More on Newton's third law | Forces and Newton's laws of motion | Physics | Khan Academy

We should talk a little more about Newton's third law because there are some deep misconceptions that many people have about this law. It seems simple, but it's not nearly as simple as you might think.

So, people often phrase it as, "For every action, there's an equal and opposite reaction," but that's just way too vague to be useful. A version that's a little better says that "For every force, there's an equal and opposite force." So this is a little better. The equal sign means that these forces are equal in magnitude, and this negative sign means that they're just different by the direction of the vector.

So these are vectors. This says that this pink vector F has the opposite direction but equal magnitude to this green vector F. But to show you why this is still a little bit too vague, consider this: If this is all you knew about Newton's third law—that for every force, there's an equal and opposite force—you might wonder. If you were clever, you might be like, "Wait a minute, if for every force F there's got to be a force that's equal and opposite, well, why doesn't that just mean that every force in the universe cancels?" Shouldn't every force just cancel then? At that point, doesn't that just mean that there's no acceleration that's even possible? Because if I go exert a force F on something, if there's going to be a force negative F, doesn't that mean that no matter what force I put forward, it's just going to get cancelled?

And the answer is no. The reason it's no is because these two forces are exerted on different objects, so you have to be careful. The reason I say that this statement of Newton's third law is still a little bit too vague is because this is really on different objects. If this is the force on object A exerted by object B, then this force over here has to be the force on object B exerted by object A. In other words, these forces down here are exerted on different objects.

I'm going to move this over to this side. I'm going to move this over to here. Let's draw two different objects to show explicitly what I mean. If there was some object A, let’s put some object A in here. So, we're going to make sure there's an object A. Let's say this is object A, and it had this green force exerted on it, F.

So this object right here is A. Well, there's going to be another object, object B. We'll just make it another circle, so we’ll make it look like this. So here's object B, and it's going to have this pink force, negative F, exerted on it. So I'm going to call this object B now.

We're okay. Now we know these forces can't cancel, and the reason these forces can't cancel is because they're on two different objects. But when you just say Newton's third law is that every force has an equal and opposite force, it's not clear that it has to be on different objects, but it does have to be on different objects.

These Newton force law pairs, oftentimes these are called force pairs, or Newton's third law partner forces, are always on different objects. The convention I'm using is that the first letter represents the force on the object that the force is on. Excuse me. So this A represents that this force F, this green force F, is on A and it's exerted by B.

This shows that it's exerted on B because the first letter is on the first one, and it's exerted by the second object A. So this pink force is exerted on B. This green force is exerted on A. They're equal and opposite. They do not cancel. They cannot cancel because they're not on the same object.

So that’s why these don't cancel, and they are the same magnitude. Even if the two objects are not the same size, this is another misconception. If object A is a planet, a big planet, or maybe a star, this is yellow, so it looks like a star. Let’s say this is some big star, and this is some smaller planet orbiting that star. This does not to scale unless this planet was enormous. So this is some planet, but this planet could be hundreds, thousands, or millions of times less massive than the star, but it would still exert the same force.

So if this star is pulling on the planet with this pink force F, negative F, then this planet has to be pulling on the star with this green force F, and they have to have the same magnitude even if they are different sizes. So people quote Newton's third law, but sometimes they don't really believe it. If I told you this planet was a million times less massive than the star, people would want to say that, "Well, then the star obviously pulls more on the planet than the planet pulls on the star." But that's not true according to Newton's third law.

Newton's third law says that they have to be the same even if they're different sizes. So if this was the Earth and this is the moon, the Earth pulls on the moon just as much as the moon pulls on the Earth. You might still object; you might say, "Wait a minute, that makes no sense. I know the star just basically sits there and the planet gets whipped around in a circle. How come this planet is getting whipped around, and the star's just staying put?" That's because just because the forces are equal, that doesn't mean the result is equal.

In other words, the forces could be equal, but the accelerations don't have to be equal. The acceleration is going to be the net force divided by the mass. So even if the force is the same, if you divide by that mass, you'll get a different acceleration. And that's why the result of the force does not have to be the same even though the forces do have to be the same because of Newton's third law.

Another misconception people sometimes make is they think there might be a delay in the creation of this Newton's third law partner force. People think maybe if I exert this first force fast enough, I can catch the universe sleeping, and there might be some sort of delay in the creation of this other force. But that's not true; Newton's third law is universal no matter what the situation, no matter what the acceleration or non-acceleration, or motion or no motion, whether one object's bigger or smaller.

If they're Newton's third law partner forces, they are equal, they are opposite, and they are always equal and opposite at every given moment in time. So even if I came in, all guns ablazing, Chuck Norris style, trying to dropkick some wall—that does not look like the correct form for a dropkick—but even if I came in flying at this wall, as soon as I start to make contact with the wall, I'm going to exert a force on the wall, and the wall has to exert a force back.

So I'd exert a force on the wall to the right, and this would be the force on the wall by my foot. There'd have to be an equal and opposite force instantly transmitted backward on my foot. So this would be the force on my foot by the wall, and this happens instantaneously. There is no delay; you can't kick this wall fast enough for this other force to not be generated instantaneously. As soon as your foot starts to exert any force on the wall whatsoever, the wall is going to start exerting that same force back on your foot.

