in classical mechanics to more sophisticated topics beyond solving Newton's laws of motion, such as the importance of conservation laws and constants of motion as they relate to symmetry, conservative versus dissipative forces, and the role of constraints.Keywords
This publication has 3 references indexed in Scilit:
- Sliding down an arbitrary curve in the presence of frictionAmerican Journal of Physics, 2017
- A block slipping on a sphere with friction: Exact and perturbative solutionsAmerican Journal of Physics, 2007
- Sliding on the Surface of a Rough SphereThe Physics Teacher, 2003