Almost rolling motion: An investigation of rolling grooved cylinders

Details Almost rolling motion: An investigation of rolling grooved cylinders Almost rolling motion: An investigation of rolling grooved cylinders

2006-06-29

arxiv.org/abs/physics/0606254v2

Am. J. Phys. vol. 66, no. 3, pp. 202-208 (1998)

Physics

Classical Physics

8 pages, 6 figures http://link.aip.org/link/?AJPIAS/66/202/1

Scientific paper

10.1119/1.18846

We examine the dynamics of cylinders that are grooved to form N teeth for rolling motion down an inclined plane. The grooved cylinders are experimentally found to reach a terminal velocity. This result can be explained by the inclusion of inelastic processes which occur whenever a tooth hits the surface. The fraction of the angular velocity that is lost during an inelastic collision is phenomenologically found to be proportional to (2*sin^2*pi/N)-(alpha*sin^3*pi/N), and the method of least squares is used to find the constant alpha=0.98. The adjusted theoretical results for the time of rolling as well as for terminal velocity are found to be in good agreement with the experimental results.

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