Core Concepts
In this article, you will gain an overview of Newton’s three laws of motion, understand related concepts and vocabulary, and how to apply that understanding to real-world situations.
Introduction
Picture this: you’re holding a skateboard, the wind blows through your hair, and the sun shines on your skin. It’s a perfect day for such a good ride. You put your board down and begin to ride. Up ahead, a railing slopes down a set of stairs; it looks perfect for a bit of grinding! You sharply kick on the back of the skateboard, pushing the front end up, jumping up onto the railing with you and your skateboard. You’re sliding down and everything feels right. You close your eyes for a moment and the front wheel of your skateboard catches on a screw in the railing. Suddenly, you’re swung around and you hit the floor. Ouch…
Why did such a small screw cause such a major screw-up? In order to understand why, let’s look to a famous physicist: Sir Isaac Newton.
Sir Isaac Newton was born in 1643 and became a mathematician, physicist, and astronomer. You’re probably familiar with the story of Newton coming up with the concept of gravity when he sat under an apple tree and an apple fell on his head. Before him, other physicists, like Galileo and Kepler, studied the cosmos and how the planets moved. However, they didn’t quite understand why those cosmic bodies moved in the way they do. Even though the concept of gravity seems so simple today, no one really understood why gravity existed or how it functioned.
It was Newton who discovered the mathematical rules for how things move. This revolutionized the way we understand motion and the physical universe. The rules that Newton came up with, Newton’s laws of motion and the universal law of gravitation, first appeared in his 1687 book Principia.
Even more than 300 years later, Newton’s laws are essential to understanding how the world works. Engineers use them to design cars, airplanes, and bridges. Astronomers use them to understand the motion of planets, stars, and even galaxies. Astronauts use them to launch rockets and explore space. Even video game developers use them to design realistic motion. Everything, from the motion of molecules, to how you ride a skateboard, to the orbits of planets around their stars, make use of Newton’s laws of motion. So, what are they?
Newton’s First Law
An object at rest stays at rest, and an object in motion stays in motion, unless an external force acts upon it.
Newton’s Second Law
The net force acting on an object is equal to its mass times its acceleration.
Newton’s Third Law
For every action, there is an equal and opposite reaction.
To a physicist, these terms are second nature. But what do words and phrases, like “an external force,” “net force,” or even “action” mean in terms of physics? Starting with Newton’s first law, let’s discuss what everything actually means.
Newton’s First Law of Motion
An object at rest stays at rest, and an object in motion stays in motion, unless an external force acts upon it.
An object at rest is pretty simple: it is simply a non-moving object. Think of a table, a park bench, or a pencil. Unless you or someone else acts to move the table, the table is not moving. Even if you push the table, it doesn’t just slide effortlessly. There is something holding the table in place. The same principle applies to a person. If you’re standing still, and then you get pushed, you may move a bit. However, you’re not necessarily going to fall over, unless the push uses enough force.
So, what’s holding an object in place? Mass, or the amount of stuff an object is made of, is what keeps it in place. The more massive something is, the more difficult it is to move. A pencil is easier to move than a car, for example, because the pencil has much less mass.
Let’s consider the other half of this law, too. It states that an object in motion stays in motion. Here, it’s helpful to envision a moving car, or a skateboarder like in our initial scenario. A moving car is hard to stop, especially if it’s moving at fast enough speeds. And even as your car slows, you (the passenger) experience a feeling of being pulled forward as your chest lightly strains against the seatbelt. That’s a resistance to change. This resistance, which is present in both pushing a table and stopping a car, is inertia.
But how does inertia work? Hold a ball in your hand. Feel its mass. In this state, it’s not very hard to move the ball, but it definitely takes something to move it. If you throw the ball up into the air and catch it, it almost feels heavier the moment it hits your hand. Usually, your hands fall ever so slightly in response to catching something, too.
Based on this, it turns out that mass isn’t the only important piece of this puzzle! Speed matters too. Speed is the rate at which something moves. The faster something moves, the harder it is to stop. Also, the heavier an object is, the harder it is to start moving that object. This is how momentum works. An object’s momentum is proportional to both its mass and, indirectly, its speed.
The same idea also applies in the opposite direction. If an object with a small mass is moving at high speed, what do you expect will happen? The small object will have a high momentum, thanks to its high speed. Another example of this phenomenon is a bullet’s motion. A bullet has very little mass, but when the immense force of combusting gunpowder is directed at the back of a bullet in its chamber, that force imparts a lot of speed onto the bullet. Contrarily, a very massive object moving very slowly (or not at all) is very difficult to move. Think of Earth getting hit by the asteroid that killed the dinosaurs: even though the impact involved a lot of force, it did essentially nothing to change Earth’s orbit.
