A bicycle wheel consists of a diameter of 64.6 cm and a mass of 1.87 kg. Suppose that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is positioned on a stationary stand and a resistive force of 125 N is exerted tangent to the rim of the tire.
(i) What force should be applied through a chain passing over an 8.96 cm diameter sprocket when the wheel is to accomplish an acceleration of 4.49 rad/s2?
(ii) What force is required when the chain shifts to a 5.57 cm diameter sprocket?