14 Examples of Newton's Third Law in Everyday Life: Action and Reaction Forces

Newton's Third Law of Motion states that for every action there is an equal and opposite reaction: whenever one object exerts a force on a second object, the second object exerts a force of the same magnitude in the opposite direction back on the first. This action-reaction principle explains why nothing that lies, stands, hangs, floats or flies simply falls through the ground, sinks or drops — each object stays put because it interacts with another object. Below are 14 examples of Newton's Third Law that govern how interacting bodies behave.

What Newton's Third Law of Motion is

Newton's Third Law is the principle of interaction: forces always come in pairs, and a single isolated force cannot exist. Isaac Newton set this down in his 1687 work Philosophiae Naturalis Principia Mathematica, alongside his first two laws of motion. Where the Newton's Second Law of Motion links force, mass and acceleration through the relationship F=ma, the Third Law describes what happens between two bodies whenever they push or pull on each other.

Definition and mathematical expression of the law

The mathematical form of Newton's Third Law is written as F₁₂ = −F₂₁, meaning the force object 1 exerts on object 2 is exactly equal in magnitude and opposite in direction to the force object 2 exerts on object 1. Force is a vector quantity — it has both magnitude and direction — so the minus sign captures the reversed direction while the equal magnitudes make the pair equal in strength. This holds true whether the two objects are a firefly and a bus in a collision or two planets separated by millions of kilometres: the forces they exchange are always equal in size.

Action and reaction force pairs

An action-reaction force pair consists of two forces that act on two different objects. This is the key point that keeps the law honest: the "action" is applied to one body and the "reaction" to the other, never both to the same body. When a swimmer pushes water backward, the water pushes the swimmer forward — the push and the return push are the action-reaction pair, and they land on separate objects. The same holds for a rocket and its exhaust gases, a foot and the ground, or an iron block and a magnet.

Common misconceptions about Newton's Third Law

The most widespread misconception is that action and reaction forces cancel each other out, leaving nothing to move anything. They do not cancel, because they act on different objects. Confusing an action-reaction pair with a balanced pair of forces on a single body is the mistake that trips up most students of dynamics.

Why action and reaction forces do not cancel each other

Action and reaction forces never cancel because cancellation requires two forces acting on the same object. A book resting on a table feels its own weight pulling it down and the table's normal force pushing it up — those two forces do act on the book and can balance, keeping it still. But the book also pushes down on the table with a force equal to the table's push on the book, and that downward push acts on the table, not the book. The Third Law pair is book-on-table and table-on-book; the balanced pair keeping the book at rest is weight-and-normal-force on the book alone.

Internal versus external forces in a system

Whether a force can move a system depends on whether it is internal or external to the chosen system boundary. Internal forces between parts of one system always come in Third Law pairs and cancel within that system, so they cannot accelerate it as a whole; only an external force applied from outside the system can. Choosing your system carefully — deciding what is inside the boundary and what is outside — is the first step in analysing any real problem, and it determines which forces you must draw on a free-body diagram.

14 examples of Newton's Third Law

Buildings, bridges, furniture in rooms, fruit on branches, trees, wires on poles, ships at sea, clouds in the sky, aircraft and balloons above the clouds — everything that lies, stands, hangs, floats or flies stays where it is only because it is in interaction with some other object. These objects — whether earth, a support, a suspension, water or air — act as a support, and the force of gravity that pulls everything toward the centre of the Earth meets a reactive response from that support.

That reactive response prevents gravity from setting objects in motion; it opposes gravity and balances it, much as one pan of a scale balances the other and stops it from dropping. This balancing lies at the heart of Newton's Third Law. A ship at anchor is in exactly the same situation, staying in place even when wind and current try to carry it off. The forces that arise in these cases are called reaction forces. They balance the force acting on the body and help it stay at rest. Here are 14 examples of such forces confirming Newton's Third Law, which appear during:

• bridge construction,
• building foundation construction,
• a parachutist's jump and sledding,
• the interaction of an iron block with a magnet,
• the attraction of the planets,
• jumping out of a boat,
• a helicopter's flight,
• motion in water,
• motion in air,
• motion along a road,
• a cart's motion along rails,
• a squirrel turning a wheel,
• a lineman climbing a pole,
• interaction with the Earth.

Bridge construction

During bridge construction, engineers must calculate in advance how far the bridge supports can counteract the load that will press down on them: whether they can bear it, and whether the supports have a sufficient reserve of counteraction — what builders call a safety margin.

These calculations use Newton's Third Law. Builders design the bridge supports so they can counteract any load that might appear on the bridge. They treat the supports as pressing on the bridge from below. Action always equals reaction — the two are equivalent and interchangeable — so structural engineers arrange the calculation whichever way is more convenient for them.

