Almost Rolling Motion: An Investigation of Rolling Grooved Cylinders

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 sin2 π/N-α sin3 π/N, and the method of least squares is used to find the constant α=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