Centripetal force | Physics | Khan Academy

You may have seen astronauts floating in the space station. Is it because there's no gravity? No, there is gravity because it's very close to Earth. Then why are they floating? Well, turns out that they are not floating. In fact, the whole space station is actually falling towards the Earth. When we are falling, we experience weightlessness. But if it's falling towards the Earth, then why doesn't it hit the ground? What's going on? Well, let's find out.

Let's stand on a very tall building, say it's so tall that it's actually above the atmosphere. Don't ask how we are breathing and stuff, but we have a ball with us and let's just throw the ball. What's going to happen? Well, it's going to fall down. What happens if you throw the ball faster? Well, it's going to fall down a little farther away. But remember, the Earth also curves down. So if you keep throwing faster and faster, look at what's going to happen—the ball curves. But because the Earth also curves, it starts going longer and longer distances.

Eventually, if you throw it at just the right speed, we'll then find that the ball curves at pretty much the same rate as the Earth curves. Even though it is completely falling, it will miss the ground completely and come back to the original position. That's exactly what's happening with our space station. Our space station is continuously falling towards the Earth, but because the Earth is curved and because it has very high sideward speeds, just like that ball, it is missing the Earth. Therefore, everything inside is in free fall and therefore, they feel weightless.

Now that brings up another question: how does it work? Like, isn't gravity supposed to pull you down and make you fall towards the Earth? So what's happening with the force of gravity? How do we make sense of all of this with Newton's laws and all of that? That's an excellent question.

So let's come back to Earth, look at some familiar examples, and then go back over here. The theme of this video is going to be investigation, so we're going to ask a lot of questions. Get ready to put your thinking caps on!

Alright, coming back to Earth, let's consider a case where a car is going around a circle, a perfect circle at a constant speed. The question for us is: is this car accelerating? What do you think? Okay, my instinct says no because the speed is the same. But then I remember that hey, acceleration is about velocity, and velocity includes not just the magnitude, which is the speed, which is constant, but also has the direction.

Clearly, the direction of the car is changing; otherwise, it would have gone in a straight line. So since the direction is changing, it must be accelerating. Now to investigate that acceleration, we need to be clear about the direction of the car. So what is the direction of the car right now?

Again, my instinct says, well, since the car is going like this in a curve, maybe the direction is this way. But remember, velocity vectors, or any vectors, cannot be curve; vectors have to be straight, straight arrow marks. So that can't be true. A good way to think about it is just to think about the direction in which it is pointing right now. Can you see? It's pointing this way.

So if you were to attach an arrow mark on the front of the car, then you would see that's what it would look like, and that itself is the direction of the velocity at this point. Similarly, a little time later when the car comes over here, look, it's pointing this way, and so the velocity is in this direction now. This length should stay the same because it's a constant speed. So the magnitude stays the same, but clearly, you can see the direction is changing.

By the way, one quick note about velocity: if you were to look at this direction, you can see that this line touches our circle at a specific point, right? Like, it's touching over here and this line is touching over here. Such lines are called tangents. In contrast, for example, if you have a line like this, it is not a tangent because it's not touching; it is cutting the curve, cutting our circle at two points. So since our velocity vectors are along the directions of tangent lines, we say velocity is tangential to the path. And this is not just true for circles; this is true for any curves.

Even if a car is going in a random curve, if you look at its velocity vectors, you will see that it's tangential. So velocity in general of any object will be tangent to the path that it is going in.

Anyways, coming back, the car is accelerating because its velocity is changing. Therefore, from Newton's Second Law, we know there must be a net force acting on the car because if there's an acceleration, there must be a net force acting on that car.

That brings us to the next and the most important question for us now: what is the direction of that force? Let's just concentrate on one point: what is the direction of that force on the car over here? There must be, right? If there was no force acting on the car, it would have gone straight (Newton's first law). Remember, so what is the direction of that force?

Again, what do you think? My first reaction is, well, I don't know. How am I supposed to know what direction the force should be? But here's how we can investigate. Let's start with some random direction. Let's say the direction of the force is this way, okay? Maybe in the same direction as the direction of the car, the direction of the velocity. But then we'll immediately see that can't be true because if this was the case, the force is in the same direction as the velocity, the car would have sped up. But the car is not speeding up, so this can't be true.

Hmm, okay, maybe the force is in the opposite direction, the net force in the opposite direction of the velocity. But that can't be true either because if this was the case—if the force is in the opposite direction of the velocity vector—it would slow it down. But the car is going at a constant speed; that can't be true either.

Okay, alright, what if the velocity was tilted like this? Well, even here you can see the force is sort of kind of tilted upwards, right? Directed upwards, so this would still increase the speed of that car a little bit, not as much as before, but a little bit. But that can't be true; it can't be tilted upwards even a little bit like this. Similarly, it can't be tilted this way because now notice it's slightly downward, so it would slightly slow down, which again can't be possible.

So what is the only way the force can be such that it neither slows it down nor speeds it up? It has to be neither tilted up nor tilted down, which means the only way it can be is perpendicular to the velocity vector. Now it's neither tilted up nor tilted down, so it will not be able to speed up or slow down the car. Now the car will go at a constant speed. Incredible, isn't it?

If you're wondering, well, why perpendicular this way and not perpendicular that way—well, we can kind of intuitively see that since the car is like curving to the left, this sounds a little bit more intuitively right compared to that one, right? So anyway, the force must indeed be perpendicular. The net force must indeed be perpendicular to the velocity vector over here, and that should be the same everywhere.

