Newton’s Third Law of Motion

Newton’s third law of motion explains why forces occur through interactions between objects. If a person pushes a box, the box pushes back on the person. If a swimmer pushes water backward, the water pushes the swimmer forward. If a rocket expels gases backward, those gases exert a forward force on the rocket. In every case, the two forces have equal magnitude and opposite direction, but they act on different objects.

The law is often remembered as “for every action, there is an equal and opposite reaction.” To apply it correctly, identify the two interacting objects and state which object exerts each force. This guide explains the definition, formula, action-reaction pairs, free-body diagrams, practical examples, worked calculations, common misconceptions, and applications of Newton’s 3rd law.

What Is Newton’s Third Law of Motion?

Newton’s third law of motion states that whenever one object exerts a force on another object, the second object simultaneously exerts a force of equal magnitude in the opposite direction on the first. The forces form an interaction pair. One force is exerted by object A on object B; the other is exerted by object B on object A. Neither force exists independently of the interaction. The law is commonly summarized as “for every action, there is an equal and opposite reaction.” In physics, action does not mean a deliberate human action, and reaction does not mean a delayed response. Both forces arise together. A person pushing a wall exerts a force on the wall, while the wall exerts an equal force back on the person. A swimmer pushes water backward, and the water pushes the swimmer forward. A rocket pushes exhaust gases backward, and the gases exert a forward force on the rocket. The defining feature is that the forces act on different objects. The force exerted by a hand on a box acts on the box. The force exerted by the box on the hand acts on the hand. They therefore do not cancel on the free-body diagram of either object considered separately. Newton’s third law is one of the three foundational laws of classical mechanics formulated by Sir Isaac Newton and published in *Philosophiæ Naturalis Principia Mathematica* in 1687. The first law describes inertia, the second relates net force to acceleration or change in momentum, and the third describes the mutual nature of interactions. Together, they provide a framework for understanding everyday motion, collisions, gravity, propulsion, and engineering systems.

Newton’s Third Law Formula

The mathematical expression is shown below. The notation identifies both the source of the force and the object receiving it.

Here, F(A on B) means the force exerted by object A on object B. F(B on A) means the force exerted by object B on object A. The minus sign indicates opposite vector directions. If a hand pushes a box to the right with 20 N, the box pushes the hand to the left with 20 N.

Force is a vector quantity. The SI unit is the newton (N), where one newton is one kilogram metre per second squared. The third-law equation identifies the paired interaction forces; it does not by itself give the net force or acceleration of either object.

How Action and Reaction Force Pairs Work

To identify a third-law pair, name the two interacting objects and describe each force in a complete sentence. For a person pushing a box, the person exerts a force on the box, and the box exerts an equal opposite force on the person. For Earth and an apple, Earth pulls the apple gravitationally toward its centre, while the apple pulls Earth toward the apple. For a book on a table, the book pushes down on the table, and the table pushes up on the book. A valid pair has five features: the forces are equal in magnitude, opposite in direction, simultaneous, of the same interaction type, and applied to two different objects. The objects do not need to touch. Contact interactions include pushing, friction, tension, and normal contact forces. Non-contact interactions include gravity, electric forces, and magnetic forces. Avoid writing only “action” and “reaction.” Those labels do not identify which object receives each force. Instead, write “hand on box” and “box on hand.” This simple naming method makes the pair clear and prevents errors in force diagrams.

Why Action and Reaction Forces Do Not Cancel

The most common misunderstanding is that action and reaction forces cancel each other. They do not cancel when considering one object because they act on different objects. Forces cancel on an object’s force diagram only when equal and opposite forces act on that same object. Imagine a student pushing a heavy box. The student applies a force to the box, and the box applies an equal opposite force to the student. The force on the student is not a force on the box. The box’s motion depends on all forces acting on the box, including the applied push, friction, gravity, and the floor’s normal force. The student’s motion depends on forces acting on the student, including the box’s contact force and friction from the ground. If the student and box are treated as one combined system, the forces they exert on each other are internal forces. They cancel in the combined system’s internal force accounting. External forces, such as friction from the floor, can still change the system’s total momentum. Always define the object or system before adding forces.

