We have an inclined cylinder, something like a funnel, which rotates around its symmetrical axis. A mass (m) resides on the wall of this cylinder and rotates with the cylinder. Now the angular velocity of the cylinder increases. Whether the newton laws (or else) can anticipate what will happen? (Don't use intuition or your previous experiments)
The Attempt at a Solution
I know that the mass remains somewhere on the inclined wall. Now it may go up the wall or may go down or remain at the same place.
First case: The mass goes up: r (rotation radius) increases, w (angular velocity) increase so it requires a greater centripetal force (mrw^2) and the normal force (N) will provide this force so N will increase.
Second case: the mass goes down: r decreases, w increases so the centripetal force (mrw^2) can increase, decrease or remain the same consequently the normal force (N) can increase, decrease or remain constant.
Third case: The mass remains at its place: r constant, w increases so mrw^2 becomes greater. Normal force increases to provide this increase.
I think nothing theoretically prevents these cases to occur.