Recently, two of us (Prior and Mele1) presented an analysis of a particle (or block) that slips on the surface of a sphere with friction. Among other results, it was pointed out that the problem can be solved exactly, and that it has a “phase diagram in the μv0 plane separating the region where the block sticks to the sphere from the region where the block continues to slip on the sphere and is released.” This diagram was not presented, but was posed as a suggested problem for the reader to construct it by a suitable computer-based analysis. The purpose of this comment is to present an exact analytic solution for the boundary.

We consider the motion of a particle which is given an initial horizontal velocity v0 at the top of a sphere of radius R. It is convenient to analyze...

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