Everyday Examples of Newton’s Third Law

Walking is possible because a foot pushes the ground backward, while the ground exerts a forward frictional force on the foot. The forward force from the ground helps accelerate the person. On slippery ice, friction is limited, so the foot may slide and produce less forward traction. When a swimmer moves through a pool, the hands and feet push water backward. The water exerts forward forces on the swimmer. A rower uses the same principle: an oar pushes water backward, and the water pushes the oar forward. The oar transfers this force to the boat through its mounting. A person jumping pushes downward on the ground. The ground pushes upward on the person, contributing to acceleration during take-off. A balloon released without being tied allows air to rush out through its opening. The balloon pushes air in one direction, and the escaping air exerts a force on the balloon in the opposite direction. When a hammer strikes a nail, the hammer exerts a force on the nail, and the nail exerts an equal opposite force on the hammer. Their different motions depend on their masses, constraints, deformation, and other forces—not on unequal third-law forces.

Newton’s Third Law in Walking and Running

During a normal step, the foot pushes backward against the ground. Static friction from the ground acts forward on the foot. This forward frictional force helps accelerate the person. The third-law partner is the backward friction force exerted by the foot on the ground. The action-reaction pair is not “the person’s weight and the ground’s normal force.” Those two forces may balance while a person stands on a level surface, but both act on the person. The partner to the ground’s upward normal force on the person is the person’s downward contact force on the ground. Running uses the same interaction, often with larger and more rapidly changing forces. During push-off, the runner exerts a backward and downward force on the ground. The ground exerts a forward and upward force on the runner. The horizontal component contributes to forward motion, while the vertical component supports and accelerates the runner. On a surface with insufficient friction, the foot may slide rather than transmit a strong horizontal force. Footwear, surface texture, and technique affect traction. Newton’s third law identifies the paired forces; friction models and Newton’s second law help determine the resulting acceleration.

Newton’s Third Law in Swimming and Rowing

A swimmer advances by pushing water backward. The water exerts a forward force on the swimmer. The hands, forearms, and feet interact with the water, changing its momentum and producing propulsion. The swimmer’s movement also depends on drag, buoyancy, body position, and stroke timing. A rowing boat illustrates the same relationship. The blade of an oar pushes water backward as the rower drives the oar through the water. The water pushes the oar forward, and the oar transfers force to the boat through the oarlock. Propulsion depends on the direction and amount of momentum transferred, as well as resistance from the water. The water is not pushing the swimmer because the swimmer intends to move. The force arises from a physical interaction: the swimmer changes the motion of water, and the water exerts a corresponding force on the swimmer.

Newton’s Third Law in Rockets and Jet Engines

Rocket propulsion is a clear application of Newton’s third law. A rocket engine expels hot gases at high speed through a nozzle. The rocket exerts a force on the exhaust gases, accelerating them backward. The exhaust gases exert an equal and opposite force on the rocket, producing thrust forward. A rocket does not need to push against air to move. It carries propellant and expels reaction mass, so it can generate thrust in the vacuum of space. This differs from a car, which relies on friction between its tyres and the road for forward traction. A jet engine also produces thrust by accelerating air and combustion products rearward. The engine takes in air, adds energy through fuel combustion, and expels a high-speed exhaust stream. The detailed performance of a jet engine involves thermodynamics, fluid dynamics, pressure differences, and momentum conservation, but the paired-force principle remains central. The magnitude of thrust depends on the rate at which mass is expelled and the change in velocity of the exhaust, along with pressure effects at the nozzle. Newton’s third law provides the interaction picture; momentum principles provide a quantitative description.

Newton’s Third Law in Collisions

When two balls collide, each ball exerts a force on the other during contact. The force on ball A from ball B has the same magnitude and opposite direction as the force on ball B from ball A at every instant of the interaction. The forces can vary as the balls compress, deform, and separate, but they remain equal and opposite at corresponding instants. Equal forces do not necessarily produce equal accelerations. Newton’s second law states that acceleration depends on net force and mass. If a small ball and a much larger ball exert equal-magnitude forces on one another, the smaller ball generally experiences greater acceleration because its mass is lower. During a collision, each object’s momentum can change. For an isolated two-object system, total momentum is conserved even though each object’s individual momentum changes. The forces exchanged during the collision are internal to the system and transfer momentum between the objects. In a car crash, the car and obstacle exert equal and opposite forces on each other. Damage and motion can differ because masses, structures, restraints, deformation, and external constraints differ. Equal interaction forces do not require identical outcomes.

Newton’s Third Law: A Book on a Table

A book resting on a horizontal table provides a common classroom example. The table exerts an upward normal force on the book. The book exerts a downward contact force on the table. These forces form a third-law pair because they act on different objects and arise from the same contact interaction. The book’s weight is a separate force: Earth exerts a downward gravitational force on the book. If the book is at rest and there is no vertical acceleration, the upward normal force balances the book’s weight in the book’s free-body diagram. These two forces act on the same object, so they can balance each other. They are not a third-law pair. The gravitational partner to Earth’s force on the book is the book’s gravitational force on Earth. The normal-force partner to the table’s upward force on the book is the book’s downward force on the table. Naming the interacting objects prevents confusion between the two pairs.

