Rolling friction and energy dissipation in a spinning disc

Abstract

This paper presents the results of both experimental and theoretical investigations for the dynamics of a steel disc spinning on a horizontal rough surface. With a pair of high-speed cameras, a stereoscopic vision method is adopted to perform omnidirectional measurements for the temporal evolution of the disc's motion. The experiment data allow us to detail the dynamics of the disc, and consequently to quantify its energy. From our experimental observations, it is confirmed that rolling friction is a primary factor responsible for the dissipation of the energy. Furthermore, a mathematical model, in which the rolling friction is characterized by a resistance torque proportional to the square of precession rate, is also proposed. By employing the model, we perform qualitative analysis and numerical simulations. Both of them provide results that precisely agree with our experimental findings.