I've just come across the following problem, and I quote(translate): A hollow hemisphere is held at rest, vertically, concave side facing upwards. A small ball placed inside against the surface, at a distance "h" from the bottom, is shot horizontally with velocity "vo". Find the value of "vo", as a function of "h", so that ball reaches the hemisphere's rim and remains turning around without leaving the hemisphere.
First, intuition says (to me, at least) that the ball will try to gain in altitude as it rotates. And this is in accordance with the fact that there is a torque provided by appropriate components of the force of gravity and the centrifugal force.
What I wished to ask you is: a) is it true that for each "vo", the ball either reaches an altitude at which it remains turning with constant angular speed or it leaves the hemisphere, and consequently there is a certain value of "vo" at which the ball just reaches the rim and remains there?; is my approach correct?
Thanks in advance for your help.