Identifying Third-Law Pairs in Free-Body Diagrams

A free-body diagram represents the forces acting on one selected object. It is not a picture of every force in the whole situation. To use Newton’s third law correctly, draw a separate diagram for each interacting object or clearly label which object each force acts on. Choose the object under investigation and draw it as a dot or simple outline. Add arrows for all forces acting on it. Label each arrow with the source of the force and its direction. For a box on a floor, the forces on the box may include Earth’s gravitational force downward, the floor’s normal force upward, an applied push horizontally, and friction opposing relative sliding or impending motion. Next, identify the interaction partner for each force. If the floor exerts an upward normal force on the box, the box exerts a downward normal force on the floor. If a person pushes the box to the right, the box pushes the person to the left. The partner forces belong on diagrams of the other objects. Never put both members of a third-law pair on the same free-body diagram. When analysing a combined system, distinguish internal forces between system components from external forces exerted by objects outside the chosen system.

How Newton’s Third Law Relates to the First and Second Laws

Newton’s first law states that an object remains at rest or continues moving at constant velocity unless acted on by a non-zero net external force. It introduces inertia and inertial reference frames. Newton’s second law relates net force to the rate of change of momentum. For constant mass in an inertial frame, it is commonly written as F(net) = ma. The net force on an object determines its acceleration. A larger net force produces a larger acceleration for the same mass; a larger mass produces a smaller acceleration for the same net force. Newton’s third law states that forces between two interacting bodies occur in equal-and-opposite pairs. It does not by itself determine the acceleration of either body because each body’s acceleration depends on the net force acting on it and its mass. Consider two skaters pushing away from one another on low-friction ice. Each skater exerts a force on the other. The forces have equal magnitude and opposite direction. If the skaters have different masses, their accelerations differ. The lighter skater generally accelerates more. The third law explains the force pair; the second law explains the different accelerations.

Newton’s Third Law and Conservation of Momentum

Momentum is the product of an object’s mass and velocity. It is a vector quantity, so direction matters. In an isolated system, total momentum remains constant when the net external force on the system is zero. During an interaction between two bodies, the equal-and-opposite forces act over the same time interval. Their impulses are equal in magnitude and opposite in direction. An impulse changes momentum. One object gains momentum in one direction while the other gains an equal amount in the opposite direction, so the total momentum of the isolated pair remains unchanged. When two ice skaters push apart from rest, the total momentum is initially zero. After the push, one skater moves in one direction and the other moves in the opposite direction. Their momenta add vectorially to zero, assuming external horizontal forces are negligible. Conservation of momentum is useful for analysing explosions, recoil, collisions, and propulsion. Newton’s third law describes the paired forces, while the momentum principle provides a system-level account of the resulting changes in motion.

Newton’s Third Law and Gravity

Gravity is a mutual interaction between masses. Earth pulls an apple downward toward its centre, and the apple pulls Earth toward the apple. The gravitational forces have equal magnitude and opposite direction. The apple’s acceleration is noticeable because its mass is small compared with Earth’s mass. Earth’s acceleration toward the apple is extremely small because Earth’s mass is enormous. Equal forces do not imply equal motion. Acceleration depends on force divided by mass. A small mass can undergo a large acceleration while a very large mass undergoes a tiny acceleration under the same interaction force. The same principle applies to the Earth-Moon system. Earth and the Moon exert gravitational forces on each other. Both bodies move around their shared centre of mass, although Earth’s movement is much smaller because Earth has much greater mass. Newton’s law of universal gravitation quantifies the attraction between two masses. Newton’s third law establishes that the gravitational interaction is mutual.

Friction and Newton’s Third Law

Friction acts parallel to surfaces in contact and opposes relative sliding or the tendency to slide. If a shoe pushes backward on the ground, the ground can exert forward static friction on the shoe. These two friction forces form a third-law pair because they act on different objects. Static friction does not always equal its maximum possible value. It adjusts as needed to prevent slipping, up to a limiting value determined by the surfaces and normal force. Kinetic friction acts when surfaces slide relative to each other. In both cases, the friction force exerted by one surface on another has an equal-and-opposite partner on the other surface. A car accelerates forward because its driven tyres push backward on the road and the road exerts forward static friction on the tyres. Braking involves a different tyre-road interaction, and friction can act to slow the vehicle. The law identifies the pair, while friction models and Newton’s second law help calculate acceleration or stopping behaviour.

