  We calculate the friction force acting on a hard cylinder or spherical ball
rolling on a flat surface of a viscoelastic solid. The rolling friction
coefficient depends non-linearly on the normal load and the rolling velocity.
For a cylinder rolling on a viscoelastic solid characterized by a single
relaxation time Hunter has obtained an exact result for the rolling friction,
and our result is in very good agreement with his result for this limiting
case. The theoretical results are also in good agreement with experiments of
Greenwood and Tabor. We suggest that measurements of rolling friction over a
wide range of rolling velocities and temperatures may constitute an useful way
to determine the viscoelastic modulus of rubber-like materials.
