# Homework Help: Rotational dynamics Find acceleration

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1. Oct 25, 2014

### ForceFail

• Posting problems as images is against forum guidelines and generatr less response
1. The problem statement, all variables and given/known data
http://imgur.com/eYoa8Ut

2. Relevant equations
Torque=rt=I(alpha)
t-mg=-ma
alpha = a/r

3. The attempt at a solution
t-mg=-ma is the equation for the hanging mass.
To find how much this turns the small wheel,
rt=I(alpha) I and r are known
rt=Ia/r

I'm not sure what to do from here. If I try and solve for a and t now, it gives an incorrect answer. I think this is due to me not doing anything with the larger wheel yet, but I'm not sure what to do with it. I know that the tension in the upper and lower part of the belt are not equal, and both produce torque of their own. Tupper should produce a clockwise moment, Tlower should produce a counterclockwise moment.

Last edited: Oct 25, 2014
2. Oct 26, 2014

### haruspex

Quite so. So include these in your torque equation for the smaller wheel and write down the torque equation for the larger wheel.

3. Oct 26, 2014

### ForceFail

So for the smaller wheel:
tr+(Tl)R-(Tu)R=I(alpha)
Larger wheel gives:
(Tu)(Rlw)-(Tl)(Rlw)=I(alpha)

So now I have 2 equations and four unknowns. t,(Tl),(Tu),(alpha)
I can write t=mg-ma and alpha as a/r, Does alpha = a/r for the small wheel use the smaller or larger radius? Since its a tangential I would assume the larger.
That gives
(mg-ma)r+(Tl)R-(Tu)R=Ia/R
and
(Tu)(Rlw)-(Tl)(Rlw)=Ia/(Rlw)

If this is right I'm now down to 3 unknowns and only 2 equations.

4. Oct 26, 2014

### haruspex

Look carefully at how Tu and Tl appear in these equations. Notice anything?

5. Oct 26, 2014

### ForceFail

I see, multiplied equation 1 by R(lw) and equation 2 by R and added them. Then Tu and Tl cancel and you can solve for a. Got the right answer Thanks.

6. Oct 26, 2014

### haruspex

Good.
Note what this means physically. Suppose the belt is elastic. Making it tighter will increase both tensions equally, but won't affect the answer to the question.