Newton's Third Law Explained

Understanding the Third Law

Newton's third law is often summarized as "for every action, there is an equal and opposite reaction," but this compact phrase can be misleading. The law specifically says that forces always come in pairs. If object A pushes on object B with a force of 50 newtons to the right, then object B pushes on object A with a force of 50 newtons to the left. The two forces are always equal in magnitude, always opposite in direction, and always act on different objects.

The "different objects" part is critical. Action-reaction pairs never act on the same object, which means they never cancel each other out. When you push against a wall, the wall pushes back on you. These forces are equal and opposite, but one acts on you and the other acts on the wall. They are part of different free-body diagrams and cannot be combined into a single net force.

The third law applies instantly and universally. There is no delay between the action and the reaction. The moment you press your hand against a table, the table presses back with exactly the same force. This simultaneity holds even for gravitational forces: Earth pulls the Moon toward it, and the Moon pulls Earth toward it with exactly the same force at every instant.

Identifying Action-Reaction Pairs

A reliable method for identifying action-reaction pairs is to state the forces using the phrase "A exerts a force on B" and then reverse it: "B exerts a force on A." The two forces have equal magnitudes and opposite directions. For example: your feet push backward on the ground (action), and the ground pushes forward on your feet (reaction). Earth pulls you downward with gravity, and you pull Earth upward with gravity.

Students often confuse action-reaction pairs with balanced forces. Balanced forces are two forces acting on the same object that sum to zero. A book on a table has gravity pulling it down and the normal force pushing it up. These forces are balanced, but they are not an action-reaction pair. The action-reaction partner of the book's weight is the book pulling Earth upward. The action-reaction partner of the normal force on the book is the book pushing down on the table.

In every interaction, both forces exist simultaneously. There is no meaningful distinction between which force is the "action" and which is the "reaction." The labels are arbitrary and either force could be called the action.

Walking, Swimming, and Driving

Walking is a perfect demonstration of the third law. When you take a step, your foot pushes backward against the ground. By the third law, the ground pushes forward on your foot, and this forward force is what propels you. Without friction between your shoe and the ground, your foot would slip backward and you could not walk, which is why walking on ice is so difficult.

Swimming works on exactly the same principle. A swimmer pushes water backward with each stroke, and the water pushes the swimmer forward. The more water a swimmer displaces backward, and the faster they push it, the greater the forward reaction force. This is why larger, cupped hands are more effective than flat, streamlined hands when swimming for propulsion.

Cars move forward because the engine spins the wheels, which push backward against the road through friction. The road pushes forward on the tires, propelling the car. On a frictionless surface, the wheels would spin freely without moving the car, because there would be no backward push on the road and therefore no forward reaction force.

In each of these cases, the object doing the pushing cannot propel itself without something to push against. This is why you cannot pull yourself up by your own bootstraps, and it is why vehicles need friction to accelerate. Something external must be involved in the force pair.

Rocket Propulsion

Rockets seem to violate the requirement for "something to push against," but they do not. A rocket engine burns fuel to produce hot exhaust gases, which are expelled at high velocity from the nozzle. The rocket pushes the exhaust gases backward (action), and the exhaust gases push the rocket forward (reaction). The rocket carries its own reaction mass in the form of propellant, so it does not need air, ground, or any external medium to push against.

This is why rockets work in the vacuum of space, where there is nothing around them. The exhaust gases themselves are the other object in the action-reaction pair. The more mass expelled and the faster it is expelled, the greater the thrust force on the rocket. This relationship is quantified by the Tsiolkovsky rocket equation, which shows how velocity change depends on exhaust velocity and mass ratio.

Jet engines work on a similar principle, but they use atmospheric air as the working fluid. The engine takes in air, mixes it with fuel, and expels the hot exhaust backward at high speed. Unlike rockets, jet engines require an atmosphere to operate because they need air as part of the action-reaction pair.

Gravity and the Third Law

Gravitational forces obey the third law perfectly. Earth's gravity pulls a 70-kilogram person downward with a force of about 686 newtons. Simultaneously, that person's gravity pulls Earth upward with a force of exactly 686 newtons. The forces are identical in magnitude. We notice the effect on the person but not on Earth because of the enormous difference in mass.

Using F = ma, the 686-newton force accelerates the 70-kilogram person at 9.8 m/s squared. The same force on Earth (mass approximately 6 times 10 to the 24th kilograms) produces an acceleration of about 1.1 times 10 to the minus 22 m/s squared, which is immeasurably small. Both objects accelerate, but the more massive one accelerates imperceptibly.

This same principle applies to the Sun and planets. The Sun pulls Jupiter toward it, and Jupiter pulls the Sun toward it with equal force. The Sun barely wobbles, but it does wobble. Astronomers detect planets around distant stars by measuring these tiny wobbles, a method called the radial velocity technique.

Collisions and Force Pairs

During a collision between two objects, the forces they exert on each other are always equal and opposite at every instant. If a truck collides with a small car, the force the truck exerts on the car is exactly equal in magnitude to the force the car exerts on the truck. This surprises many people, who intuitively feel the truck must exert a larger force.

The difference in outcomes comes from Newton's second law, not the third. Equal forces on different masses produce different accelerations. The small car, with less mass, experiences a much larger acceleration (and therefore a more violent change in velocity) than the heavy truck. This is why occupants of smaller vehicles are typically at greater risk in collisions.

The same principle explains why catching a baseball hurts less if you let your hand move backward with the ball. The force between ball and hand is equal and opposite at every instant, but by extending the collision time, the average force decreases. The impulse must equal the ball's change in momentum regardless, but spreading it over more time reduces peak force.

Clearing Up Misconceptions

The biggest misconception is that action-reaction pairs cancel each other. Since the forces are equal and opposite, it seems like they should sum to zero. But they act on different objects, so they appear in different free-body diagrams and never combine into a single net force. A horse pulling a cart illustrates this: the horse also pushes backward on the ground, and the ground pushes the horse forward. As long as the ground's forward push exceeds the cart's backward pull, the system accelerates.

Another misconception is that the "action" happens first and the "reaction" follows. The two forces are perfectly simultaneous. There is no cause-and-effect ordering. The names are historical artifacts that suggest a time sequence that does not exist.

A third misconception is that stronger or heavier objects exert larger forces. They do not. When a bug hits a car windshield, the force the bug exerts on the windshield is exactly equal to the force the windshield exerts on the bug. The bug is destroyed because its small mass experiences enormous acceleration, while the car barely notices.