A ring of mass M is constrained to move in one dimension . A bead of mass m sticks to its circumference. The system rolls without slipping on a horizontal surface with coefficient of friction μ between ring and surface. What will be the angle made by the line joining bead with centre of ring with vertical passing through the centre of ring ? Doubt: If we reduce the ring to its COM then we have a two mass system with new COM' on line joining centre of ring and bead. So two forces are responsible for motion of system. 1. Gravity acting at COM'. 2. Friction tangential to circumference of ring. I am unsure of location of axis of rotation, Relation between θ and μ for system to be at rest. And type of equilibrium shown by system.