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

[Cri85]

Homework Statement

[/B]
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

Homework Equations

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 ?

 

[Bystander]

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?

 

[Cri85]

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]

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

 

[Cri85]

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]

Yes.

 

[Cri85]

ok, thanks :)