So Newton's third law is universal, but people still have trouble identifying these third law partner forces. One of the best ways to do it is by listing both objects. As soon as you list both objects, well, to figure out where the partner force is, you can just reverse these labels. So I know over here if one of my forces is the force on the wall by my foot, to find the partner force to this force, I can just reverse the labels and say it's got to be the force on my foot by the wall, which I drew over here.

So this is a great way to identify the third law partner forces because it's not always obvious what force is the partner force. To show you how this can be tricky, consider this example: say we've got the ground and a table. This example drives people crazy for some reason. If I've got a box sitting on a table, we'll call it box A. Box A is going to have forces exerted on it. One of those forces is going to be the gravitational force, so the force of gravity is going to pull straight down on box A.

If I were to ask you what force is the third law partner force to this force of gravity, I'm willing to bet a lot of people might say, "Well, there's an upwards force on box A exerted by the table." And that's true, and if box A is just sitting here, not accelerating, these two forces are going to be equal and opposite, so it's even more tempting to say that these two forces are equal and opposite because of the third law. But that's not true.

These two forces are equal and opposite because of the second law. The second law says if there's no acceleration, then the net force has to be zero; the forces have to cancel, and that's what's happening here. These forces are equal and opposite; they're canceling on box A, which is a way to know that they are not third law partner forces because third law partner forces are always exerted on different objects. They can never cancel if they're third law partner forces.

So what's going on over here? We've got two forces that are canceling; they're equal and opposite, but they're not third law partner forces. Their partner forces are somewhere else. I haven't drawn their partner forces yet, so let's try to figure out what their partner forces are. Let’s get rid of this. Let's come back to here; let's slow it down to figure out what the partner force is. Name the two objects interacting.

So this force of gravity, I shouldn't be vague; I should call it the force on object A, or box A, exerted by—well, you can't just say gravity. Gravity is not an object. The object that is exerting this gravitational force on A is the Earth. So this force, really, this gravitational force, if I want to be careful, is the force on object A exerted by the Earth.

Now it's easy to figure out where the partner force is. The partner force can be found just by reversing these labels. So instead of the force on A by the Earth, there’s got to be an equal force, which is the force on the Earth by box A. So opposite means it has to point up, so that has to be an upward force, and that upward force has to be exerted on the Earth by box A.

This is kind of weird because you may not have realized it, but if the Earth is pulling down on a box—or you—that means you are pulling up on the Earth. This might seem ridiculous. I mean, if you jump up, you jump up, you fall back down, you move around, but the Earth just sits there. If your forces are equal, how come the Earth doesn't move around like you do?

Again, it's because just because the forces are the same, the acceleration doesn't have to be the same. The mass of the Earth is so big compared to your mass, there's basically no acceleration even though the forces on you and the forces on the Earth are the same. So these two are third law partner forces. These two are joined together forever. They have to be equal no matter what happens; these two forces will always be equal.

I don't care if this box is accelerating or not accelerating, whether there's motion or no motion, whether it's hitting a wall, sitting on a table, or falling through space; these two forces must always be equal and opposite because of the third law.

So how about this other force, this force that the table was exerting? This is the force on A by the table. If I want to label it correctly, I'd call it the force on box A exerted by the table. Now finding the third law partner force is easy. I can just reverse these labels, and I’d get that there must be an, instead of an upward force, a downward force on the table by A.

So I'm going to have another force here on the table; it's going to be a downward force, downward force on the table by A. That's the third law partner force to this upward force that the table is exerting. These two forces are also third law partner forces. These forces are going to be equal and opposite no matter what happens.

This force on box A by the table and this force on the table by box A must be equal no matter what happens. But the force on box A by the table does not have to be equal and opposite to the force on A by the Earth. It happens to be equal and opposite in a case where there's no acceleration, but if we stuck this whole situation into an elevator or a rocket that had some huge acceleration upwards, even if there's acceleration upwards, these partner forces have to be equal.

So the force on A by the table and the force on the table by A will have to be equal. Similarly, the force on the Earth by A and the force on—by the Earth have to be equal. But no longer will these two forces have to be equal because they're not partner forces. They might be equal and opposite in some circumstances, but they don't always have to be equal and opposite.

If we're accelerating upwards, this upward force on the box must be bigger than the downward force on the box, and so these won't be equal. Recapping quickly, Newton's third law is a statement about the forces on two different objects. Because it's about two different objects, those forces can never cancel.

To find the Newton's third law partner force, just reverse the label after you've identified the two objects that are interacting. The third law partner forces have to be equal in magnitude even if one object is larger than the other or has more charge or any property that might seem like it would convey more force than another object. If those are the two objects interacting, their forces must be of equal magnitude in opposite directions.

The force is instantaneously generated. These partner forces must be equal and opposite. Be careful; some forces might seem like partner forces, and they might be equal and opposite, but they're not necessarily third law partner forces. They may just be equal and opposite for other reasons.