Variation of the Friction Coefficient for a Cylinder Rolling down an Inclined Board.

A cylinder rolling down an inclined board is a commonly seen and interesting object to study and it is also easy to experiment with and model. Following what has become a popular practice, we use smartphones to measure the angular acceleration of a cylinder rolling down a plane of different inclining angles. The friction force deviates from the theoretical result near the critical angle, showing an anomalous bump for the angular acceleration in the neighbourhood of the transition point from pure rolling to rolling with slipping. To give a concise and plausible explanation, we assume that the friction coefficient bears a random component along the rolling down process, which has both an average value and a random component. Based on the formulation, the numerical simulation matches the experimental data well, which confirms the validity of our assumption.