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

A sphere moving down the surface of a static sphere and a simple phase diagram