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.

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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:
$\frac{m v^{2}}{R} = m g \Rightarrow v^{2} = R g \Rightarrow v = \sqrt{R g}$

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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.

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: mv2R=mg⇒v2=Rg⇒v=Rg

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:
$\frac{m v^{2}}{R} = m g \Rightarrow v^{2} = R g \Rightarrow v = \sqrt{R g}$