The following table shows how different amounts of force yield different effects on an object depending on that object’s mass.
| Low-Mass Object (pencil) | Medium-Mass Object (table) | Massive Object (Earth) | |
| Small Force (flick of a finger) | Pencil moves across a desk | Negligible | Negligible |
| Medium Force (combustion of gunpowder) | Pencil gets shot across a room | Table moves a few feet | Negligible |
| Large Force (meteor that killed the dinosaurs) | Pencil gets blown off the planet or vaporized | Table gets blown across an ocean/continent or vaporized | Mass extinction, but little to no change in orbit |
We can also consider momentum to be the quantification of movement and inertia. More mass, and/or more speed, means more momentum; less mass and/or less speed means less momentum, too. In this way, small objects can have a large momentum if their speed is high enough, and even unmoving objects can have a large momentum if they’re massive enough.
So, it turns out the reason you swung forward and hit the floor was because you had a lot of momentum. Your body intended to keep moving in the same direction, but the screw embedded in the railing was able to stop you from moving forward, making you maintain that momentum and slam into the floor. But, how much force did you hit the floor with? And how can we go about calculating it? To answer these questions, we’ll refer to the next law.
Newton’s Second Law of Motion
The net force acting on an object is equal to its mass times its acceleration.
Simply stated, a force is anything that does something to an object. A similar concept, the net force, is the sum of all the forces acting on an object.
We typically measure force in — you guessed it! — newtons (N). A newton can be broken down further into other SI units, so you may see it written as “kilogram-meter per second squared” (kg * m / s2).
To further explore forces, let’s discuss what forces are acting on a ball that is still on the floor. Assuming that the ball is on Earth, the force of Earth’s gravity is pulling the ball down. There’s also a normal force, or the ground’s resistance to not fall out from underneath the ball. The normal force is always perpendicular, or 90°, to the ground.
In our scenario, the ball is in equilibrium (as it is unmoving). The force of gravity and the normal force add together. When they do, they cancel out because these forces acting on the ball are equal in magnitude, which is why the ball is unmoving. Since the forces cancel out, the net force is equal to zero.
The image above is known as a free body diagram. It shows all of the forces acting on an object. Notice how the force of gravity and the normal force shown using arrows of the same size. In physics, a force arrow’s size represents the magnitude of that force. In this image, the two forces have the same size arrows, so they have the same magnitude as each other. Note, however, that the forces have opposite direction.
Next, let’s briefly revisit mass. Recall that mass is the amount of stuff that something is made of, and more massive objects are harder to move. When it comes to motion, the important thing about mass is that the more mass something has, the more force you need to apply to accelerate. Note that mass is different from weight (which is what we get when we apply the force of gravity to an object’s mass).
To understand the last part of this law, acceleration, we need to discuss motion itself. Motion involves three components: position, velocity, and acceleration.
- Position is simple: it describes where an object is. We measure position in units of distance, like meters or centimeters.
- Velocity is the object’s measured change in position. While this sounds reminiscent of speed, velocity and speed are not quite the same. Velocity, unlike speed, also takes into account the direction that the object is moving in. We measure velocity in distance traveled per unit time, commonly meters per second (m/s), but you might be more familiar with units like miles per hour (mph).
- Finally, acceleration is the object’s measured change in velocity over time. If you’ve ever ridden in a car, you have felt acceleration. It’s that feeling of being pulled back into your seat as the car (and therefore you) speed up, or being drawn to the side during a turn. Acceleration is typically measured in distance traveled per unit time squared, so you’ll often see meters per second squared or (m/s2) in physics problems.
Here is a summary of the key concepts that we’ve discussed so far:
| Definition | SI Units | |
| Force | Anything that does something to an object | N or kgm/s2 |
| Mass | The amount of matter that an object is made of | kg or g |
| Position | Where an object is located in space (relative to something else) | m |
| Velocity | An object’s measured change in position over time | m/s |
| Acceleration | An object’s measured change in velocity over time | m/s2 |
We can visualize these concepts through some examples. Imagine that you drop the ball from 100 meters in the air. Before the ball’s drop, its position is 100 m above the ground, its velocity is 0 m/s (because it’s not moving yet), and its acceleration is also 0 m/s2 (because its change in velocity is 0 m/s).
The moment the ball is dropped, the force of gravity acts on the ball. The result is that the force of gravity pulls the ball down toward the ground, with a constant acceleration of -9.81 m/s2. This acceleration is the average force of gravity across Earth. Notice how the sign of the acceleration is negative in this case, as the ball is moving in a downward direction.
After dropping the ball, its velocity increases linearly. After two seconds, the ball’s velocity is double what its velocity was after one second. Three seconds after being dropped, its velocity is three times as fast as the velocity was after one second.
The ball’s position is a little more complicated, as it gives us a quadratic function in this case. We can interpret this as its position is changing faster than its velocity. The ball’s position two seconds after the drop is exactly four times farther down than its position after one second. Its position after three seconds is exactly nine times the position after the first second.
As you can see, these aspects of motion all follow a very distinct pattern. We can visualize these patterns through the graphs below:
Let’s inspect these graphs a bit more closely. Notice how the acceleration vs. time equation is a constant: a flat line. The object’s acceleration, -9.81 m/s2, stays the same throughout the entire duration of the ball’s fall. That’s because the force of Earth’s gravity stays the same during the entirety of the ball’s fall, as the ball is always on Earth.
