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Newton created the modern concept of force starting from his insight that all the effects that govern motion are interactions between two objects: unlike the Aristotelian theory, Newtonian physics has no phenomena in which an object changes its own motion.

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Is one object always the “order-giver” and the other the “order-follower”? As an example, consider a batter hitting a baseball. The bat definitely exerts a large force on the ball, because the ball accelerates drastically. But if you have ever hit a baseball, you also know that the ball makes a force on the bat—often with painful results if your technique is as bad as mine!

How does the ball’s force on the bat compare with the bat’s force on the ball? The bat’s acceleration is not as spectacular as the ball’s, but maybe we should not expect it to be, since the bat’s mass is much greater. In fact, careful measurements of both objects’ masses and accelerations would show that mballaballmballaball is very nearly equal to −mbatabat−mbatabat, which suggests that the ball’s force on the bat is of the same magnitude as the bat’s force on the ball, but in the opposite direction.

Forces occur in equal and opposite pairs: whenever object A exerts a force on object B, object B must also be exerting a force on object A. The two forces are equal in magnitude and opposite in direction.

In one-dimensional situations, we can use plus and minus signs to indicate the directions of forces, and Newton’s third law can be written succinctly as FA on B=−FB on AFA on B=−FB on A.

There is no cause and effect relationship between the two forces in Newton’s third law. There is no “original” force, and neither one is a response to the other. The pair of forces is a relationship, like marriage, not a back-and-forth process like a tennis match. Newton came up with the third law as a generalization about all the types of forces with which he was familiar, such as frictional and gravitational forces. When later physicists discovered a new type of force, such as the force that holds atomic nuclei together, they had to check whether it obeyed Newton’s third law. So far, no violation of the third law has ever been discovered, whereas the first and second laws were shown to have limitations by Einstein and the pioneers of atomic physics.

The English vocabulary for describing forces is unfortunately rooted in Aristotelianism, and often implies incorrectly that forces are one-way relationships. It is unfortunate that a half-truth such as “the table exerts an upward force on the book” is so easily expressed, while a more complete and correct description ends up sounding awkward or strange: “the table and the book interact via a force,” or “the table and book participate in a force.”

To students, it often sounds as though Newton’s third law implies nothing could ever change its motion, since the two equal and opposite forces would always cancel. The two forces, however, are always on two different objects, so it doesn’t make sense to add them in the first place—we only add forces that are acting on the same object. If two objects are interacting via a force and no other forces are involved, then both objects will accelerate—in opposite directions!

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