Newton's third law of motion

Suppose, for the sake of argument, that there are only two bodies in the Universe. Let us label these bodies $a$ and $b$. Suppose that body $b$ exerts a force ${\bf f}_{ab}$ on body $a$. According to to Newton's third law of motion, body $a$ must exert an equal and opposite force ${\bf f}_{ba}=-{\bf f}_{ab}$ on body $b$. See Fig. 22. Thus, if we label ${\bf f}_{ab}$ the ``action'' then, in Newton's language, ${\bf f}_{ba}$ is the equal and opposed ``reaction''.

Suppose, now, that there are many objects in the Universe (as is, indeed, the case). According to Newton's third law, if object $j$ exerts a force ${\bf f}_{ij}$ on object $i$ then object $i$ must exert an equal and opposite force ${\bf f}_{ji}=-{\bf f}_{ij}$ on object $j$. It follows that all of the forces acting in the Universe can ultimately be grouped into equal and opposite action-reaction pairs. Note, incidentally, that an action and its associated reaction always act on different bodies.

Figure 23: Newton's third law

Why do we need Newton's third law? Actually, it is almost a matter of common sense. Suppose that bodies $a$ and $b$ constitute an isolated system. If ${\bf f}_{ba}\neq -{\bf f}_{ab}$ then this system exerts a non-zero net force ${\bf f} = {\bf f}_{ab}+{\bf f}_{ba}$ on itself, without the aid of any external agency. It will, therefore, accelerate forever under its own steam. We know, from experience, that this sort of behaviour does not occur in real life. For instance, I cannot grab hold of my shoelaces and, thereby, pick myself up off the ground. In other words, I cannot self-generate a force which will spontaneously lift me into the air: I need to exert forces on other objects around me in order to achieve this. Thus, Newton's third law essentially acts as a guarantee against the absurdity of self-generated forces.