Then, notice how the velocity equation is a linear graph. It gains more speed with every passing second of the fall, so the magnitude of its velocity is increasing as time passes. The velocity has a negative sign because the motion is happening in a downward direction.
Finally, notice how the position equation is a negative quadratic equation. If you’ve taken calculus, you might also recognize two interesting points: velocity is an integral of acceleration with respect to time, and position is an integral of velocity with respect to time.
Below are more generic models of the above graphs. We’ve replaced the numbers with variables that can be replaced with any value. Variables with the subscript “i” refer to initial conditions at the start of the scenario, like our 100 meters above the ground.
Acceleration: a = ai
Velocity: v = vi + ait
Position: d = di + vit + ½ait2
Together, position, velocity, and acceleration define motion. Simultaneously, external forces on an object’s mass influence how the object moves.
Now that we have a better understanding of what each term in Newton’s second law of motion means, we can look at how they come together to form the much simpler equation:
F = ma
Force = Mass * Acceleration
This equation highlights the relationship between force, mass, and acceleration. We can see that the amount of force is directly proportional to both mass and acceleration, while mass and acceleration are inversely related.
This relationship shows us that the more mass something has, the more force is required to accelerate it or increase its movement. It also implies that an object with less mass requires less force to move it. Think back to our pencil and table: it’s significantly harder to move a table than a pencil because of this relationship, which is also indirectly describing how inertia and momentum work. Inertia is the qualitative property of matter to resist change, whereas momentum is a quantitative property referring to the amount of motion that an object has.
All of these concepts are intertwined. More mass means more momentum; more momentum means more force required to move; more force required to move means more inertia! So, really, it was your mass and your initial speed that made you have such a high momentum. When you slammed into the ground, your high momentum caused that impact to have so much force. And it was that change in speed and direction that you felt on your downward fall.
We’ve learned a lot so far about what makes objects move and the different components of their motion. Now, let’s explore how the third law shows the relationships between forces.
Newton’s Third Law of Motion
For every action, there is an equal and opposite reaction.
This sounds like it might be the hardest of the three laws to understand, but it’s actually quite simple. In our example with the ball, you can think of the normal force as our balancing force: it is the equal and opposite reaction to the force of gravity on the ball. It’s equal because its arrow is the same size as the force of gravity’s arrow, and it’s opposite because its arrow points in the opposite direction as the force of gravity’s arrow.
But this example was of an object in equilibrium, where the net force on the ball was zero. What about in a moving system, like a moving car?
Intuitively, a scenario about motion may appear to break this law. After all, if there were always an equal and opposite reaction on the car, it would never move, right? This is not the case, though — the equal and opposite reaction is still there. It’s just not exerted on the same objects.
In the case of our moving car, assuming everything is on Earth, the force of gravity and the normal force balance with each other. This means that the car doesn’t float up nor fall through the floor. The engine puts energy into the tires, making them turn, which, in turn, makes them roll across the road. Also, the tires have friction that doesn’t allow them to spin freely. The end result is that the car is pushed forward and the earth is pushed backward.
We can visualize this better with two equally sized wheels (or marbles, or cogs) rolling around one another. When the blue wheel rolls around the red wheel, unless something is holding the red wheel in place, the red wheel is simultaneously rolling around the blue wheel. In the same way, we can think of two unequally-sized wheels, our blue wheel being our larger of the two. As the smaller red wheel rolls around the larger blue wheel, the blue wheel is also rolling around the red wheel.
The fun thing about this is that we can keep scaling this scenario indefinitely, to the point where we have one wheel being a car’s tire, with the other wheel being the whole Earth.
Even when something is not rolling (like in our example where we dropped our ball), an equal and opposite force is being applied. That is the force of gravity, described by Newton’s law of universal gravitation, which basically states that all objects with mass attract one another with the same amount of force. This relationship is evident in the universal gravitation law’s equation:
Because the two masses in the equation are the two masses being affected, the force of gravity is actually being experienced by both the object and the celestial body that it’s on. In this case, it’s Earth exerting its gravity on you, and you exerting your gravity on Earth, with both of those forces being the same. It’s just that Earth is so much larger and has so much more momentum than you, so the effect that the Earth experiences from your gravity is basically negligible.
This is exactly the case for what happened with you and your skateboard. Both you and Earth experienced the same things! But because Earth is significantly more massive than you, its change was much less apparent than yours.
Conclusion
So, why did that little screw send you flying? Newton’s first law says that you have inertia and so much momentum that you had to keep moving. His second law says that the amount of force was proportional to your mass times your acceleration. Since you got swung around so fast, all of that force was put on your body as you hit the concrete. Finally, his third law states that, while you experienced that fall, the screw on the railing experienced an equal and opposite force imparted on the bigger system (Earth), which experienced a negligible change. Motion is a complex and dynamic phenomenon, and Newton’s laws of motion lay the groundwork that helps us understand and predict how an object moves.
