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 73.5 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 8.00 cm in diameter. Calculate the speed of a link of the chain relative to the bicycle frame, m/s Calculate the angular speed of the bicycle wheels. rad/s Calculate the speed of the bicycle relative to the road. 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

Explanation / Answer

W = angular velocity; V = linear velocity; r=radius
*note: you are given diameters only. To get radius, just divide the diameter by two, and don't forget to convert the cm to m.
a)W(pedal) = W(front sprocket)
W = given =73.5 rev/min
v(front srpocket) = r(front sprocket)*w(front sprocket)
*convert cm to m, and convert revolutions/min to radians/s by multiplying the given angular velocity (w) by (2pi/60)
w(front sprocket) = 73.5 * (2pi/60) =7.693 rad/s
a) v(front sprocket) =0.152*w(front sprocket)= 0.152*7.693 rad/s=1.17 m/s
b) v(front sprocket) = v(chain) = v(rear sprocket)
v(rear sprocket) = w(rear sprocket)*r(rear sprocket)
w(rear sprocket) = v(rear sprocket)/r(rear sprocket)
w(rear sprocket) = 1.17/(0.08/2) = 29.25 rad/s
c) w(rear sprocket) = w(wheel)
v(wheel) = r(wheel)*w(wheel)
v(wheel) = (0.673/2) * 29.25 =9.84 m/s
d) lengh of pedal cranks

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