# Force, torque with a motor + a wheel + a belt

• Cri85
In summary, the motor accelerates the wheel without friction and the belt gives forces at only one point. If the mass of the belt is zero, the belt gives the same torque to the wheel as the motor provides. If the mass of the belt is greater than the motor, the belt provides a higher torque to the wheel.
Cri85

## Homework Statement

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A motor accelerates more and more a wheel without friction. It is supposed the belt gives forces F1 and F2 at only one point.

http://imageshack.com/a/img674/1437/Uh0XIp.png

None

## The Attempt at a Solution

I would like to know if I drawn all forces:

http://imageshack.com/a/img674/2809/o4uI79.png 1) Is it correct ?

2) The motor is turning clockwise at ω, so the wheel is turning at ωR1/R2 ?

3) The motor needs to give F1R1ωt, so the wheel receives F2R2ωR1/R2=FR1ωt because |F1|=|F2|, correct ?

4) The sum of forces on the belt is F3-F4, if the motor accelerates this could say the belt is accelerating too, then F3 must be higher than F4, so F1 must be higher than F2 (the absolute value not the vector) ? I'm not sure, if F2 is lower the torque on the wheel is lower too, so the last calculation is false ?

Last edited by a moderator:
Cri85 said:
1) Is it correct ?
Looks pretty good.
Cri85 said:
2) The motor is turning clockwise at ω, so the wheel is turning at ωR1/R2 ?
Correct.
Cri85 said:
3) The motor needs to give F1R1ωt, so the wheel receives F2R2ωR1/R2=FR1ωt because |F1|=|F2|, correct ?
Appears to be.
Cri85 said:
then F3 must be higher than F4,
Are you absolutely certain?

The belt is accelerating, like F=ma, for me there is a little difference, the motor gives an energy for accelerate the belt and the disk, a little part must go to the belt and the main part for the disk, no ?

Have you been given masses and moments of inertia? Ordinarily (not absolutely guaranteed) for problems like this, you're given a "massless" belt.

Yes, it's for that, if the mass of the belt is 0, |F3|=|F4| but if the belt has a mass |F3|>|F4|, correct ?

Yes.

Cri85
ok, thanks :)

## What is force?

Force is a push or pull that changes the motion of an object. It is measured in Newtons (N) and can be represented by a vector with both magnitude and direction.

## What is torque?

Torque is the measure of the force that can cause an object to rotate around an axis. It is calculated by multiplying the force applied by the distance from the axis of rotation.

## How does a motor generate force and torque?

A motor uses electromagnetic principles to convert electrical energy into mechanical energy, producing force and torque. This is achieved through the interaction between the magnetic field of the motor and the current flowing through its coils.

## What role does a wheel play in the system?

The wheel acts as a lever in the system, transferring the torque generated by the motor to the object being moved. It also reduces friction between the motor and the surface it is moving on.

## Why is a belt used in this system?

A belt is used to transmit the force and torque from the motor to the wheel. It also allows for speed and direction control, as different sized pulleys can be used to change the gear ratio between the motor and the wheel.

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