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

## 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 [Broken]

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## The Attempt at a Solution

I would like to know if I drawn all forces:

http://imageshack.com/a/img674/2809/o4uI79.png [Broken]

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 ?

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Bystander
Homework Helper
Gold Member
1) Is it correct ?
Looks pretty good.
2) The motor is turning clockwise at ω, so the wheel is turning at ωR1/R2 ?
Correct.
3) The motor needs to give F1R1ωt, so the wheel receives F2R2ωR1/R2=FR1ωt because |F1|=|F2|, correct ?
Appears to be.
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 ?

Bystander
Homework Helper
Gold Member
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 ?

Bystander