Isaac Newton studied the physics of forces – how they can be created, how they interact with one another, and how they create the world we experience every day. While Newton may not have perfectly defined how everything works at every scale in the universe, Newton’s Laws are still revered and studied today. Throughout this piece, you’ll learn what these laws are, see some examples of Newton’s Laws, and understand why they are still so important today.

There have been few times in history where a new scientific discovery shook our fundamental understanding of how the universe functions as a whole. The discovery of Newton’s Laws is one of them. Before Newton, scientists believed that objects had an inherent amount of energy to move and that things stopped moving when they ran out of energy. While this may make some sense at first glance, Newton looked beyond that. He dared to question what would happen to a ball that rolled without encountering friction without putting biological constraints on it.

Newton’s First Law of Motion

Newton’s First Law states that an object will maintain a constant speed and direction unless affected by a net outside force.

You could also say that an object will maintain constant velocity unless affected by an outside force, as velocity accounts for both speed and direction. It’s worth noting that this includes a velocity of 0\text{ m/s}, as a stationary object will not begin moving unless an outside force causes it to do so.

If you’re not quite comfortable with the idea of an “outside force” it means that the force is coming from something outside of the object. For example, if you were to stand behind a car stuck on the ice and push on it, it would eventually begin moving if you were able to apply enough force. If, however, you were to sit inside the car and push on the dashboard, it wouldn’t move. The difference here is that the first time you are applying the force outside of the car while the second time you’re applying the force from inside the car. Outside forces may also sometimes be called external forces.

A net force means a non-zero force that is not balanced by other forces. Force is a vector with a magnitude and direction. When there is a 5\text{ N} force acting to the right and a 5\text{ N} acting to the left, these two forces cancel out and there is zero net force. The two forces are balanced.

You may have heard this paraphrased in a different way: “a body in motion tends to stay in motion while a body at rest tends to stay at rest”. While that is a relatively accurate interpretation, it is also simplistic and does not explain how the body will continue moving as our original two statements do.

What is another name for Newton’s First Law of Motion?

Much like how we can restate Newton’s First Law in many ways, it can also be called different things. Another name for Newton’s First Law of Motion is the Law of Inertia. Inertia is a measure of how difficult it is to change an object’s motion. Newton’s First Law tells us that only an outside force can change how an object is moving. Calling it the Law of Inertia makes sense as both refer to an object needing effort from an outside source to change the velocity.

Examples of Newton’s Laws: Newton’s First Law of Motion

Let’s start to look at some examples of Newton’s Laws starting with Newton’s First Law of Motion. We’ll begin with familiar, everyday experiences and then move to less common ones.

Example 1: A Ball on a Playing Field

A player kicks a ball on a level playing field under normal, on-Earth conditions. Assuming the ball doesn’t bump into anything and no one else touches it, what will happen to the ball?

1. Stop and change direction.
2. Not stop but will change its direction.
3. Stop but will not change direction.
4. Neither stop nor change direction.

You may be tempted to say 4 because we just learned about Newton’s First Law. Remember, though, we said we were operating under normal, on-Earth conditions. On Earth, there’s always at least a little friction. After all, when was the last time you pushed something and it never came to rest?

On Earth, friction tends to act as the outside force that causes things to stop moving. The ball never bumps into anything and there are no other forces that will change the direction of motion. Taking all of this into account, the correct answer to this problem is 3, the box will stop, but will not change direction.

You may be wondering how Isaac Newton figured out his first law seeing as how he lived on Earth. Excellent question! He considered what truly made things stop moving – whether they ran out of energy or were affected by something like friction. When he decided it must be an external force, he created a relatively frictionless experiment to test his hypothesis.

Example 2: A Ball on an Infinite, Frictionless Plane

Let’s consider another example of Newton’s First Law. Instead of kicking the ball onto a playing field, the player kicks it onto an infinitely long, frictionless plane. Assuming the ball doesn’t bump into anything and no one else touches it, what will happen to the ball?

1. Stop and change direction.
2. Not stop but will change its direction.
3. Stop but will not change direction.
4. Neither stop nor change direction.

There are no external forces acting on the ball so even if it attempted to stop itself, it couldn’t. It also can’t speed itself up. The ball will continue sliding over the infinite plane at the same velocity until the end of the universe itself. We again have no outside forces to change the ball’s direction. The correct answer here is 4, the box will neither stop nor change direction.

Newton’s Second Law of Motion

Newton’s Second Law of Motion states that the net force on an object is equal to its mass times its acceleration.

