Question:
A thin spherical shell of radius $R$ lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?
Solution:
$v_{C}=R \omega$ (Pure Rolling)
By angular momentum conservation
$m v_{C} h=I \omega$
$m v_{C} h=\left(\frac{2}{3} m R^{2}\right)\left(\frac{v}{R}\right)$
$h=\frac{2 R}{3}$