Chapter 10, Problem 89GP

Bicycle gears: (a) How is the angular velocity ω_R of the rear wheel of a bicycle related to the angular velocity ω_T of the front sprocket and pedals? Let N_F and N_R 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 ${\omega }_{\text{R}}/{\omega }_{\text{F}}$ when the front and rear sprocket have 52 and 13 teeth, respectively, and (c) when they have 42 and 28 teeth.