Almost rolling motion: An investigation of rolling grooved cylinders

Lawrence R. Mead; Frank W. Bentrem

doi:10.1119/1.18846

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arXiv · physics/0606254

Almost rolling motion: An investigation of rolling grooved cylinders

Lawrence R. Mead·Frank W. Bentrem

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Abstract

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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Lawrence R. Mead, Frank W. Bentrem. 2009-06-29. Almost rolling motion: An investigation of rolling grooved cylinders. https://doi.org/10.1119/1.18846

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