symmetry
4.4 Newtons Third Law of Motion: Symmetry in Forces There is a passage in the musical Man of la Mancha that relates to Newtons third law of motion. Sancho, in describing a fight with his wife to Don Quixote, says, Of course I hit her back, Your Grace, but shes a lot harder than me and you know what they say, Whether the stone hits the pitcher or the pitcher hits the stone, its going to be bad for the pitcher. This is exactly what happens whenever one body exerts a force on anotherthe first also experiences a force equal in magnitude and opposite in direction . Numerous common experiences, such as stubbing a toe or throwing a ball, confirm this. It is precisely stated in Newtons third law of motion. Newtons Third Law of Motion Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts. This law represents a certain symmetry in nature: Forces always occur in pairs, and one body cannot exert a force on another without experiencing a force itself. We sometimes refer to this law loosely as action-reaction, where the force exerted is the action and the force experienced as a consequence is the reaction. Newtons third law has practical uses in analyzing the origin of forces and understanding which forces are external to a system. We can readily see Newtons third law at work by taking a look at how people move about. Consider a swimmer pushing off from the side of a pool, as illustrated in Figure 4.9. She pushes against the pool wall with her feet and accelerates in the direction opposite to that of her push. The wall has exerted an equal and opposite force back on the swimmer. You might think that two equal and opposite forces would cancel, but they do not because they act on different systems. In this case, there are two systems that we could investigate: the swimmer or the wall. If we select the swimmer to be the system of interest, as in the figure, then F wall on feet is an external force on this system and affects its motion. The swimmer moves in the direction of.