  The laws of friction are reasonably well understood for the case of blocks in
contact with rough plane surfaces. However, as far as bodies with circular
sections are concerned, the physics of friction becomes more involving and it
is not possible to adopt a simple conceptual framework to explain all
phenomena. In particular, there is no approach so far to the problem of the
resistance force that opposes to circular bodies that remain at rest while
acted upon by small forces. Here we fill this gap by introducing a mechanical
model based on both the elasticity theory and Hertz contact mechanics. Our
approach furnishes a quantitative expression for the critical force beyond
which rest can no longer be maintained. Besides confirming the expected
proportionality of the resistance force with the load, our result contains no
free parameters and is expressed solely in terms of physical properties of the
problem, such as the pressure of the body per unit of superficial area, a
relation between the Young modulus of the surface and its Poisson ratio, and
the symmetry of the contact.
