Many students grapple with Newton’s Laws of Motion, notably the Third Law as often stated in textbooks. Chapter Six (full chapter as PDF at link) presents Newton’s Laws, notably a restatement of the Third Law: ‘All forces come as action-reaction pairs’ and a list of properties of those pairs, starting with ‘the forces in an action-reaction pair are always on two different objects.’ A sampling from that chapter:
Newton’s three Laws of Motion are:
The Second Law, which tells us that
dp /dt = F.
In this equation, F is the total force on the mass m due to all forces acting on it. Forces are vectors and add as vectors.
The First Law (which is actually a corollary of the Second Law) tells us that if there is no force on an object, then the object continues to move in a straight line without changing its speed.
And, finally, there is The Third Law, which I will give as all forces come in action-reaction pairs. Newton gave a somewhat different phrasing for this law, one which is a bit hard to follow. You’ll find that my phrasing and explanation of the Third Law makes things much clearer.
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My statement of the Third Law is quite different from the one you will have encountered elsewhere, the statement represented as an exact translation of Newton’s words. The form you will read here does have exactly the same content. However, the point of having the Third Law is to get across a certain amount of information, not to repeat the not very good English translation, from centuries ago, of Newton’s original book, which was, of course, written entirely in Latin, in the form of a plane geometry text.
The Third Law tells us:
All forces come in action-reaction pairs. If we call the two forces of an action-reaction pair F_1 and F_2, their properties are as follows.
1) The forces of an action-reaction pair are always on two different bodies. Two forces on the same body are never an action-reaction pair.
2) The forces in an action-reaction pair are equal in magnitude, so that F_1 = F_2.
3) The forces in an action-reaction pair point in opposite directions, so that F_1 = -F_2. (Note plain face for magnitudes, bold face for vectors.)
4) The forces in an action-reaction pair have the same physical basis. What do I mean physical basis? The answer will become clearer after further discussion.
5) The action and reaction forces are simultaneous. By simultaneous I mean that it is incorrect to ask which force is the action force and which force is the reaction force. The two forces always come as a pair. If you call one of the two forces the action force, then the other of the two forces is the reaction force, but it does not matter which of the two forces you called the action force. …
As a modest qualification, if one studies intermolecular forces there are also three-body forces in which three molecules put a force on each other that cannot be split into a trio of pair forces. Three-body forces are actually quite important in properties of liquids, but for this course we will neglect three-body forces.