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 75.5 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter. Calculate the speed of a link of the chain relative to the bicycle frame. Note that 15.2 cm is the diameter of the front sprocket, not the radius, m/s Calculate the angular speed of the bicycle wheels. How are the speeds of points on the rims of the two sprockets related? Recall that there is a chain connecting the two. rad/s Calculate the speed of the bicycle relative to the road. Note that 67.3 cm is the diameter of the wheel, not the radius, m/s What piece of data, if any, are not necessary for the calculations? diameter of front sprocket diameter of wheels angular rate length of pedal cranks diameter of rear sprocket none of these The chain ensures that the tangential speeds at the edge of the sprockets is the same. What determines the relationship between the angular speeds of the two sprockets?

Explanation / Answer

a) Links of the chain rotate around the front sprocket.
The front sprocket ro-tates at 79.0 rev/min and has a
diameter of 15.2 cm. Links on the chain will consequently
have a
linear speed of:

v = r fr fr =(0 . 1502 × 75.5 × 2 / 60 )/2

= 0.593m/s

b) The bicycle wheels and the rear sprocket have the same angular speed
that we can calculate from the linear speed of the chain links
(links rotate around the rear sprocket also)

rear = v r rear =(0 . 593 / . 07)*2 = 16.94rad /s

c) Again the rear sprocket and the rear wheel rotating with the
same angular speed will give rise to a linear speed for both wheels
and the bicycle:

v = r wheel × rear =( 0 . 673 × 16.94)/2 = 5.70 m /s

d) lengh of pedal cranks

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