Newton’s Third Law in Sports

A footballer’s foot exerts a force on a ball, and the ball exerts an equal opposite force on the foot. The ball accelerates because the net force on it during contact is large relative to its mass. The player’s foot also experiences a force, which can be felt during impact. A tennis racket exerts a force on the ball, changing the ball’s velocity. The ball exerts an equal opposite force on the racket. In boxing, a glove exerts a force on an opponent, and the opponent exerts an equal opposite force on the glove. In cycling, the tyres push backward on the road at the contact patch when the rider pedals. The road exerts a forward friction force on the tyres, propelling the bicycle. In jumping, the athlete pushes down on the ground and the ground pushes upward on the athlete. Movement arises through interaction with another object or medium.

Applications in Engineering and Transport

Engineers apply Newton’s third law when designing vehicles, aircraft, ships, rockets, sports equipment, structures, and machines. A vehicle’s tyres exchange horizontal forces with the road. A propeller accelerates air or water in one direction and experiences thrust in the opposite direction. A ship’s propeller pushes water backward, producing a forward force on the vessel. In structural engineering, forces between connected components occur in pairs. A beam exerts forces on its supports, and the supports exert corresponding forces on the beam. Engineers use equilibrium equations, material properties, and structural analysis to determine whether components can withstand loads. In aerospace engineering, rocket thrust depends on accelerating exhaust gases. In aviation, wings interact with surrounding air, producing aerodynamic forces. The detailed explanation of lift involves pressure distributions and momentum changes in airflow, not merely a slogan that a wing pushes air down. Newton’s laws and fluid mechanics provide complementary descriptions. In mechanical engineering, gears, bearings, springs, linkages, and robotic grippers transmit forces between components. Accurate force diagrams are essential for calculating loads, stresses, motion, and stability.

Simple Experiments Demonstrating Newton’s Third Law

A balloon rocket is a simple demonstration. Thread a straw onto a long piece of string, stretch the string between two supports, inflate a balloon without tying it, and tape the balloon to the straw. Release the balloon opening. Air rushes backward and the balloon moves along the string in the opposite direction. The string constrains the balloon’s path, making the motion easy to observe. A pair of low-friction carts can demonstrate interaction forces. Place two carts together with a compressed spring or mechanism that pushes them apart. Release it. The carts move in opposite directions. If their masses differ, their accelerations and speeds may differ, while the interaction forces remain equal and opposite during the push. Two force sensors can measure the interaction directly. Attach them so they pull on each other. When one sensor pulls, the other records a force of equal magnitude in the opposite direction, within measurement uncertainty and calibration limits. Graphing both readings over time makes the simultaneous relationship visible. For a classroom investigation, identify the independent variable, measured quantities, controlled conditions, and likely sources of error. Repeat trials, record units, and distinguish the force on each sensor from the force exerted by each sensor.

Worked Examples: Applying Newton’s Third Law

Example 1: A person pushes a box to the right with a force of 35 N. The third-law partner is a 35 N force to the left exerted by the box on the person. The forces are equal, opposite, simultaneous, and applied to different objects. The box’s acceleration cannot be calculated from the push alone unless its mass and other forces are known. Example 2: Two skaters have masses of 50 kg and 75 kg. During a push, each exerts a horizontal force of 90 N on the other. If these are the net horizontal forces, the first skater’s acceleration magnitude is a = F/m = 90/50 = 1.8 m/s². The second skater’s acceleration magnitude is 90/75 = 1.2 m/s². The directions are opposite. The forces are equal; the accelerations differ because the masses differ. Example 3: A book rests on a table. The table exerts an upward normal force on the book, and the book exerts a downward normal force on the table. Earth’s gravitational force on the book pairs with the book’s gravitational force on Earth. The book’s weight and the table’s normal force both act on the book, so they are not a third-law pair. Example 4: A rocket engine exerts a 12,000 N backward force on exhaust gases. The gases exert a 12,000 N forward force on the rocket. This is the thrust interaction. The rocket’s acceleration still depends on its mass and all other forces.

