Newton's Third Law of Motion
By Alexander Wasil spring 2026
Main Idea
Newton’s Third Law of Motion states that all forces occur in pairs as a result of an interaction between two objects. When object A exerts a force on object B, object B simultaneously exerts a force equal in magnitude and opposite in direction on object A. These forces are part of a single interaction; neither exists without the other.
I overhauled the conceptual section to clarify that these force pairs are always the exact same type of force. For example, if you push a wall with a normal force, the wall pushes back with a normal force. These pairs never act on the same object, which is why they don't just "cancel out" and prevent motion from happening in the first place.
Common examples of this interaction include gravitational pull and contact forces. The Earth exerts a downward gravitational force on a projectile, and the projectile exerts an equal upward gravitational force on the Earth. When a person walks, they exert a backward frictional force on the ground, and the ground exerts an equal forward frictional force on the person.
A Mathematical Model
The law is modeled using vector notation to account for both magnitude and direction.
[math]\displaystyle{ \vec{F}_{A \text{ on } B} = -\vec{F}_{B \text{ on } A} }[/math]
Because the forces are equal and opposite, their sum is zero when considering the two objects as a single system.
As an example using SI units, consider a person with a mass of 60 kg standing on a flat surface. The gravitational force (weight) acting on the person is approximately 588 N downward. The person exerts a 588 N contact force downward onto the ground. Simultaneously, the ground exerts a normal force of 588 N upward onto the person.
[math]\displaystyle{ | -588 \text{ N} | = | 588 \text{ N} | }[/math]
A Computational Model
GlowScript model showing colliding spheres with identical force magnitudes of 6 N, proving that action-reaction pairs stay equal regardless of mass.
Examples
Simple
Question
Car B is stopped at a red light. The brakes in Car A have failed, and Car A is traveling toward Car B at 60 km/h. Car A collides with the back of Car B. What is the relationship between the force Car A exerts on Car B and the force Car B exerts on Car A?
Answer
Car B exerts the exact same amount of force on Car A as Car A exerts on Car B. Even though Car A is the one moving, the forces are equal in magnitude and act in strictly opposite directions.
Middling
Question
Blocks with masses of 1.0 kg, 2.0 kg, and 3.0 kg are lined up in a row on a frictionless horizontal table. All three are pushed forward by an 8.0 N applied force pushing on the 1.0 kg block.
(a) How much force does the 2.0 kg block exert on the 3.0 kg block?
(b) How much force does the 2.0 kg block exert on the 1.0 kg block?
Answer
(a)
First, define the system as all three blocks to find the total acceleration.
Total Mass: [math]\displaystyle{ 1.0 \text{ kg} + 2.0 \text{ kg} + 3.0 \text{ kg} = 6.0 \text{ kg} }[/math]
[math]\displaystyle{ \begin{aligned} F_{\text{net}} &= m_{\text{total}} \cdot a \\ 8.0 \text{ N} &= (6.0 \text{ kg}) \cdot a \\ a &= 1.33 \text{ m/s}^2 \end{aligned} }[/math]
The acceleration is [math]\displaystyle{ 1.33 \text{ m/s}^2 }[/math] for all blocks in the system.
To find the force of block 2 on block 3, define block 3 as the system.
[math]\displaystyle{ \begin{aligned} F_{2 \text{ on } 3} &= m_3 \cdot a \\ F_{2 \text{ on } 3} &= (3.0 \text{ kg}) \cdot (1.33 \text{ m/s}^2) \\ F_{2 \text{ on } 3} &= 4.0 \text{ N} \end{aligned} }[/math]
(b)