A ball of mass

m

is attached to a light inextensible string of length

l

. The ball is whirled around so that it moves in a horizontal circle with constant angular speed

ω

Find the angle $θ$ between the string and the vertical. Show that the angle $θ$ is given by $\cos^{- 1} \frac{g}{l ω^{2}}$ .

Now increase the angular velocity. What happens to the ball?

What is the smallest angular velocity with which the ball can whirl in a circle on the end of the string in this way?