A point particle of mass m is initially at rest on top of a frictionless hemisphere with radius R and mass M. The hemisphere rests on a frictionless horizontal table, and is also initially at rest. The particle gets a tiny kick and slides down the (recoiling) hemisphere. Find the velocity of the particle and the hemisphere as a function of the angle 0 of the mass m, measured from the top of the hemisphere. (Eventually the particle leaves the hemisphere. Consider only the part of the motion where the particle is sliding down the hemisphere.) 1.

A point particle of mass m is initially at rest on top of a frictionless hemisphere with radius R and mass M. The hemisphere rests on a frictionless horizontal table, and is also initially at rest. The particle gets a tiny kick and slides down the (recoiling) hemisphere. Find the velocity of the particle and the hemisphere as a function of the angle 0 of the mass m, measured from the top of the hemisphere. (Eventually the particle leaves the hemisphere. Consider only the part of the motion where the particle is sliding down the hemisphere.) 1.