Question:
A stone is fastened to one end of a string and is whirled in a vertical circle of radius $\mathrm{R}$. Find the minimum speed the stone can have at the highest point of the circle.
Solution:
At highest point
$\mathrm{T}+\mathrm{mg}=\frac{m v^{2}}{R}$
For minimum speed, $\mathrm{T}=0$
$m g=\frac{m v^{2}}{R}$
$V=\sqrt{\mathrm{Rg}}$