This is probably the one that comes up the most obviously and frequently in life. It’s why larger vehicles need extra power to accelerate to the same speed. It explains why pushing a full dresser or bookcase is more difficult than pushing an empty one. It’s even why you want a heavy end to your side of the rope in a tug-of-war. The second law is also the only one with a corresponding equation.

What is the formula for Newton’s Second Law?

Like we said before, Newton’s Second Law says that the net force acting on an object is equal to mass times acceleration. Naturally, the equation shows the same information:

Newton’s Second Law F=ma

…where F is the net force, m is mass, and a is acceleration. You’ll see this equation come up a lot throughout your physics career in a few different forms, so it’s best to start getting a firm understanding of it now.

Examples of Newton’s Laws: Newton’s Second Law of Motion

Let’s look at some examples of Newton’s Second Law to demonstrate both the concept and the calculation.

Example 1: Applying the Concept

Which of the following situations will require the largest net force?

1. A small mass is given a small acceleration
2. A large mass is given a large acceleration
3. A large mass is given a small acceleration
4. A small mass is given a large acceleration

The correct answer here 2. A large mass is given a large acceleration. If we look back at Newton’s Second Law, it’s easy to see why. If the net force is the product of mass and acceleration, then increasing either one will increase the overall force needed. Therefore, giving a large mass a large acceleration will require the most force.

Odds are that if you see conceptual questions like this in the future, they’ll use more concrete examples using specific objects and accelerations. Regardless, the point will be figuring out the combination that creates the greatest product of mass and acceleration. When you get these kinds of questions, it may be best to run the numbers just to make sure, especially if you’re looking at a standardized test.

Example 2: Solving for Force

Here is another example of Newton’s Second Law. A 1{,}000\text{ kg} spaceship begins accelerating on its journey out of the solar system at 6\text{ m/s}^2. What is the net force being applied to the spaceship?

We discussed the steps for solving a Physics problem in a previous post. We’ll be following those same steps here. If you get a bit lost or just want a refresher on how to solve a complex problem, it may be worth reviewing that particular post.

Step 1: Identify What you Know

• m=1{,}000\text{ kg}
• a=6\text{ m/s}^2

Step 2: Identify the Goal

• F=\text{?}

Step 3: Gather Your Tools

• F=ma

Step 4: Put it All Together

F=ma

F=1{,}000\text{ kg}\cdot 6\text{ m/s}^2=6{,}000\text{ N}

Example 3: Rearranging the Equation

In our last example of Newton’s Second Law, we will practice rearranging the equation. A rogue planet with a mass of 1.3\times 10^{22}\text{ kg} passes close enough to a star to feel a gravitational force of 100\text{ N} drawing it toward the star. What is the acceleration of the planet as it moves toward the star?

At this point, it hopefully isn’t too surprising that you can rearrange physics equations to solve for different values. We’ve seen it a lot before and we’re going to do it here again so we can use Newton’s Second Law to solve for acceleration.

Step 1: Identify What you Know

• m=1.3\times 10^{22}\text{ kg}
• F=100\text{ N}

Step 2: Identify the Goal

• a=\text{?}

Step 3: Gather Your Tools

• F=ma

Step 4: Put it All Together

We’ll start by rearranging the equation.

F=ma

a=F/m

Now we’ll plug in our values and solve.

a=\frac{100\text{ N}}{1.3\times 10^{22}\text{ kg}}

a=7.7\times 10^{-21}\text{ m/s}^2

Newton’s Third Law of Motion

Newton’s Third Law states that for every action there is an equal and opposite reaction.

You’ve probably heard this one in terms of things like karma, but in physics, it actually refers to force pairs. Generally, there are balanced forces (when the forces are equal and opposite and cancel each other out) and unbalanced forces (when one force is greater than the other). If you were looking closely, you may have guessed Newton’s Third Law deals mostly with balanced forces and balanced force pairs. The reason forces are always balanced when we talk about Newton’s Third Law is that we aren’t looking at forces acting on a single object, we’re looking at an action force and the corresponding reaction between two objects.

Action-Reaction Pairs

Action-reaction pairs occur when one object applies a force to another. Newton’s Third Law states that if you exert a force on a baseball to throw it, then the baseball exerts a force of equal magnitude back on you in the opposite direction. At first, it may seem a bit odd. After all, Newton’s Second Law just told us that applying a force creates an acceleration.

If instead, you think about how Earth’s gravity hasn’t pulled you down to its core yet, it may make a bit more sense. Your weight creates a force that pushes on the ground that would pull you to the Earth’s core if the ground didn’t apply an equal and opposite force back on your feet. The same thing happens when you lean against a wall. Your body puts a force on the wall, but the wall is able to exert the exact same force back because of Newton’s Third Law. In that case, you leaning against the wall would be the action and the wall supporting you would be the reaction. Together, they make an action-reaction pair.

