Rolling as a continuing collision

TL;DR

This paper establishes a direct relationship between the restitution coefficient for particle collisions and the rolling friction coefficient for spheres, enabling new experimental methods to measure these parameters.

Contribution

It introduces a novel theoretical link between collision and rolling motion coefficients, allowing determination of one from the other using material constants.

Findings

Derived a quantitative relation between  and _{roll}

Provided formulas to calculate coefficients from material properties

Suggested a new experimental technique for measuring these coefficients

Abstract

We show that two basic mechanical processes, the collision of particles and rolling motion of a sphere on a plane, are intimately related. According to our recent findings, the restitution coefficient for colliding spherical particles \epsilon, which characterizes the energy loss upon collision, is directly related to the rolling friction coefficient \mu_{roll} for a viscous sphere on a hard plane. We quantify both coefficients in terms of material constants which allow to determine either of them provided the other is known. This relation between the coefficients may give rise to a novel experimental technique to determine alternatively the coefficient of restitution or the coefficient of rolling friction.