A ring is made to rotate about its diameter at a constant angular speed of `omega_(0)` . A small insect of mass m walks along the ring with a uniform angular speed `omega` relative to the ring (see figure). Radius of the ring is R.
(a) Find the external torque needed to keep the ring rotating at constant speed as the insect walks. Express your answer as a function of `theta`. For what value of q is this torque maximum? [given your answer for `0 le theta le 90^(@)` ]
(b) Find the component of force perpendicular to the plane of the ring, that is applied by the ring on the insect. For what value of `theta` is this force maximum? Argue quantitatively to show that indeed the force should be maximum for this value of `theta`. [Give your answer for `0^(@) le theta le 90^(@)` ]
