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, $$ v=\sqrt{gR}=\sqrt{(9.80)(0.600)}=2.42m/s$$

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