1. The bicycle gear system shown has a 120 mm chainwheel (front sprocket) connec

Question

1. The bicycle gear system shown has a 120 mm chainwheel (front sprocket) connected via the bicycle chain to a 45 mm rear sprocket.
(a) For each revolution of the bicycle’s chainwheel, how many revolutions does the rear sprocket turn? (b) Assuming a cadence (chainwheel angular rotation rate) of 60 rpm, what is the angular velocity of the rear sprocket in rad/s? (c) If the rear wheel has a diameter of 26 in, what is the bicycle’s velocity in mph?

1. The bicycle gear system shown has a 120 mm chainwheel (front sprocket) connected via the bicycle chain to a 45 mm rear sprocket. 45 (a) For each revolution of the bicycle's chainwheel, how many revolutions does the rear (b) sprocket turn? is the Assuming a cadence angular rotation rate) of 60 rpm, what angular velocity of the rear sprocket in rad/s? (c) If the rear wheel a diameter of 26 in, what is the bicycle's velocity in mph? has

Explanation / Answer

(A) velocity of chain will be same everywhere.

(velocity constraints)

and v = w r

so w1 r1 = w2 r2

w1 (45 mm) = w2 (120 mm)

w1 = (8/3) w2

so for every revolution of chainwheel, sprocket will rotate 8/3 times OR 2.67 times.

(B) w2 = 60 rpm

w1 = 60 x 8 /3 = 160 rpm

w1 = 160 x 2pi rad / 60 s

= 16.76 rad/s

(C) w = 16.76 rad/s

v = w r = (16.76 rad/s) ( 17 x 0.0254 m) = 7.23 m/s

v in mph =7.23 x (1/1609 miles) / (1/3600 hrs)

= 16.2 mph

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