  A small sphere placed on the top of a big static frictionless sphere, slips
until it leaves the surface at an angle $\theta_{l}=\cos^{-1}{2/3}$. On the
other extreme, if the surface of the big sphere has coefficient of static
friction, $\mu_s\to\infty$, the small sphere starts rolling and continues to do
so until it leaves the surface at an angle $\theta_{l} =\cos^{-1}{10/17}$. In
the case where, $0\leq\mu_s<\infty$, we get a simple phase diagram. The three
phases are pure rolling, rolling with slipping and detached state. One phase
line separates pure rolling from rolling with slipping. This diagram is
obtained when stopping angles for pure rolling are plotted against static
friction coefficients $\mu_s$. Study in this article is restricted to the case
when the mobile sphere starts at the top of the static sphere with
infinitesimal kinetic energy.
