Elastic work involved in rolling a sphere on another surface

Abstract

A theoretical calculation is made of the elastic work involved in rolling a ball over another surface. The analysis is based on Hertz's equation for the static deformation of spherical surfaces since it is assumed that the additional stresses produced by rolling are small compared with those produced by the normal load. The results show that the work involved in rolling a sphere on a flat surface is substantially the same as that involved in rolling a sphere in a groove of almost the same curvature as the sphere. This conclusion is in line with certain previous work by the author on the rolling friction of steel spheres on rubber.