# What is Newton's third law?

Learn about the fact that forces come in pairs.

## What is Newton's third law?

You probably know that the Earth pulls down on you. What you might not realize is that you are also pulling up on the Earth. For example, if the Earth is pulling down on you with a gravitational force of 500 N, you are also pulling up on the Earth with a gravitational force of 500 N. This remarkable fact is a consequence of Newton's third law.
Newton's third law: If an object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A.
This law represents a certain symmetry in nature: forces always occur in pairs, and one body cannot exert a force on another without experiencing a force itself. We sometimes refer to this law loosely as action-reaction, where the force exerted is the action and the force experienced as a consequence is the reaction.
We can readily see Newton’s third law at work by taking a look at how people move about. Consider a swimmer pushing off from the side of a pool, as illustrated below.
A swimmer pushes on the wall with her feet, which causes the wall to push back on her feet due to Newton's third law. Image credit: Adapted from Openstax College Physics
The swimmer pushes against the pool wall with her feet and accelerates in the direction opposite to that of her push. The wall has exerted an equal and opposite force back on the swimmer. You might think that two equal and opposite forces would cancel, but they do not because they act on different systems. In this case, there are two systems that we could investigate: the swimmer or the wall. If we select the swimmer to be the system of interest, as in the image below, then $F_{\text{wall on feet}}$ is an external force on this system and affects its motion. The swimmer moves in the direction of $F_{\text{wall on feet}}$. In contrast, the force $F_{\text{feet on wall}}$ acts on the wall and not on our system of interest. Thus $F_{\text{feet on wall}}$ does not directly affect the motion of the system and does not cancel $F_{\text{wall on feet}}$. Note that the swimmer pushes in the direction opposite to that in which she wishes to move. The reaction to her push is thus in the desired direction.

## What are other examples of Newton's third law?

Other examples of Newton’s third law are easy to find. As a professor paces in front of a whiteboard, she exerts a force backward on the floor. The floor exerts a reaction force forward on the professor that causes her to accelerate forward.
Similarly, a car accelerates because the ground pushes forward on the drive wheels in reaction to the drive wheels pushing backward on the ground. You can see evidence of the wheels pushing backward when tires spin on a gravel road and throw rocks backward.
In another example, rockets move forward by expelling gas backward at high velocity. This means the rocket exerts a large backward force on the gas in the rocket combustion chamber, and the gas therefore exerts a large reaction force forward on the rocket. This reaction force is called thrust. It is a common misconception that rockets propel themselves by pushing on the ground or on the air behind them. They actually work better in a vacuum, where they can more readily expel the exhaust gases.
Helicopters similarly create lift by pushing air down, thereby experiencing an upward reaction force. Birds and airplanes also fly by exerting force on air in a direction opposite to that of whatever force they need. For example, the wings of a bird force air downward and backward in order to get lift and forward motion.
1. "Newton’s Third Law of Motion: Symmetry in Forces" from Openstax College Physics. Download the original article free at http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a@9.1:26/Newtons-Third-Law-of-Motion-Sy.

## What do examples involving Newton's third law look like?

### Example 1: Fridge push

A person drives a cart, Cart 1, to the right while pushing another cart, Cart 2, that has a massive refrigerator on it. The total mass of Cart 2, cart plus fridge, is three times the total mass of Cart 1, cart plus person. If the person is driving with enough force that the two carts accelerate to the right, what can be said for sure about the magnitudes of the forces on the carts?

The correct answer is that the force on Cart 2 exerted by Cart 1 is equal in magnitude to the force on Cart 1 exerted by Cart 2.
It doesn't matter whether there is acceleration or whether the mass of one object is larger than another object. Force reaction pairs are always equal in magnitude. We know the forces in this question are force reaction pairs since exchanging the order of the objects in the phrase "force exerted on Cart 2 by Cart 1 gives us "force exerted on Cart 1 by Cart 2. Exchanging the order of the objects involved in a force—i.e., the object exerting the force and the object the force is exerted on—is an easy way to identify a third law force pair.

### Example 2: Third-law-force pairs

A box sits at rest on a table as seen in the image below. Various forces are listed in the table below the image.
Drag the forces in the right column so that they're lined up with their Newton's third law partner force in the left column.
First force of a third-law pair
Second force of a third-law pair
• Downward force of gravity on the box exerted by Earth
• Downward force on the table exerted by the box
• Downward force on the ground exerted by the table
• Downward force of gravity on the table exerted by Earth
• Upward force of gravity on Earth exerted by the table
• Upward force on the box exerted by the table
• Upward force of gravity on Earth exerted by the box
• Upward force on the table exerted by the ground

To find the Newton's third law partner force, we can simply reverse the order of the objects in the force description. For example, the pairs listed below all form Newton's third law force pairs.
The partner force for the downward force of gravity on the box exerted by Earth would be the upward force of gravity on Earth exerted by the box.
The partner force for the downward force on the table exerted by the box would be the upward force on the box exerted by the table.
The partner force for the downward force on the ground exerted by the table would be the upward force on the table exerted by the ground.
The partner force for the downward force of gravity on the table exerted by Earth would be the upward force of gravity on Earth exerted by the table.