What is the correct method for calculating the speed of a bicycle chain?

[freeurmind101]

Homework Statement

A bicycle has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady angular rate of 71.5 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 6.45 cm in diameter.

Homework Equations

v=rw

The Attempt at a Solution

I converted the revs/min to rad/s and then used that value times the radius of the front sprocket and got 1.138 m/s but this is wrong. I then tried to calculate the tangential velocity at the back sprocket with the same rate of pedaling and that radius and added it to the value I got from the front sprocket but this was wrong as well. Do i need to take into account the length of the pedal crank?

 

[Delphi51]

Welcome to PF, Free.
Looks interesting, but there is no question. What are you trying to find?

 

[freeurmind101]

Homework Statement

A bicycle has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady angular rate of 71.5 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 6.45 cm in diameter. (a) Calculate the speed of a link of the chain relative to the bicycle frame.

Homework Equations

v=rw

The Attempt at a Solution

I converted the revs/min to rad/s and then used that value times the radius of the front sprocket and got 1.138 m/s but this is wrong. I then tried to calculate the tangential velocity at the back sprocket with the same rate of pedaling and that radius and added it to the value I got from the front sprocket but this was wrong as well. Do i need to take into account the length of the pedal crank?

Sorry lol, I forgot to include the question. (a) Calculate the speed of a link of the chain relative to the bicycle frame.

 

[Delphi51]

I converted the revs/min to rad/s and then used that value times the radius of the front sprocket and got 1.138 m/s but this is wrong.

The method sounds good, but I don't agree with the answer!
Can you show the details of the calculation so we can look for the error?

 

[freeurmind101]

(1min/60sec)*(71.5revs/min)*(0.152m)*(2*pi rad/1rev)=1.138

 

[freeurmind101]

Wow, I just realized I forgot to divide the diameter by 2 to get the radius lol. I'm such an idiot lol.

 

[Delphi51]

Ah, I knew it had to be some little thing. Easy to do!
I should have noticed I had half your answer.