Building foundations

Engineers designing building foundations proceed in the same way. They know that ordinary soil can resist the weight of a building with a force of roughly two to three kilograms per square centimetre of foundation. Under this condition the action — the weight of the whole building — and the reaction — the soil's resistance — compress the foundation from above and below.

Two equal forces directed in opposite directions act on the foundation, exactly as Newton's Third Law describes. Such forces balance and cannot shift the foundation from its place, but they do squeeze it; and if the foundation's safety margin is insufficient, it will fail and the building will collapse.

The parachutist and the sled

A parachutist leaps from an aircraft and falls in a free-fall dive. The action here is obvious — the parachutist falls. But where is the reaction that Newton speaks of? It is completely imperceptible, and countless examples like this can be found.

Children who climb a snowy hill slide down it on a sled; a skier jumps from a ramp. An avalanche breaking loose from a mountain, raindrops falling from a cloud — in every case of falling the reaction is invisible and unfelt. But that does not mean it does not exist.

The parachutist falls because the Earth attracts him. But the attraction is mutual: the Earth pulls the parachutist toward itself, and the parachutist pulls the Earth toward himself. The parachutist falls toward the Earth, and the Earth "falls" toward the parachutist.

Because the parachutist's mass is negligible compared with the mass of the Earth, his motion is rapid, while the Earth's mass is enormous and its answering, oncoming motion is utterly undetectable — a direct consequence of the mass–acceleration relationship. All of this applies equally to a sled sliding down a hill. The sled's motion is also a fall, but one that takes place along a sloping path.

The interaction of an iron block with a magnet

This idea is illustrated by Newton's experiment with an iron block and a magnet floating in little boats. Newton became convinced that it is not the magnet attracting the iron, nor the iron being attracted to the magnet, but that both bodies interact — they pull toward each other. In Newton's experiments the magnet and the iron were equal in weight.

But imagine that for this experiment you took a very large, heavy magnet and a tiny iron block. In that case the magnet would move only slightly toward the iron, while the iron block would float toward the magnet far faster.

The same thing would happen if the piece of iron were large and the magnet small: the motion of the light object would be noticeable and clear, while the answering motion of the heavy object would be imperceptible.

The attraction of the planets

The same happens with the planets, governed by Newton's Law of Universal Gravitation, where the force between two bodies depends on their masses and the distance between them. If some large celestial body were to pass close to the Earth, the consequences of their mutual gravitation would become noticeable — and this actually occurs.

Sometimes the large planets of the solar system — Jupiter and Saturn — are positioned in space so that their gravitational pull causes the Earth to move slightly away from the Sun. When that happens, the length of our year — the time of the Earth's revolution around the Sun — increases by a few minutes. Later the large planets move farther along their orbits, and our year shortens again.

For example, the year 1946 was shorter than 1945 by roughly ten minutes, and 1945 was shorter than 1944 by about eleven minutes. Such changes in the length of our Earth's year, dependent on the positions of the other planets in the solar system, reveal how the third law of motion works far beyond the Earth — in the boundless expanse of space.

Jumping out of a boat

A person about to jump from a boat onto the shore should not forget that Newton's Third Law of Motion exists. Their action will inevitably produce an equal and oppositely directed reaction: at the moment of the jump the boat moves backward, and the careless person ends up not on the shore but in the water.

Cursing Newton's Third Law is useless — the jumper should have asked those in the boat to brace an oar against the bottom.

A helicopter in flight

The history of technology records a case in which the inventors of an important and useful machine — the helicopter — failed to think through the design carefully enough and overlooked the third law of motion.

A helicopter, unlike an ordinary airplane, can rise into the air not with a run-up but vertically upward.

The lifting force of this machine comes from a large propeller rotating on a vertical axis. When the first helicopter was tested at an airfield, the third law of motion made itself known. Because the lifting propeller rotated from right to left, the Third Law caused the helicopter's body to rotate in the opposite direction — from left to right.

The helicopter turned into a kind of flying carousel that no passenger would agree to sit in. This defect was eliminated by fitting two lifting propellers rotating in opposite directions. Then the unpleasant carousel motion of the machine stopped at once, because the rotors turned in opposite directions and their harmful effects cancelled each other out, while the upward lifting force was preserved. Single-rotor helicopters carry an additional tail rotor that counteracts the rotation of the body.

How things that swim in water move

Everything that swims in and on the water — fish, ducks, beavers, eels, frogs, diving beetles (more here: Enemies of fish) and other water creatures, as well as steamers, motorboats and rowboats — moves forward only because it is in interaction with the water, just as Newton describes.

With propellers, oars, fins, tails and paws they push the water backward, and by the answering reaction they themselves move forward. Fish propulsion through water and swimming both rely on this reaction force.