Common Misconceptions About Newton’s Third Law

Misconception: action happens first and reaction later. Correction: both forces arise simultaneously as part of one interaction. Misconception: action and reaction cancel. Correction: they act on different objects, so they do not cancel on an individual object’s free-body diagram. Misconception: the larger object exerts a larger force. Correction: the interaction forces have equal magnitude. Different masses can produce different accelerations. Misconception: a stationary object has no forces acting on it. Correction: several forces can act while their vector sum is zero. A book on a table has weight and a normal force. Misconception: the normal force is always equal to weight. Correction: this is true only in particular conditions, such as a stationary object on a horizontal surface with no other vertical forces. Misconception: the law applies only when objects touch. Correction: gravitational, electric, and magnetic interactions can also form force pairs. Misconception: a rocket cannot move in space because there is no air to push against. Correction: a rocket expels propellant and exchanges momentum with its exhaust. Misconception: equal forces mean equal accelerations. Correction: acceleration also depends on mass and the other forces acting on each object.

A Reliable Method for Solving Newton’s Third-Law Questions

Use a consistent sequence. First, identify the two interacting objects. Second, state the force exerted by object A on object B. Third, state the force exerted by object B on object A. Fourth, check that the forces have equal magnitude and opposite direction. Fifth, confirm that they act on different objects. For numerical questions, write the vector relationship and substitute the given magnitude and direction. If the problem asks for acceleration, identify all forces on the object and calculate the net force before applying Newton’s second law. Do not assume the third-law partner belongs on the same free-body diagram. For a system question, define the system boundary. Internal force pairs cancel in the total-force accounting for the system, while external forces can change the system’s momentum. State assumptions such as negligible air resistance, a level surface, constant mass, or an isolated system when relevant. In written explanations, use complete labels. “The wall pushes back” is less precise than “the wall exerts a force on the person’s hands opposite to the force exerted by the hands on the wall.” Precision makes the physics easier to check.

How to Explain Newton’s Third Law in an Exam

A strong short-answer response should include the complete law, the equal-magnitude and opposite-direction relationship, and the fact that the forces act on different objects. A suitable answer is: “When object A exerts a force on object B, object B simultaneously exerts a force of equal magnitude and opposite direction on object A. The two forces act on different objects.” For an application question, identify both objects and describe both forces. If asked why a person moves when walking, explain that the foot pushes backward on the ground and the ground exerts a forward friction force on the foot. If asked why a rocket accelerates, explain that the rocket expels gases backward and the gases exert forward thrust on the rocket. For a diagram question, draw forces on separate objects. Label each arrow with the force source and recipient. Avoid drawing both members of a third-law pair on one object. If asked about acceleration, explain that equal forces do not require equal accelerations because the masses can differ.

Isaac Newton and Classical Mechanics

Sir Isaac Newton (1642–1727) presented the laws of motion in *Philosophiæ Naturalis Principia Mathematica*, first published in 1687. The work established a mathematical framework for describing motion and force and connected terrestrial mechanics with celestial motion. Newton’s laws became central to classical mechanics and influenced later developments in physics and engineering. Newton’s first law describes inertia, the second relates force to changes in motion, and the third describes mutual interactions. These laws are used together. Analysing a collision may require the third law to identify interaction forces, the second law to relate forces to acceleration, and momentum conservation to understand the motion of the complete system. Classical mechanics remains effective for many everyday systems, machines, vehicles, structures, and planetary motion. At very high speeds, very small scales, or in strong gravitational fields, more advanced theories may be required. For ordinary introductory mechanics, Newton’s laws provide the standard foundation.

Scope and Limitations of the Classical Model

Newton’s third law is a foundational principle in classical mechanics. Its simplest formulation is appropriate for ordinary mechanical interactions and most school and early university problems. In electromagnetic systems, momentum can also be carried by fields. A complete account of interacting charges and electromagnetic radiation may require including field momentum. At relativistic speeds, Newtonian definitions of momentum and force need modification. At quantum scales, classical trajectories and force pictures may no longer be the most useful description. These refinements define the range of the introductory model; they do not make it irrelevant. For standard classroom questions involving contact forces, gravity, collisions, and propulsion at ordinary speeds, identify the interacting bodies, pair the forces, and distinguish them from the net forces on each object.

Frequently Asked Questions About Newton’s Third Law

Key Points to Remember

Newton’s third law states that forces between two interacting objects occur in equal-magnitude, opposite-direction pairs. They act simultaneously on different objects. They may be contact forces, such as normal force and friction, or non-contact forces, such as gravity and electric force. The law explains interactions involved in walking, jumping, swimming, rowing, collisions, rocket propulsion, and engineering systems. It does not say that the forces cancel on one object, and it does not say that the two objects must have equal accelerations. To analyse motion, combine the third law with free-body diagrams and Newton’s second law. When solving a problem, name both objects, identify each force’s direction, and place each force on the correct object’s diagram. This prevents common errors and makes the law easier to apply in conceptual and numerical questions.