The figure below shows the drive train of a bicycle that has wheels 67.3 cm in d

Question

The figure below shows the drive train of a bicycle that has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady cadence of 82.0rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 6.00 cm in diameter.

(a) Calculate the speed of a link of the chain relative to the bicycle frame.

m/s

(b) Calculate the angular speed of the bicycle wheels.

rad/s

(c) Calculate the speed of the bicycle relative to the road.

m/s

Explanation / Answer

Wheel diameter (Dw) = 67.3 cm
Crank diameter (Dc) = 35 cm
Angular velocity () = 82.0 rev/min = 1.3 rev/s = 432°/s = 2.4 rad/s
Front sprocket diameter (Df) = 15.2 cm [f = 2.4 rad/s]
Rear sprocket diameter (Dr) = 6.00 cm

A) Calculate the speed of a link of the chain relative to the bicycle frame. (m/s)
Cf = Df = 47.75 cm = 0.4775 m
vf = f x Cf = 1.2 rev/s x 0.4775 m = 0.573 m/s Linear velocity of front sprocket

v = 0.573 m/s Linear velocity of chain link

B) Calculate the angular speed of the bicycle wheels. (rad/s)
Dc/Dw = w/c
35/67.3 = w/2.4
67.3(w) = 84
w = 84/67.3
w = 1.25 rad/s Angular velocity of wheel

C) Calculate the speed of the bicycle relative to the road. (m/s)
Cw = Dw = 2.114 m
vw = w x Cw = 0.625 rev/s x 2.114 m = 1.3 m/s Linear velocity of bicycle

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