Question

A bicyclist notes that the pedal sprocket has a radius of rp = 9.5 cm while the wheel sprocket has a radius of rw = 4.5 cm. The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R = 65 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every t = 1.7 s. When pedaling, the wheel sprocket and the wheel move at the same angular speed. (a) Calculate the angular speed of the wheel sprocket ωw, in radians per second. (b) Calculate the linear speed of the bicycle v, in meters per second, assuming the wheel does not slip across the ground. (c) If the cyclist wanted to travel at a speed of v2 = 3.5 m/s, how much time, in seconds, should elapse as the pedal makes one complete revolution?

Answer 1

Answer:

Explanation:

a) ωp = 2π radians / 1.7 s = 3.7 rad/s

b) ωs = 3.7 rad/s(9.5 cm / 4.5 cm) = 7.8 rad/s

  v = (ωs)R = 7.8(65) = 507 cm/s or 5.1 m/s

c) ωs = 3.5 m/s / 0.65 m = 5.38 rad/s

ωp = 5.38(4.5 cm / 9.5 cm) = 2.55 rad/s

t = θ/ω = 2π / 2.55 = 2.463... 2.5 s