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

  • Thread starter Thread starter Arman777
  • Start date Start date
  • Tags Tags
    Bicycle Torque
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
3 replies · 2K views
Arman777
Insights Author
Gold Member
Messages
2,163
Reaction score
191

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.there's no external force and radius is same.

Any ideas
 

Discussion

Physics news on Phys.org
Arman777 said:

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.there's 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
 
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 ?
 
Arman777 said:
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.