# Relation between force couple and newton's third law

1. Aug 14, 2014

### swayne221b

After being through with Newton's 3rd law of action reaction pairs, there arise a doubt regarding the categorization of force couple (related to torque) of being or NOT being an example of action reaction pairs.

2. Aug 15, 2014

### Simon Bridge

Not.

3. Aug 15, 2014

### swayne221b

Can you briefly explain?

4. Aug 15, 2014

### Simon Bridge

Action-reaction pairs have the same line of action.

5. Aug 15, 2014

### swayne221b

Got it, thanks.

6. Aug 15, 2014

### D H

Staff Emeritus
That's the strong form of Newton's third law. The weak form does not require that condition. It merely requires that action-reaction pairs be equal but opposite.

However, even in the context of the weak form of Newton's third law, the forces in a couple do NOT constitute an action-reaction pair. There's another very important part of Newton's third law that applies in both the weak and strong forms of the law: The forces in the action-reaction pair operate on two different objects. In the case of the question posed in the opening post, the two forces are acting on but one object, so they are not an action-reaction pair.

Below are some simple tests to determine whether two forces constitute an action-reaction pair:
1. Are the forces equal in magnitude but opposite in direction?
If they aren't, the forces are not an action-reaction pair.
2. Do the forces act on two different objects?
If both forces act on the same object they are not an action-reaction pair.
3. Are the two objects responsible for the forces?
In other words, object A must be responsible the force acting on object B, and object B must be responsible for the force acting on object A. If this is not the case, the forces in question do not constitute an action-reaction pair.
4. Is it the same force?
If not, the forces do not constitute an action-reaction pair. For example, the reaction to gravitation is gravitation and the reaction to the Coulomb force is the Coulomb force. The action-reaction pair of forces are caused by a single interaction between pairs of objects.

Consider a book sitting on a table in a vacuum chamber at the South pole. The forces on the book are the downward force of gravitation toward the Earth as a whole and the upward normal force exerted by the table. While these are equal but opposite forces (so they pass test #1), they do not constitute an action-reaction pair. These forces fail tests #2 and #4. Both forces act on the book, and the underlying causes of these forces are very different. The third law counterparts to these two forces are the gravitational force the book exerts on the Earth and the normal force the book exerts on the table.

7. Aug 15, 2014

### swayne221b

D H, I owe you one. Cleared every minute detail.