Examples of Newton’s Laws: Newton’s Third Law of Motion

Newton’s Third Law is only asked about conceptually and usually in relation to the other two laws. Let’s look at some examples together.

Example 1: Discovering Your Own Power

On average, Earth exerts a force of about 700\text{ N} on each person strolling about its surface. What force do you exert on the Earth?

Well, let’s think about it. Newton’s Third Law tells that every action (the Earth exerting a force on you) has an equal and opposite reaction (you exerting a force on the Earth). By that logic, the force you exert on the Earth should be -700\text{ N}. You may see questions like this being answered with the absolute value of that force (700\text{ N} instead of -700\text{ N}), but if the question doesn’t specifically ask for that, it’s best to include a positive or negative sign as needed.

Example 2: Extending Your Universal Influence

Sagittarius A is a supermassive black hole at the center of our galaxy. It has a mass of about 8.26\times 10^{36}\text{ kg} and the gravitational field it creates is what keeps our Sun in orbit through the galaxy. You exert a gravitational force on Sagittarius A of about 6.07\times 10^{-13}\text{ N}. What force does Sagittarius A exert on you?

By the same logic we used last time, you exert a force on our host black hole (the action) and it exerts a force on you (the reaction). Therefore, Sagittarius A exerts a force of about -6.07\times 10^{-13}\text{ N}. 

This side effect of Newton’s Third Law, that you are as powerful as even the biggest, coolest, and most mysterious bodies in the universe and that they only have power because you exist, in some ways is one of the coolest (albeit least scientific) lessons we can pull from physics. 

Putting All of the Laws into Action

Believe it or not, you’ve been watching all three of these laws interacting and even relying on that interaction your entire life. The example we’ll use here is one you aren’t likely to end up in, but we’ll use it anyway because space makes it really easy to ignore air resistance and friction.

Examples of Newton’s Laws with a Space Explorer

Let’s consider an example to show how all of Newton’s Laws of Motion work together. An intrepid space explorer exits their ship to complete some necessary maintenance. They attach themselves to the ship with a safety cord but fail to notice that it has come undone from where they attached it to the ship. As they begin using it to pull themselves back toward the door, they realize that it has come undone. They are now floating just out of reach of their ship and moving farther away. How could they save themselves?

The Law of Inertia

Let’s start with Newton’s First Law. If no outside force is applied, they will continue on their path away from their ship for forever… or until they bump into a planet. Either way, it’s a journey they are unlikely to survive. That being said, there’s also nothing causing them to move away more quickly and they have plenty of oxygen left to think things through so this is a solvable problem. Seeing as there is no air or floor for them to push on, they can’t walk or swim back to the ship. They’ll need another way to generate a force outside of themselves.

Action-Reaction Pairs

Next, let’s jump to Newton’s Third Law. This one tells us that for every action there is an equal and opposite reaction. While they can’t do anything to themselves to generate an external force, they do still have their failed safety cord… perhaps it could still save them. If they were to throw the cord as hard as they could away from the ship, it would apply the same force back on our intrepid explorer pushing them toward the ship.

Generating Unbalanced Forces

Next up is Newton’s Second Law. The intrepid explorer puts all the force they can into sending the cord away from the ship. The relatively light cord moves quite quickly while they start heading back somewhat slowly as a larger mass with the same force will always get a smaller acceleration. Still, they are headed back to the safety of their ship.

An Object in Motion Stays in Motion

Lastly, Newton’s First Law again. There’s nothing standing (or floating) between our space adventurer and their ship. There’s nothing around that could apply an external force to either the adventurer or their ship. All that’s left is to gently collide with the ship and then crawl across its exterior to the door and to safety.

You’re likely to encounter examples of Newton’s laws like this throughout your physics career. You may see people floating through space, trapped on a frictionless lake, or rolling around on frictionless skateboards. If you have one person with an object or a pair of people stuck in such a perilous situation, Newton’s Laws can step in to save the day.

Why are Newton’s Laws Important?

You’ve learned Newton’s Laws of Motion and explored different examples of Newton’s Laws. From helping you figure out the force necessary to create a certain motion, to saving the lives of intrepid astronauts, these laws will come up in your daily life again and again. They also form the foundation of just about everything you learn from here to the end of your physics career. Isaac Newton revolutionized the way we think about how things move – large and small. Only a small update has been needed during the last century to account for the very, very small and the very, very large. The way we view the world we interact with was shaped by Newton’s Laws and hopefully, you’ll be able to start noticing them and putting them to good use making your own life just a little bit easier to navigate.