A vertical rod is rotating about its axis with a uniform angular speed ` omega` . A simple pendulum of length l is attached to its upper end what is its inclination with the rod ?

Explanation

Let the radius of the circle in which the bob is rotating is, the tension in the string is T, weight of the bob mg, and inclination of the string `theta`. Then T cos `theta` balances the weight mg and T sin `theta` provides the centripetal force necessary for circular motion.
That is -
T cos `theta` = mg
and T sin `theta = m omega^(2)` x
but x = l sin `theta`
`therefore " " T = m omega^(2)` l
and cos `theta = (mg)/(T) =(mg)/(m omega^(2))` l
or ` theta = cos^(-1) ((g)/(omega^(2) l))`