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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