Try this beautiful problem, useful for the Physics Olympiad, based on Minimum Speed of a Rotating Pail of Water.
The Problem: Minimum Speed of a Rotating Pail of Water
You tie a cord to a pail of water and you swing the pail in a vertical circle of radius (0.6m). What minimum speed must you give the pail at the highest point of the circle if no water is to spill from it?
SET UP: The water moves in a vertical circle. The target variable is the speed v.
Calculate: We calculate (a) and then get v from (a=\frac{v^2}{R}). We write
the force equation as $$ mg=m\frac{v^2}{R}$$
Therefore, $$ v=\sqrt{gR}=\sqrt{(9.80)(0.600)}=2.42m/s$$