How everything that flies moves

Everything that flies — airplanes, helicopters, birds, butterflies, mosquitoes, bats, and also aerosleds and hydroplanes — moves only because it is in interaction with the air. They push the air backward, and by the answering reaction they themselves move forward. Bird flight and airplane flight are both applications of this same action-reaction principle, with drag opposing the motion.

But what land dwellers push backward — creatures that move using legs and wheels — remains unclear until we look at how they interact with their support.

How cars and trains move

They push against what serves as their support: locomotives push against the rails; cars and horses push against the asphalt of highways and pavements. The rails and the road surface are firmly bound to the earth, so everything moving over the ground pushes against the Earth, and the globe ought to turn in the direction opposite to the motion of the locomotive or the car.

The motion of objects as tiny compared with the Earth as locomotives and cars has no effect on the rotation speed of our planet. Moreover, all trains and cars move in different directions, and when one train travels to the right, another at the same moment travels to the left.

Every car returns after work to the garage — to the place it left in the morning. With oncoming traffic, its effect on the Earth cancels out mutually. This wheel-and-road interaction, driven by friction, is precisely what lets a car accelerate forward.

A cart's motion along rails

Imagine a long, light cart standing on rails. Its axles turn in ball bearings, the bearings are well greased, and so the cart can roll from one end of the rails to the other with almost no friction. A person stands at one edge of the cart. Ask that person to run across the cart to its other end.

As soon as the person runs, the cart also begins to move: it rolls in the direction opposite to the person's motion. The person stops, and the cart stops. The person runs back, and the cart rolls the other way.

The person's motion in one direction forces the cart to move in the opposite direction. The action produces a reaction, and the two are equal: if the cart has the same mass as the person, then relative to the ground it rolls aside exactly as far as the person advances. This is momentum conservation in action, and it follows directly from Newton's Third Law.

A squirrel in a wheel

Long ago people invented a toy that demonstrates the law of interaction — Newton's Third Law — in a simple and convincing way. Hunters sometimes bring home little squirrel pups for children to play with. The pups grow, get used to people and to life in captivity, and become tame. Yet it is hard for them to live in cramped houses.

In the forest a squirrel is in motion all day — from branch to branch, from tree to tree — but indoors there is nowhere for it to turn. And so, perhaps a thousand years ago, people invented "physical education" for squirrels: a wheel built like a drum so the squirrel could run inside it. The squirrel is let into the wheel, it starts to run, and the wheel begins to turn in the opposite direction, spinning as long as the squirrel runs inside.

Of course the squirrel wheel must be stopped from time to time to let the animal out to rest and eat, since squirrels are foolish and may run to exhaustion. The squirrel wheel is a remarkable and vivid proof of the third law of motion: the interaction of two bodies causes both — squirrel and wheel — to move.

Here the action and the reaction produce visible motion. The action and the reaction are equal: when the squirrel runs slowly, the wheel turns slowly, and when the squirrel speeds up, the wheel turns faster. And the action and reaction are opposite: the squirrel runs one way while the wheel spins the other.

On foot up a pole

Telecom workers and electricians, who often have to climb telegraph poles, carry a very simple device called "cat spikes" or gaffs. These are two iron arcs with sharp teeth and a small platform for the foot; in shape they resemble sickles or the large mandibles of a stag beetle.

The lineman straps the gaffs onto his feet and — walking awkwardly, because moving over the ground in them is very uncomfortable — approaches the pole. There he wraps one gaff around the pole and its spikes bite into the wood or concrete.

Holding onto the pole with his hands, the lineman shifts his whole body weight onto that gaff and at the same time swings the second gaff up so it grips higher than the first. Then he transfers his weight to the second gaff and moves the first one still higher.

In this way he "walks" up a smooth vertical pole as if up a staircase. The sharp teeth of the gaffs give the lineman a reliable interaction with the pole — good purchase for the foot. Without interaction with the pole the lineman could not climb it, and it is precisely this that Newton captured in his law.

Interaction with the Earth

In short, everything that runs, crawls, jumps, walks, flies, swims and climbs can move only because it is in interaction with the earth, water, air, rails, tree trunks, poles, ropes or the lianas of a tropical forest.

In every case, without exception, the action of one object always meets an equal and oppositely directed reaction from the other surrounding objects. The word "reaction" that Newton used should not be taken literally — the reaction exerted on a moving object does not hinder it, does not act against it or in defiance of it; on the contrary, it is precisely what helps and enables the motion.

What appears is simply a reaction force directed opposite to the action force.

It should be noted that action and reaction are always applied to different objects: the action goes to the earth, water, air, the pole, the rails, ropes, poles, the highway asphalt and so on, while the reaction goes to legs, paws, wheels, hooves, tracks, wings, fins, ships' propellers, aircraft propellers and the linemen's gaffs.

