title: 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.
authors.affiliation: State Key Laboratory for Turbulence and Complex Systems , College of Engineering, Peking University , Beijing 100871, People's Republic of China.
authors.forename: Daolin
authors.initials: D
authors.lastname: Ma
authors.affiliation: State Key Laboratory for Turbulence and Complex Systems , College of Engineering, Peking University , Beijing 100871, People's Republic of China.
authors.forename: Caishan
authors.initials: C
authors.lastname: Liu
authors.affiliation: School of Aeronautic Science and Engineering, Beihang University , Beijing 100191, People's Republic of China.
authors.forename: Zhen
authors.initials: Z
authors.lastname: Zhao
authors.affiliation: State Key Laboratory for Turbulence and Complex Systems , College of Engineering, Peking University , Beijing 100871, People's Republic of China.
authors.forename: Hongjian
authors.initials: H
authors.lastname: Zhang
keywords: Euler's disc; energy dissipation; rolling friction