Perturbation analysis of rolling friction on a turntable

American Journal of Physics

Volumn 64, Issue 9, 1996, Pages 1130-1139

  Soodak, Harry ^a   Tiersten, Martin S ^a  

^a CITY COLLEGE OF NEW YORK   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030489665     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18333     Document Type: Article

References (14)

1. Robert H. Romer, "Motion of a sphere on a tilted turntable," Am J. Phys. 49, 985-986 (1981).
2. Klaus Weltner, "Stable circular orbits of freely moving balls on rotating discs," Am. J. Phys. 47, 984-986 (1979).
3. Joseph. A. Burns, "Ball Rolling on a Turntable: Analog for Charged Particle Dynamics," Am. J. Phys. 49, 56-58 (1981).
4. J. Gersten, H. Soodak, and M. S. Tiersten, "Ball moving on stationary or rotating horizontal surface," Am. J. Phys. 60, 43-47 (1991).
5. A. V.Sokirko, A. A. Belopolskii, A. V. Matsytsyn, and D. A. Kossakowski, "Behavior of a ball on the surface of a rotating disk," Am. J. Phys. 62, 151-156 (1994).
6. Klaus Weltner, "Central drift of freely moving balls on rotating disks: A new method to measure coefficients of rolling friction," Am. J. Phys. 55, 937-942 (1987).
7. R. Ehrlich and J. Tuszynski, "Ball on a rotating turntable: Comparison of theory and experiment," Am. J. Phys. 63, 351-359 (1995).
8. The center of the ball also moves in a plane for significant deformations as long as the deformation pattern remains fairly constant throughout the motion.
9. Frank Philip Bowden and David Tabor, Friction, An Introduction to Tribology (Anchor Doubleday, Garden City, NY, 1973), pp. 7 and 136.
10. g, which are identical to the exact results to first order in the parameter b/IΩ.
11. We used Mathematica, A System for Doing Mathematics by Computer, by Stephen Wolfram.
12. We used the Runge-Kutta package of Mathematica (Ref. 11).
13. The trajectories were computed by numerical integration of the slipping equation of motion analogous to Eq. (13) for rolling motion, using initial conditions that describe the onset of slipping. A paper on slipping motion is in preparation.
14. r.