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

• Arman777
In summary: Now, in summary, the conversation is about calculating the torque on the rear wheel gear of an 18-speed bicycle, given different gear radii and a force of 343 N applied to the pedal. The torque ratio can be determined by comparing the radii of the gears, which explains why a bike with 18 speeds is needed for varying terrain and conditions.
Arman777
Gold Member

## 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

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.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

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.

## 1. What is torque in a bicycle?

Torque in a bicycle refers to the measure of force that causes an object to rotate around an axis. In simpler terms, it is the amount of power or force that a cyclist needs to apply to the pedals to move the bicycle forward.

## 2. How is torque calculated in a bicycle?

To calculate torque in a bicycle, you need to multiply the force applied to the pedals by the length of the crank arm. The formula for torque is T = F x r, where T is torque, F is force, and r is the length of the crank arm.

## 3. What is the importance of torque in a bicycle?

Torque is important in a bicycle because it determines how quickly and efficiently a cyclist can pedal and move the bicycle forward. It also affects the power and acceleration of the bicycle, making it crucial for performance and speed.

## 4. How can torque be adjusted in a bicycle?

Torque can be adjusted in a bicycle by changing the gear ratio. A lower gear ratio will provide more torque, making it easier to pedal on steep inclines. A higher gear ratio will provide less torque, but more speed on flat terrain.

## 5. Does the weight of the cyclist affect torque in a bicycle?

Yes, the weight of the cyclist can affect torque in a bicycle. A heavier cyclist will require more torque to pedal and move the bicycle forward, while a lighter cyclist will require less torque. This is why bicycles often have weight limits for optimal performance.

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