How Do You Calculate the Angular Speed of a Bicycle Wheel?

[klopez]

1. 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 angular rate of 76.5 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.25 cm in diameter.



2. v = r*w



3. First I tried to find the velocity of the rear sprocket.

radius of rear sprocket is 0.0363 m
angular speed of pedaling is 8.01 rad/s

v = 0.0363 * 8.01
v = .291 m/s

radius of wheels is 0.337 m

So I used the velocity of the rear sprocket to calculate the angular speed of the wheel

w = .291/.337
w = .864 rad/s

I am using WebAssign, and when I entered this answer, it said my answer differed by orders of magnitude. Any help would be greatly appreciated, since I only have one more shot at getting the answer right. Thanks

Kevin

 

[Doc Al]

Can you post the figure?

 

[klopez]

there u go

 

[Doc Al]

3. First I tried to find the velocity of the rear sprocket.

radius of rear sprocket is 0.0363 m
angular speed of pedaling is 8.01 rad/s

v = 0.0363 * 8.01
v = .291 m/s

But you used the angular speed of the front sprocket, not the rear sprocket.

Hint: Since they are connected by a chain, the tangential velocity (v, not angular speed) of each sprocket is the same.