We analyze the rotational and translational motion of two close spheres in a fluid at low Reynolds number to investigate if their surfaces come into mechanical contact. The rotational motion of a sphere settling close to another fixed ball is calculated from a model in which contact interactions between the spheres are added to the gravitational and hydrodynamic forces. The model predicts a transition from pure rolling to rolling with slip, determined by the Coulomb’s law, when the ratio of the mechanical friction to the load increases up to the static friction coefficient. The dependence of the angular and translational velocities on the kinetic friction coefficient and on the separation between the particle surfaces is analyzed. The angular and translational velocities of a millimeter size bead in a viscous oil, close to a fixed bead of a similar size, are measured from video images. Interferometric data on translational motion are also collected according to the method introduced in our earlier studies. A systematic fitting procedure of the model to the experiment is developed and applied to the rotational and translational measurements. The model parameters are determined.