The Rolling Motion of a Disk on a Horizontal Plane
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Recent interest in the old problem of the motion of a coin spinning on a tabletop has focused on mechanisms of dissipation of energy as the angle alpha of the coin to the table decreases, while the angular velocity Omega of the point of contact increases. Following a review of the general equations of motion of a thin disk rolling without slipping on a horizontal surface, we present results of simple experiment on the time dependence of the motion that indicate the dominant dissipative power loss to be proportional to the Omega^2 up to and including the last observable cycle.
v2 adds experimental data on the role of friction at small angles, and adds several references. Thanks to A. Chatterjee, C. Gray and A. Ruina v3 adds discussion of the case of zero friction; thanks to Martin Olsson
v2 adds experimental data on the role of friction at small angles, and adds several references. Thanks to A. Chatterjee, C. Gray and A. Ruina v3 adds discussion of the case of zero friction; thanks to Martin Olsson