Newton's Third Law of Motion and Its Examples

Newton's third law of motion states: to every action there is an equal and opposite reaction, or more precisely, whenever one body exerts a force on a second body, the second body simultaneously exerts a force of exactly equal magnitude, but in exactly the opposite direction, back on the first body. This pair of forces is called an action-reaction pair. Two features of this pair are worth stating carefully, because they are the two most common sources of confusion:

First, the two forces of an action-reaction pair act on two different bodies, never on the same body, and this is exactly why they never cancel each other out even though they are equal and opposite -- forces can only be added together (to find whether a body is in equilibrium) when they act on the same body. Second, neither force in the pair is somehow the "cause" and the other the "effect" -- the two forces appear together, at the very same instant, as a single physical interaction between two bodies; there is no meaningful sense in which one happens first.

A frequent conceptual trap is to mistake a book resting on a table for an example of the third law: the book's weight $mg$ (pulled down by the Earth) and the table's normal reaction $N$ (pushed up on the book) do happen to be equal in magnitude when the book is in equilibrium, but they act on the same body -- the book -- and are related instead by Newton's first law (equilibrium: net force zero), not the third. The genuine third-law pairs in this situation are, instead: the book pushes down on the table with a force $N'$ (acting on the table), and the table pushes back up on the book with $N$ (acting on the book), with $N = N'$; and separately, the Earth pulls the book down with force $mg$ (acting on the book), and the book pulls the Earth up with an equal force $mg$ (acting on the Earth, though its effect on so vast a mass is utterly negligible).

The action-reaction pairing shows up throughout ordinary experience. When a person walks, their foot pushes backward against the ground; by the third law, the ground simultaneously pushes the foot forward with an equal force, and it is this reaction force from the ground that actually propels the person forward. A swimmer pushes backward on the water with their hands and feet, and it is the water's equal, forward-directed reaction that propels the swimmer ahead (see the figure). The recoil felt when firing a gun is the gun pushing back on the shoulder with a force exactly equal to the forward force the gun exerts on the bullet -- Section 4.6 works through this quantitatively using momentum conservation. …