A light, inextensible string of length 4m is threaded through a smooth ring at the point O. One end of the string has a particle, P, of mass 4 kg, which is 1.2 m vertically below O. Particle Q, of mass 1.6 kg, is attached to the other end of the string. Particle Q is describing horizontal circles, with the string OQ making an angle of 20° with the downward vertical.

a. If particle P does not move during the motion, find the angular speed of Q.

b. Find the number of complete circles described per minute.