I was just wondering if the rotating pulley of an Atwood machine is considered as undergoing uniform circular motion? If we consider the system below, the rotating pulley undergoes uniform acceleration with net force acting downwards (not always perpendicular to tangential velocity). Hence does it still constitute as uniform circular motion?
No. The "uniform" in uniform circular motion means the motion has a constant angular velocity, i.e. the speed of the edge of the pulley would have to be constant. Since the masses are accelerating, the edge of the pulley has a changing speed, and hence the motion of the pulley is not uniform circular motion.