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Question
A stone is fastened to one end of a string and is whirled in a vertical circle of radius R. Find the minimum speed the stone can have at the highest point of the circle.
Solution
Let m be the mass of the stone.
Let v be the velocity of the stone at the highest point.
R is the radius of the circle.
Thus, in a vertical circle and at the highest point,
we have :
\[\frac{\text{mv}^2}{\text{R}} = \text{mg}\]
\[ \Rightarrow \text{v}^2 = \text{Rg}\]
\[ \Rightarrow \text{v} = \sqrt{\text{Rg}}\]
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