A particle of mass m sits on top of a frictionless hemisphere of equal mass M. The particle is given a kick and slides down the hemisphere, losing contact at angle θ. To find θ, an equation relating θ must be derived and solved for the special case where m = M. The equation will be cubic and for equal masses can be solved to find the angle where the particle loses contact.

1. Week 87 (5/10/04)
Leaving the hemisphere
A point particle of mass m sits at rest on top of a frictionless hemisphere of mass
M, which rests on a frictionless table, as shown. The particle is given a tiny kick
and slides down the hemisphere. At what angle θ (measured from the top of the
hemisphere) does the particle lose contact with the hemisphere?
In answering this question for m = M, it is sufficient for you to produce an
equation that θ must satisfy (it will be a cubic). However, for the special case of
m = M, this equation can be solved without too much difficulty; find the angle in
this case.
M
m