Torque on a pulley (2 masses connected by a string hanging from 2 pulleys)

[Mohmmad Maaitah]

Homework Statement

As in the picture provided

Relevant Equations

As in the picture.

I am not understanding how is the net torque like that
And genarally how to analysis such problem?
When I try I get totally the inverse results here is the problem and my attempt to solve.

 

[haruspex]

Because the problem specifies $m_2>m_1$, the author has chosen to take acceleration as positive up for $m_1$ and positive down for $m_2$. Correspondingly, rotations have been taken as positive clockwise.

In solving problems, you can set your sign conventions however you like, as long as you are consistent, but the author should have stated them.

 

[kuruman]

I am not sure you have sorted out your torques correctly. You say that one pulley spins CCW and the other CW. Does this look right to you? The mass on the right is descending while the mass on the left is ascending. Do the pulleys spin in opposite directions?

 

[Mohmmad Maaitah]

I am not sure you have sorted out your torques correctly. You say that one pulley spins CCW and the other CW. Does this look right to you? The mass on the right is descending while the mass on the left is ascending. Do the pulleys spin in opposite directions?

Oh I missed that.

 

[Mohmmad Maaitah]

Still not able solve this problem for example

* I end up with 5 formulas which I can't relate to each other to find the acceleration

 

[haruspex]

You say that one pulley spins CCW and the other CW.

I'm not seeing that. The image of handwritten work in post #1 only seems to show torques on the left hand pulley, one acting CW, one CCW.

 

[haruspex]

Still not able solve this problem for example
View attachment 327308
* I end up with 5 formulas which I can't relate to each other to find the acceleration

Please post your working.

 

[Mohmmad Maaitah]

I'm not seeing that. The image of handwritten work in post #1 only seems to show torques on the left hand pulley, one acting CW, one CCW.

No he is right I thought that way

 

[Mohmmad Maaitah]

I do make a_1=a_2
But after that i cant link information

 

[haruspex]

I do make a_1=a_2
But after that i cant link information
View attachment 327310

What is the relationship between $a$ and $\alpha$? (Be careful with signs.)

 

[Mohmmad Maaitah]

What is the relationship between $a$ and $\alpha$? (Be careful with signs.)

a = α r
but how is the acceleration of the masses related to the angular acceleration of the pulley?

 

[haruspex]

a = α r
but how is the acceleration of the masses related to the angular acceleration of the pulley?

By (something very like) that equation. The strings do not slip on the pulleys, so the distances the masses move are directly related to the angles through which the pulleys turn.
But I said to be careful with signs. In your torque equations, you have taken $\alpha$ as positive anticlockwise; in your linear acceleration equations, you have taken $a$ as positive up on the left and positive down on the right. Think about it.

 

[Mohmmad Maaitah]

I read the chapter again and I still don't get how to determine the signs.
can you refer to something that explain it?

 

[Mohmmad Maaitah]

I know how to deal with signs when torque isn't in
but when it is to be computed I don't know how to chose right signs and should I have same positive and negative for all masses and pulleys or what is it!

 

[erobz]

I know how to deal with signs when torque isn't in
but when it is to be computed I don't know how to chose right signs and should I have same positive and negative for all masses and pulleys or what is it!

There is no single "correct" answer, but there are some choices that can give you a headache.

I would use a single convention. Focusing on one of the masses for the moment: We suspect the mass $M_2$ is moving downward? I would make $\downarrow^+$. I would then choose an angular convention such that a positive angular acceleration of the pulley corresponds to a positive linear acceleration of $M_2$. For my choice that implies $\circlearrowright^+$.

Write all equations (for both masses and pulleys) in terms of that single convention ( $\downarrow^+$, $\circlearrowright^+$) and the constraints (inextensible rope).

The important part is that you imagine correctly what is happening throughout the system if the mass you chose, is moving in the direction you chose. It is not important that you correctly identify which way the mass you chose to focus on actually moves.

 

[haruspex]

I read the chapter again and I still don't get how to determine the signs.
can you refer to something that explain it?

The way you have used $a$ and $\alpha$ in your equations, if the right hand mass descends then $a$ is positive but $\alpha$ will be negative. Do you see that?
That is ok, but it means that $a=r\alpha$ must be wrong. What is correct relationship?

 

[erobz]

Please take a few moments to learn how to typeset mathematics in the forum. See LaTeX Guide

 

[Mohmmad Maaitah]

The way you have used $a$ and $\alpha$ in your equations, if the right hand mass descends then $a$ is positive but $\alpha$ will be negative. Do you see that?
That is ok, but it means that $a=r\alpha$ must be wrong. What is correct relationship?

Should had a minus over there.
I got the problem thanks guys.