# Torque bicycle Question

1. Dec 13, 2015

### Arman777

1. The problem statement, all variables and given/known data
Consider a 18 speed bicycle, 3 gears are rotating with the pedal and 6 gears are rotating with rear wheel. Consider that the ones rotating with pedal, have radii 10 cm, 7 cm and 5 cm and the other ones have radii 3 cm, 4 cm, 5 cm, 6 cm, 7 cm and 8 cm. Calculate the torque on rear wheel gear for each different case if you apply to the pedal a force of magnitude 343 N. The force is vertical to the pedal, and it has a length of 17 cm. Explain why a bike needs that much speed, i.e. 18 speed.

2. Relevant equations
Equations about the torque and momentum

3. The attempt at a solution
I couldnt do anything.Actually τ=dL/dt
I thought that Fxr1=F'xr2
here r1 is the pedal radius
here r2 is the rear wheel radius

cause torques must be same why τ=dL/dt And L is equal to rxp which they are not chaning during the time.Theres no external force and radius is same.

Any ideas

2. Dec 13, 2015

### SteamKing

Staff Emeritus
Haven't you ever studied gear ratios and how they affect torque?

https://en.wikipedia.org/wiki/Gear_train

3. Dec 13, 2015

### Arman777

Here theres rope so v=wr here w is same for both object. v/r=v'/r' and also τ=Fr so τ'=F'r' So here I guess torque ratio will be the radius ratio ?

4. Dec 13, 2015

### SteamKing

Staff Emeritus
Well, a chain instead of a rope.
Yes, radius or diameter can be used to calculate the ratio.

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