Kinematics of an Elastic Sphere Rolling on a Plane and Between Two Planes

Abstract

A sphere rolling between a stationary and a spinning plane traces out a spiral path, even under quasistatic conditions. Published theory suggests that radial creep due to pivot produces the spiral path. We show experimentally a component of the sphere’s angular velocity not considered in the published analysis, raising questions about pivot in producing the spiral. We give a general expression for the sphere angular velocity vector which accommodates a linear, circular or spiral path, pivot or no pivot, and one or two planes in contact. We show that a sphere can roll in a circle on one or between two plane without pivot, but not between a stationary and a spinning plane. We show that a circumferential component of angular velocity results in a spiral path. A symmetry argument suggests that the spiral might be due to elastic deformation in the planes rather than to pivot, but the question is still open.