KAHIBARO
Table of Contents
Seeing Forces as Pairs
Newton's third law says that forces always come in pairs. When one object exerts a force on a second object, the second object exerts a force of equal magnitude and opposite direction on the first object.
If object A pushes or pulls object B, then object B pushes or pulls object A.
In symbols, this is written as
$$
\vec{F}_{A \to B} = -\vec{F}_{B \to A}
$$
This is called an action reaction pair. The word "action" does not mean the force happens first. Both forces happen at the same time. They are simply two forces that belong together.
For every force, there is a matching force on another object.
$$
\vec{F}_{A \to B} = -\vec{F}_{B \to A}
$$
These two forces are equal in size, opposite in direction, and act on different objects.
What Makes a True Action-Reaction Pair
To identify an action reaction pair correctly, look for three things. The two forces must be of the same type, they must be equal and opposite, and they must act on two different objects.
This last point is the most important. Many beginners incorrectly think that two opposite forces on the same object are an action reaction pair. They are not. Forces on the same object may cancel, but they do not form a third law pair.
For example, a book resting on a table has a downward weight force from Earth and an upward normal force from the table. These two forces act on the same object, the book. Therefore they are not an action reaction pair.
The true pairs are different:
| Force on one object | Matching force on the other object |
|---|---|
| Table pushes up on book | Book pushes down on table |
| Earth pulls down on book | Book pulls up on Earth |
Example of Pushing
Imagine a person pushing a wall. The person exerts a force on the wall. At the same time, the wall exerts an equal and opposite force on the person.
If the person pushes the wall with a force of $50 \, \text{N}$ to the right, then the wall pushes the person with a force of $50 \, \text{N}$ to the left.
The two forces do not cancel each other because they act on different objects. One acts on the wall, the other acts on the person.
Example of Walking
Walking is possible because of action reaction pairs. When your foot pushes backward on the ground, the ground pushes forward on your foot. That forward force helps move you ahead.
This is a very important idea. You move forward not because your foot pushes yourself forward directly, but because the ground pushes you forward in response to your push backward.
Example of a Rocket
A rocket moves by ejecting gas backward. The rocket pushes the gas backward, and the gas pushes the rocket forward. This is an action reaction pair.
Even in empty space, the rocket can move because it does not need air to push against. It pushes exhaust gases backward, and those gases push the rocket forward.
A rocket does not need to push on air.
It moves because of the force pair between the rocket and its expelled gases.
Example of Gravity
Action reaction pairs also occur in gravitational forces. Earth pulls on a falling apple, and the apple pulls on Earth.
The forces are equal in magnitude and opposite in direction. But the motions are very different because Earth has a huge mass and the apple has a small mass. So the apple accelerates noticeably, while Earth's acceleration is extremely tiny.
This helps explain an important point. Equal forces do not always produce equal motions.
Why Equal Forces Do Not Always Mean No Motion
Students often ask, "If the forces are equal and opposite, why does anything move?" The answer is that the equal and opposite forces act on different objects.
If a horse pulls a cart, the horse pulls the cart forward and the cart pulls the horse backward. These are equal and opposite, but they do not cancel because they act on different bodies.
Whether an object speeds up depends on the net force on that object alone. To study motion, always isolate one object and examine only the forces acting on it.
How to Find Action-Reaction Pairs
A good method is to ask two questions. First, what object is exerting the force? Second, what object is receiving the force?
If you can name the force as "A on B," then the matching force is "B on A."
Here are some examples:
| Force name | Matching third law partner |
|---|---|
| Hand on ball | Ball on hand |
| Earth on person | Person on Earth |
| Tire on road | Road on tire |
| Magnet on nail | Nail on magnet |
This naming method prevents confusion.
To find a third law pair, write forces as
"A on B" and "B on A"
If both forces are on the same object, they are not a third law pair.
Common Misunderstandings
A very common mistake is to pair the wrong forces. Consider a hanging lamp. The string pulls up on the lamp, and Earth pulls down on the lamp. These forces may balance, but they are not an action reaction pair because both act on the lamp.
The correct pairs are the string on lamp with lamp on string, and Earth on lamp with lamp on Earth.
Another misunderstanding is to think the larger object exerts the larger force. Newton's third law says this is not true. In any interaction, both objects exert forces of equal magnitude.
A Simple Interaction Diagram
It is often useful to picture two objects connected by a mutual interaction.
The two arrows represent one third law pair. They are always opposite and equal.
The Core Rule to Remember
Newton's third law is a rule about interactions between objects. It does not by itself tell which object moves faster or whether anything is at rest. It tells us that forces are mutual.
Every interaction involves two forces, not one.
If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.
When you analyze any physical situation, train yourself to ask, "What is the matching force on the other object?" That question is the key to recognizing action reaction pairs correctly.