The conclusion is somewhat surprising. It turns out we move not so much because of our own action as because of the reaction. When we walk, the effort of our legs is aimed at pushing the earth, yet we go forward only because the earth pushes us. This may seem strange, but it is exactly so.

In a world without friction — that is, without interaction between bodies — a person could only shuffle his legs and would never manage to move from the spot.

When a person walks, he does not notice how the earth "pushes" him. Everyone thinks he walks by himself, but this small illusion arises because he directs his own action — it catches the eye — while the reaction draws no attention. Yet it is possible to arrange things so that the direct action and the reaction become equally noticeable, as in Newton's experiments.

Further examples from nature and technology

Beyond the classic fourteen, action-reaction pairs show up in propulsion, sport, and everyday objects. Each of the following is a real-world application of Newton's Third Law in which the reaction force does the useful work.

Recoil when a cannon fires

When a cannon fires, the gun barrel pushes the shell forward while the shell pushes the barrel backward with an equal force — the recoil. The same holds for rifles: the rifle drives the bullet forward and the bullet drives the rifle back into the shooter's shoulder. Because the bullet's mass is tiny and the rifle's is large, the bullet gains a huge acceleration while the rifle recoils only slightly, again reflecting the mass–acceleration relationship of Newton's Second Law. A gun fired by someone standing on a skateboard would send the shooter rolling backward for exactly the same reason.

Jet propulsion of a rocket and a balloon

A rocket rises because it throws hot exhaust gases downward and backward, and the gases push the rocket forward with an equal reaction force called thrust. This is why rockets work in the vacuum of space, where there is nothing external to push against — the rocket pushes on its own expelled gas. Release the neck of an inflated balloon and it darts around the room on the same principle: the balloon pushes air out one way and the escaping air pushes the balloon the other way.

Bird flight and pushing against the air

Birds fly by beating their wings downward and backward against the air, and the air pushes back up and forward with an equal reaction, producing lift and forward thrust. Air resistance, or drag, opposes the bird's motion, but the reaction of the pushed-aside air is what keeps the bird aloft. Airplanes and helicopters generate the same action-reaction effect through wings and rotors rather than flapping feathers.

A ball bouncing off a surface

When a ball strikes the ground it pushes down on the surface, and the surface pushes back up on the ball with an equal force. This reaction, combined with the elasticity of the ball, is what launches it back upward. The harder the ball hits — the greater its action force — the greater the reaction and the higher it rebounds.

Jet propulsion in water: the octopus and the jet ski

An octopus moves by drawing water into its body cavity and forcing it out through a siphon; the expelled water pushes the octopus in the opposite direction, giving it a burst of speed. A jet ski uses the same idea mechanically, drawing in water and shooting it out backward so the reaction drives the craft forward. Both are aquatic versions of rocket-style jet propulsion.

A book on a table: the normal force

A book lying on a table presses down on the table with a force equal to its weight, and the table presses up on the book with an equal reaction — the normal force, which always acts perpendicular to the contact surface. It is worth repeating that this book-on-table / table-on-book pair is the true Third Law pair, while the balanced forces that keep the book at rest (its weight and the normal force acting on the book) are a separate matter. The normal force is a contact force, distinct from action-at-a-distance forces such as gravity and magnetism.

Solving problems with Newton's Third Law

To solve real dynamics problems involving several objects, define your system, draw a free-body diagram for each object showing only the forces acting on it, and apply Newton's Second Law (F=ma) to each. A reliable habit is to check that any two forces you call an action-reaction pair act on two different objects and are of the same type — if they act on the same body, they are not a Third Law pair. Careful system selection turns an intimidating multi-object problem into a set of manageable equations.

Block systems and contact forces

When two blocks are pushed together across a surface, the front block pushes back on the rear block exactly as hard as the rear block pushes on the front — a contact-force action-reaction pair. To find the acceleration of the whole system, treat both blocks as one system and divide the external force by the combined mass. To find the contact force between them, draw a free-body diagram for a single block and apply F=ma to that block alone. The same approach handles a cart towing equipment or any chain of connected objects.

The Atwood machine

An Atwood machine — two masses hanging from a rope over a pulley — is a classic setting for applying Newton's laws with tension and gravity. In an ideal string over a frictionless, massless pulley the tension is the same throughout, and the tension the rope exerts on each mass pairs with the pull each mass exerts on the rope. Writing F=ma for each mass separately, then combining the two equations, gives the system's acceleration and the rope tension. This equilibrium-and-tension analysis extends to rope tension in climbing, pulley systems in gym equipment, and elevator cables, where the same Third Law pairs and tension reasoning apply.