What are the common challenges in determining the direction of couple moments?

[Dino311]

Homework Statement

This is not a specific homework question, but it is a coursework question.

I am having trouble with determining the direction for the moment of a couple. I understand that with couples in general, there is a force negative and a force positive separated by some perpendicular distance.

Homework Equations

vector M = vector r X vector F

The Attempt at a Solution

When I do the cross product, my answer does not always give me the right direction.
When I use the right hand rule, which force do I align my hand with? Negative or positive?

Also, when doing the cross product with my TI-89 calculator, which force do I include, negative or positive? I understand that the cross product is not communicative, and my book is very sketchy about this. I have been trying to figure this out on my own for a few days with no success.
Thank you.

 

[PhanthomJay]

Homework Statement

This is not a specific homework question, but it is a coursework question.

I am having trouble with determining the direction for the moment of a couple.

The terms 'moment', 'torque', and 'couple' are sometimes used interchangeably, but there are slight distinctions between 'moment' and 'couple', notably, the 'moment' of a force is r x F, where its direction is determined by the right hand rule, (clockwise(conventionally as minus) versus counterclockwise (conventionally as plus)), whereas a couple is already a moment, clockwise or counterclockwise, independent of any r or F vector, or it may be 2 equal and forces separated by a perpendicular distance, where the plus or minus sign are determined using the same criteria.

I understand that with couples in general, there is a force negative and a force positive separated by some perpendicular distance.

actually, it's equal and opposite forces separated by a perpendicular distance.

Homework Equations

vector M = vector r X vector F

The Attempt at a Solution

When I do the cross product, my answer does not always give me the right direction.
When I use the right hand rule, which force do I align my hand with? Negative or positive?

It doesn't matter. With the fingers of your right hand lined up with either force, fingertips pointing toward the force arrow, and your thumb perpendicular to your fingers, curl your fingers toward the other force. The direction of your thumb toward the thumbnail is the direction of the moment, and the curl of your fingers will determine clockwise versus counterclockwise.

Also, when doing the cross product with my TI-89 calculator, which force do I include, negative or positive? I understand that the cross product is not communicative, and my book is very sketchy about this. I have been trying to figure this out on my own for a few days with no success.
Thank you.

Determine the sign of the moment on your own, clockwise is minus, counterclockwise is plus . The vector direction of the moment or couple is always perpendicular to the plane of the moment or couple.

 

[Dino311]

It doesn't matter. With the fingers of your right hand lined up with either force, fingertips pointing toward the force arrow, and your thumb perpendicular to your fingers, curl your fingers toward the other force. The direction of your thumb toward the thumbnail is the direction of the moment, and the curl of your fingers will determine clockwise versus counterclockwise.Determine the sign of the moment on your own, clockwise is minus, counterclockwise is plus . The vector direction of the moment or couple is always perpendicular to the plane of the moment or couple.

Here lies my problem, and I wish I had a scanner to depict this, but I will describe it:

a horizontal force directed right and is 200N --------->
another horizontal force directed left and is 200N <---------
the perpendicular distance is .2m

Now, when I align my hand along either force and curl towards the other, I always get a negative moment (clockwise). However, my book says the moment is positive. The only way that I could see the moment would be positive is if I aligned my right hand opposite the arrow and curled toward the other force.

What can I do in situations such as this?

 

[PhanthomJay]

The terms positive and negative, as applied to couples, moments, or torques, are a matter of convention or choice. The important fact here is the the couple is clockwise and its direction points into the plane of the screen (into the 3rd dimension 'z' axis in the pointing direction of your thumb). You can call that direction either positive or negative. Your book calls that direction positive...by convention, the 'into' direction is often called the negative direction. It is largely a matter of choice. In the same way, a clockwise moment per your book is called positive, whereas convention usually calls a clockwise moment as negative. It doesn't really much matter, as long as you are consistent. Your right hand rule method is correct.

 

[Dino311]

Thank you very much for your help. Unfortunately, my book defines counterclockwise direction as positive, which is why I was thoroughly confused. When I use the right hand rule with the problem I mentioned above, I always wind up pointing into the book and making clockwise motion with curling my fingers. Thank you.

 

[PhanthomJay]

Thank you very much for your help. Unfortunately, my book defines counterclockwise direction as positive, which is why I was thoroughly confused. When I use the right hand rule with the problem I mentioned above, I always wind up pointing into the book and making clockwise motion with curling my fingers. Thank you.

Yes, you are correct, it is a clockwise moment pointing into the book, so I don't understand the signage mixup either.

 

[pongo38]

The reason anticlockwise is positive is that the system is set up so that positive rotations are clockwise looking away from the origin, whichever axis it is. That is why, when you start trigonometry with an x-y frame of reference, the radius vector is said to rotate anticlockwise from Ox. You are looking towards the origin when you draw that figure.

 

[Dino311]

Okay, I have asked a teacher, and he says that occasionally the book switches from counterclockwise as positive to clockwise as positive, so that the answer won't be full of negatives, without first making a note of that change, even though the book mentions several times that clockwise is negative. We just have to pay extra attention to the sign conventions before the answer.

Thank you very much for your help.