The drivetrain of a bicycle that has wheel 67.3 cm in diameter and pedal cranks

Question

The drivetrain of a bicycle that has wheel 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady cadence of 76.0 rev/min. The chain and engages with a front sprocket 15.2 cm in diameter and a rear 7.00 cm in diameter. A) Calculate the speed of a link of the chain relative to the bicycle frame. B) Calculate the angular speed of the bicycle wheels. C) Calculate the speed of the bicycle relative to the road. D) What pieces of data, if any are not necessary for the calculations?

Explanation / Answer

(a) according to the problem let us consider a tooth onthe front sprocket v = r ? = (0.152 m / 2) (76 rev / min) (2p rad / 1 rev) (1 min / 60 s) = 0.604 m / s (b) consider the chain link engaging a tooth on the rearsprocket ? = v / r = v / (0.070 m / 2) = 16.94 rad / s (c) now consider the wheel tread road a thread could be unwinding from the tire with thisspeed relative to the frame v = r ? = (0.673 / 2) (?) = 5.542m / s D) length of pedal cranks

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