Dynamics of a Spinning Disk

A spinning disk on a rough horizontal surface is a familiar example presented in the textbooks of classical mechanics. Recent studies have revealed that this simple system would exhibit an intriguing phenomenon that cannot be well examined by existing theories. Reason for that is due to the lack of reasonable understanding for the influence of combined sliding and rolling friction on the disk dynamics. To unveil how the two types of friction affect the disk motion, this paper presents a combined investigation of experiments and simulations on the dynamics of a spinning disk. We employed a pair of high-speed cameras to perform omnidirectional measurements for the six degrees-of-freedom in describing the disk motion. Numerical calculations are implemented under an integrated model including both the Coulomb friction law and a viscous rolling friction model. Exposure for the details of the disk motion in experiments and simulations sheds light on a novel mechanism underlying the rolling friction: the rolling friction exhibits viscosity relating to the square of rolling velocity.