Bicycle gears: (a) How is the angular velocity of the rear wheel of a bicycle related to the angular

Bicycle gears: (a) How is the angular
velocity  of the rear wheel
of a bicycle related to the angular velocity F of the front sprocket and pedals? Let NF and NR
be the number of teeth on the front and rear sprockets, respectively, Fig.
10-64. The teeth are spaced the same on both sprockets and the rear sprocket is
firmly attached to the rear wheel. (b) Evaluate the ratio  when the front and rear sprockets have 52 and 13 teeth,
respectively, and (c) when they have 42 and 28 teeth.