Calculating Torque on Rear Wheel Gear: 18-Speed Bicycle Question Explained

[Arman777]

Homework Statement

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.

Homework Equations

Equations about the torque and momentum

The Attempt at a Solution

I couldn't 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

 

[SteamKing]

Homework Statement

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.

Homework Equations

Equations about the torque and momentum

The Attempt at a Solution

I couldn't 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

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

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

 

[Arman777]

Here there's 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 ?

 

[SteamKing]

Here there's 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 ?

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