For example, even at this point it has to be because remember the speed needs to be the same, so this will be the case all the time. Now if you look at the direction of that force, you can see that the force is always directed towards the center of this circle. Therefore, we give a name to this force: we call it the centripetal force. It means a center-seeking force, the force directed towards the center of that circle.

Now, the first time I heard about centripetal force, I thought of a new kind of force. But it's not. For example, over here, who is providing which force is this? Well, if the car is going on a road, this is actually the force of friction. I mean, imagine if the road had no friction; if it was completely slippery, the car would just skid forward. Without friction, it wouldn't be able to do that. So centripetal force is not a new kind of force; it's the friction that is playing the role of the centripetal force.

Think of centripetal force as just an indicator of the direction of that force. Just like how we have upward force or downward force, we have center-directed force: the centripetal force.

Let's take another example. Consider a person who's swinging a yo-yo like this in a perfect circle. Again, assume constant speed. Well then, something similar must be happening over here; since the whole thing is going at a constant speed, there must be a force because it is still accelerating. The velocity is changing, but that force must be perpendicular to the velocity.

This time, who is providing the centripetal force? Well, we can imagine it's the string. You can imagine the string being very taut at this point, and so it's this tension force which is acting now as the centripetal force.

So in short, if the force is in the same direction as the velocity, its effect is to speed it up. We've already seen this. If the net force is in the opposite direction of the velocity, its effect is to slow it down; again, we've seen this. But now we have one more thing that we can add to our toolbox: if the force is perpendicular to the velocity vector, its speed will stay constant and it'll go in a curve.

That force ends up becoming towards the center of that curve; therefore, the force becomes a centripetal force. But remember, if you want your car or your yo-yo to keep going in a perfect circular path, then the force needs to be continuously directed towards the center, and even the strength must stay the same. If that changes in between, the path will change.

For example, imagine what would happen over here if the string suddenly broke. What will then be the path of the yo-yo? I'll give you a couple of options. One option could be the yo-yo goes just straight like this (again, we're ignoring gravity; don't worry about gravity), or maybe it'll go like this, or maybe because it's spinning, it will just continue spinning like this.

Which of the three cases do you think would happen? Again, my instinct is that, hey, it was spinning like this so it'll continue spinning. But let's think about this. Why is the car or the yo-yo moving? It was moving because of its own inertia, not because of force. Remember, first law: things in motion tend to stay in motion.

They have a natural tendency to go straight due to inertia. But because there is a centripetal force, that's the one that curves it; that's the effect of the centripetal force. Now when the string broke, that centripetal force is gone. So what'll happen? Because of inertia, it will tend to continue going in a straight line.

So this is what it would go; this would be the path of the yo-yo. Once the string breaks, it'll go straight. Of course, if there's gravity, it'll also curve down because of gravity. In general, things can be more complicated. For example, along with friction, let's say we also had thrust somehow—it was a rocket booster and there was thrust over here.

So there will be an additional force acting upwards, which is not a centripetal force. Now, things will be more complicated, but we can still intuitively think using these three things. We could now understand, hey, the thrust force will speed it up, the centripetal force will make it curve, and so it kind of goes in a curve but a larger curve like this.

So this way, even though things can be really complicated, just by using these three things, we can still intuitively kind of figure out how that curve will look, what will happen to its speed, and all of that.

Alright, one last question before we go to space—a important one. We know that the people who are sitting inside over here, when the car takes a sharp left turn, they get thrown to the right. Imagine this person is inside the car. I'm just showing it outside, but that person would get thrown to the right. If that car door was not closed, he would get actually thrown off of the car to the right. Why does that happen?

Does that mean there is an outward force acting on him, which we often call the centrifugal force? An outward force? The answer is no; centrifugal force is not a real force. It just feels like that because we're looking at things from the car which is taking a turn.

If you were to look at things from outside, then we know that this person who's traveling forward has a natural tendency to just go forward. But it's the car that is curving because of the centripetal force. Now let's look at what happens if there was no friction acting on him. He would just go straight. The car is the one that turns to the left, and as a result, he's not getting thrown out of the car—he's just maintaining his straight line velocity due to inertia (Newton's first law).

It's the car that is curving away from him. That's why it feels from inside the car as if he's being thrown out. So that feeling is just because of inertia, very similar to how when a bus accelerates forward, you get thrown backwards; same inertial push, same—it’s because of inertia you get thrown outwards.

So there is no centrifugal outward force; it's not a real force. There's only one real force: the centripetal force. That's why you wear seat belts, so that seat belts, along with the friction between the seat and you, all of them will also provide you the centripetal force so that you also curve along with the car.

Alright, now we are ready to get back to space. The satellite is going this way, the space station is going this way, right? So what is the direction of the velocity? Remember, velocity direction is always tangential to it. What is the direction of the net force acting on it? Well, gravity is the only force and gravity is acting towards the center of the Earth.

What do you see? You see that the force of gravity is perpendicular to the velocity! But since our satellite has just the right speed so that it curves at the same rate the Earth is curving, look, that gravity always stays perpendicular to the velocity vector. Therefore, gravity always becomes a centripetal force.

Since it's always perpendicular, it cannot change the speed of the satellite. The satellite speed stays exactly the same; all of gravity is used up to curve it, and therefore the satellite goes in a perfect circular curve. It's completely falling, and everybody inside is weightless. Isn't it beautiful? That's how all of it works out.

But of course, the last question we could have is: this would be the case provided the space station has just the right speed. But what if it had slightly more speed or slightly less speed? What happens then? Does it still remain circular? What happens now?

Well, we're going to learn all about that in the next video when we'll deal with orbits and look at the path of the orbits and all of that.