A circular loop has a small bead which can slide on it without friction. The radius of the loop is r. Keeping the loop vertically it is rotated about a vertical diameter at a constant angular speed `omega`. What is the value of angle `theta`, when the bead is in dynamic equilibrium ?

Explanation

Centripetal force is provided by the horizontal component of the normal reaction N. The vertical component balances the weight. Thus
N sin `theta = m omega^(2)x" "and " N cos" theta = mg`
Also x = r sin `theta rArr " N " = m omega^(2)`r
cos `theta = (g)/(omega^(2)r) " or " theta = cos^(-1)((g)/(r omega^(2)))`