(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How is the angular speed of the rear wheel (Wr) of a bicycle related to that of the pedals and front sprocket (Wf)? That is derive a formula for Wr/Wf. Let Nf and Nr be the number of teeth on the front and rear sprockets respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly. Then evaluate the ratio of Wr/Wf when fron and rear sprockets have 52 and 13 teeth respectively

2. Relevant equations

W = v/r

Circumference (c) = 2pi*r (i am not sure if this is relevant)

3. The attempt at a solution

v for both front and back sprocket is the same (note W is not)

Wf = v/Rf

Wr = v/Rr

Since distances between teeth are same in back and front:

C = 2pi*Rr/Nr = 2pi*Rf/Nf

so...

Wr = v/(Nr*Rf/Nf*Rr)

Wf = v/(Nf*Rr/Nr*Rf)

Wr/Wf = Nf^2*Rr^2/Nr^2*Rf^2

but i do not think that is right because the question implies that your only variable should be N.....

HELP!!! (if i seem unclear about anything...do tell)

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# Homework Help: Rotational Motion Problem (a bike)

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