1. Dec 4, 2005

### Pseudo Statistic

Hey,
I recently got Schaum's Outlines: Enginering Mechanics: Statics and Dynamics and started reading up on it...
Here's what confuses me from the text:
"A couple consists of two forces equal in magnitude and parallel, but oppositely directed."
Would that be similar to saying "A couple is pretty much a third-law force pair"?
That's what I "got" from that sentence, but hey, maybe I'm wrong.
Now, it proceeds to talk about replacing a single force:
"A single force F acting at point P may be replaced by (a) an equal and similarly directed force acting through any point O and (b) a couple C = r x F, where r is the vector from O to P."
Can someone explain why it would be justified to replace a single force by a couple? (Maybe I need a clarification on what a couple actually is)
Thanks a lot for any responses.

2. Dec 4, 2005

### Cexy

The definition given doesn't mention that a couple isn't co-linear - it's not clear from your post whether or not you realise this. A couple (or torque) is like an angular force - instead of acting to accelerate an object in a straight line, it accelerates it rotationally - i.e. starts to turn it about some axis.

3. Dec 4, 2005

### Staff: Mentor

Absolutely not! While it's true that the two forces comprising a couple are equal and opposite, they act on the same body. Third-law force pairs are always between two different interacting bodies and act along the same line.

They are not replacing a force by a couple! They are replacing one force by a second force (equal to the first but acting at a different point) plus a couple.

Realize that an applied force has two effects on an object: a "linear" effect (contributing to the net force on the object) and a "rotational" effect due to whatever torque it generates about some point. The "linear" effect is the same no matter where the force is applied, but the torque generated by a force depends on the point of application.

A couple exerts a torque but no net force. The original force F acting at point P exerts both a linear force (F) on the object plus a torque about point O. Applying the force F at point O would give the same linear force as before, but the torque about O would be zero. So, to properly duplicate the effect of the original force, you must add a couple to represent the torque about O.