  We investigated the dynamics of driven vortices in high-$T_c$ superconductor
as an ideal model system to study the physics of friction. The waiting-time
dependence of the maximum static friction force, $F_s(t_w)$, was measured in
La$_{2-x}$Sr$_x$CuO$_4$ thin films with different structures, sample sizes and
pinning force. We found various kinds of $F_s(t_w)$ in the $B$-$T$ phase
diagram and in different types of samples. The results suggest that the
relaxation by thermal fluctuation is strongly affected by the pinning strength,
the vortex bundle size and the system size. Based on these results, we found
crucial conditions to determine the validity of the Amontons-Coulomb's law, and
proposed a criterion.
