British scientist Isaac Newton spent a great deal of his career studying motion and the causes of motion. His studies led him to develop three laws that he believed governed all motions in the universe. With his laws, Newton could explain, analyze, and predict all kinds of motions from falling an apple from a tree to the motion of the moon and planets in the heavens. This article discusses the third of Newton’s laws of motion, commonly known as Newton’s third law of motion.
Newton’s third law of motion may be older than you think
They say, “the universe always balances her books”. You may not have heard this one before, but you are sure to have come across one of its popular variants. The following phrases are thrown around in everyday language:
- What goes around comes back around
- You reap what you sow
- Curses come home to roost
- Trash in, Trash out
- “Karma”
These sayings have been around for ages. The concept of Karma, for instance, dates back to 1500 BCE.
So I find it interesting that it was only a little over 300 years ago that the scientific equivalent of these sayings was formalized. It took the genius mind of Isaac Newton to notice this underlying pattern of the universe and summarise it in his third law of motion which states,
For every action, there is an equal and opposite reaction
Ever since Isaac Newton put forward this law, similar scientific principles that reflect a certain balance of the universe have been formalized. For instance, today we know that:
- Motion doesn’t just stop; it jumps from one body to another – conservation of linear momentum
- Energy doesn’t just disappear; it is transformed from one form to another – conservation of energy
- Rotation doesn’t just stop; it is transferred from one body to another – conservation of angular momentum
- The mass of an element at the beginning of a chemical reaction is will equal the mass of that element at the end of the reaction – conservation of mass
It may be interesting to know that two of these principles can be directly derived from Newton’s third law of motion.
Defining force in Newtonian physics
When two or more bodies come close enough to one another, they may interact. The interaction manifests itself in many forms that we call “force”.
Additionally, these “interactions” may happen through contact (such as dragging a box along the floor) or non-contact (such as the attraction of iron fillings by a magnet).
Most scientists are comfortable defining force simply as a pull or push to a layperson. Obviously, we cannot “see” or “touch” a pull or a push, we can feel it, observe it, and measure it.
Force and Newton’s third law of motion
Before we get to Newton’s third law of motion itself, it is important that we clear the air around some basic properties of force.
Force involves more than one body.
Force is a two-way street. It comes in pairs; there is no such thing as an isolated force.
As stated earlier, forces are invoked when a body interacts with another body in its vicinity, whether through contact or non-contact. Isolated bodies cannot exert force on themselves. In fact, Isaac Newton discovered that isolated bodies can never change their state of motion or rest unless compelled to do so by an “external force” caused by another body in its environment. This is Newton’s first law of motion.
Force happens between bodies
Forces don’t just involve more than one body; they happen across different bodies.
All physical cases involve body “A” exerting a force on body “B” and vice versa. Whenever the term “force” is used in a physics context, it refers to an interaction happening between bodies. As stated earlier, an isolated body cannot exert a force on itself. And even if it could, it cannot change its state of rest or motion as that would be in violation of Newton’s first law of motion. Now that we are clear on this, let’s proceed to Newton’s third law of motion.
Introduction to Newton’s third law of motion
Newton’s third law of motion states,
“When one body exerts a force on another, the second exerts a force on the first. These two forces are always equal in magnitude and opposite in direction.”
Let’s break this down.
- It involves more than one body. This is consistent with the behavior of forces as we pointed out earlier.
- Force happens between bodies i.e. body A exerts a force on body B and vice-versa. Again, this is consistent with the behavior of forces.
- The third part is the crux and the most confusing and misunderstood part of the law. The two forces are always equal in magnitude and opposite in direction.
At glance, this seems to suggest that the forces will cancel out, resulting in a zero net force. However, this is not what Newton’s third law of motion predicts. It is important to remember that the action and reaction forces always act on different bodies.
Of course, there are situations where two equal and opposite forces act on the same body. A common example of this is when we measure the weight of a body by hanging it from a spring balance. Or when a Spiderman toy is hanging mid-air in an upside position as shown below,
In this case, the Spiderman toy remains at rest in mid-air because the tension force in its web strands balances off with the gravitational force of its weight as shown below,
However, these forces cannot be action-reaction pairs because they act on the same body, the spiderman toy. In a true action-reaction pair as used in Newton’s third law of motion, one force acts on body A and another equal and opposite force on body B.
Examples of action and reaction pairs in Newton’s third law of motion
In our hanging Spiderman toy example, Newton’s third law of motion may be illustrated as follows:
The Earth pulls on the Spiderman toy with a downward force F, but the Spiderman toy does not accelerate downwards because the effect of this force is balanced off by an equal and opposite force T exerted on the Spiderman toy by the string as shown above.
Even though F and T are indeed equal and opposite, they do not form an action-reaction pair.
Here is why.
Because they act on the same body – the Spiderman toy. The two forces add up to zero and this explains why the toy remains stationary in mid-air. According to Newton’s third law of motion, each of these forces must have a corresponding reaction force somewhere.
But where?
The reaction force to the downward force of gravity on the toy is the force with which the toy Spiderman attracts the Earth, as shown below. Newton’s third law asserts the Spiderman toy is also pulling up on the Earth with as much force as the Earth is pulling it down.
The reaction force of the Spiderman toy pulling on the string is balanced off by the tension in the string, which pulls on the Spiderman toy.
Other examples of action-reaction forces include the following
| Action | Reaction |
| Force on a book due to table | Force on the table due to book |
| Force on Moon due to Earth | Force on Earth due to Moon |
| Force on an electron due to the nucleus | Force on the Nucleus due to an electron |
| Force on load due to a spring balance | Force on spring balance due to load |
| Force on baseball by bat | Force on the bat by a baseball |
This article borrowed some wonderful insights from the book, Fundamentals of Physics 5th Edition Volume 1 by Krane, Resnick, and Halliday available on Amazon via the link (not an affiliate),
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