Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on a second object, the second object simultaneously exerts a force of equal magnitude and opposite direction on the first object. These two forces are known as an action-reaction pair.
A key insight of this law is that forces always occur in pairs; an isolated force cannot exist. This principle is fundamental to understanding how objects interact, from celestial bodies in orbit to the propulsion of a rocket in the vacuum of space.
Originally stated by Isaac Newton in his 1687 Principia Mathematica as "To every action there is always opposed an equal reaction," this law revolutionized the understanding of interactions. It forms the basis for the principle of conservation of momentum and is essential for analyzing systems in fields like structural engineering, collision dynamics, and propulsion.
Newton's Third Law describes the fundamental nature of force interactions as paired, equal, and opposite. It is a universal law that governs how any two objects interact, regardless of their mass or motion.
| Property | Details |
|---|---|
| Nature | Forces are vector quantities that always occur in pairs. An 'action' force on one object is always accompanied by a 'reaction' force of the same type on the other interacting object. |
| Magnitude | The magnitude of the action force is always exactly equal to the magnitude of the reaction force. If object A exerts a force on B, then F_AB = F_BA. |
| Direction | The direction of the reaction force is always exactly opposite (180 degrees) to the direction of the action force. As vectors, F_AB = -F_BA. |
| Action-Reaction Pairs | The two forces in a pair act on two different objects. They never act on the same object and therefore never cancel each other out in a free-body diagram for a single object. |
| Conservation Law | This law is a direct statement of the conservation of linear momentum. For an isolated system of interacting particles, the net internal force is zero, and thus the total momentum is conserved. |
| Dimensional Formula | As the law describes force, its dimensional formula is [M][L][T]^-2. |
| Symbol | Quantity | SI Unit | Description |
|---|---|---|---|
| \(\vec{F}_{AB}\) | Force on B by A | Newton (N) | The vector force that object A exerts on object B. |
| \(\vec{F}_{BA}\) | Force on A by B | Newton (N) | The vector force that object B exerts on object A. This is the 'reaction' force to \(\vec{F}_{AB}\). |
Newton's Third Law can be understood as a direct consequence of the conservation of momentum for an isolated system. Consider a system consisting of two interacting particles, A and B, with no external forces acting on them.
1. The total momentum of the isolated system is the sum of the individual momenta:
2. Because the system is isolated, its total momentum is conserved, meaning its time derivative is zero.
3. From Newton's Second Law, the rate of change of an object's momentum is equal to the net force acting on it (\(\vec{F}_{net} = d\vec{p}/dt\)). The only force on particle A is from B (\(\vec{F}_{BA}\)), and the only force on particle B is from A (\(\vec{F}_{AB}\)).
4. Rearranging the equation yields Newton's Third Law.
Newton's Third Law is a universal principle that does not have different types or special cases. Instead, it is applied consistently across various scenarios involving different kinds of forces.
| Type / Case | Description | When to Use |
|---|---|---|
| Contact Forces | Forces that act at the point of physical contact between two objects. The action-reaction pair consists of the contact forces exerted by each object on the other. | Analyzing scenarios like pushing a box (normal force), friction between surfaces, tension in a rope, or collisions between objects. |
| Non-Contact Forces | Forces that act over a distance without direct physical contact. The action-reaction pair still exists between the two interacting objects. | Analyzing gravitational attraction (e.g., Earth and Moon), electrostatic forces between charges, or magnetic forces between magnets or currents. |
| Static vs. Dynamic Systems | The law applies equally whether the objects are at rest (static) or in motion (dynamic). The equality of action-reaction forces holds true at every instant in time. | Used in both statics problems (e.g., a book resting on a table) and dynamics problems (e.g., a rocket expelling gas to accelerate). |
Transportation: Car wheels push the road backward, and the road pushes the car forward. An airplane propeller pushes air backward, and the air pushes the plane forward. A rocket expels hot gas downward, and the gas pushes the rocket upward.
Sports: A swimmer pushes water backward, and the water propels the swimmer forward. A runner's foot pushes the ground backward, and the ground pushes the runner forward, enabling motion.
Engineering: In structural design, the load of a bridge pushes down on its supports, and the supports exert an equal upward force to maintain equilibrium. The law is critical for analyzing forces in any mechanical system or structure.
Astronomy: The Earth exerts a gravitational pull on the Moon, and the Moon exerts an equal and opposite gravitational pull on the Earth. This interaction governs their orbits around a common center of mass.
Walking on the Ground: Your foot pushes backward on the ground (action). The ground, through static friction, pushes forward on your foot with an equal force (reaction). This forward push from the ground is what propels you forward.
A Book on a Table: The book's weight (gravity from Earth) pulls it down, causing it to exert a downward force on the table (action). The table exerts an equal upward normal force on the book (reaction), keeping it stationary. The gravitational action-reaction pair is actually between the book and the Earth itself.
Jumping: To jump, you push down hard on the ground with your feet (action). The ground responds by pushing up on you with an equal and opposite force (reaction). If this upward force is greater than your weight, you accelerate upward into the air.
The unit of force is derived from Newton's Second Law (\(F=ma\)). The dimensional formula for force is the product of the dimensions of mass and acceleration.
| Quantity | Symbol | SI Unit | Dimensional Formula |
|---|---|---|---|
| Force | \(F\) | Newton (N) | \([M][L][T]^{-2}\) |
In SI base units, one Newton (N) is equivalent to one kilogram-meter per second squared (1 N = 1 kg·m/s²).
The formula is written as F_AB = -F_BA. It signifies that the force exerted by object A on object B (F_AB) is perfectly equal in magnitude and opposite in direction to the force exerted by object B on object A (F_BA). The law describes the nature of force as an interaction between two objects.
F_AB is the force vector exerted by object A on object B, while F_BA is the force vector exerted by object B on object A. Both are forces measured in Newtons (N) in the SI system. The subscripts identify which object is exerting the force and which is experiencing it.
This law is fundamental for analyzing any system with interacting objects, such as collisions, contact forces (like normal force and friction), and gravitational or electrostatic interactions. It is crucial for defining a system and applying conservation laws, particularly the conservation of momentum, as it establishes that internal forces always occur in pairs.
A common mistake is believing that action-reaction forces cancel each other out. These forces can never cancel because they act on two different objects. For forces to cancel, they must be acting on the same object; action-reaction pairs, by definition, always act on separate bodies.
A swimmer demonstrates this law by pushing water backward with their hands and feet (the action). In response, the water exerts an equal and opposite force forward on the swimmer (the reaction). It is this reaction force from the water that propels the swimmer through the pool.
Newton's Third Law states that for an interaction between two objects in an isolated system, their mutual forces are equal and opposite (F_AB = -F_BA). Since impulse is force multiplied by time, the impulses on each object are also equal and opposite. This means the change in momentum for each object is equal and opposite, so the total momentum of the system remains unchanged (conserved).