Identifying centripetal force for cars and satellites | AP Physics 1 | Khan Academy

So here we have something that you probably have done in the last, maybe in the last day. If we're in a car and we're just making a turn, let's say at a constant speed on a road that is flat, so it's not a banked racetrack or anything like that, what is keeping the car from just veering off in a straight line?

This one's a little bit less intuitive because we don't have any string here that's tethering the car to the center of the curve of our road. So what's keeping it from going in a straight line here? Pause the video and think about that.

Well, in this situation, we could think about other forces that are at play. Once again, I'll assume we're in a vacuum, although you could think about air resistance as well, and think about what is counteracting the air resistance. It turns out that that's friction. But the other forces at play—you of course have the force of gravity pulling downward on the car—force of gravity, and that's being counteracted by the normal force, that's being counteracted by the normal force, the normal force of the road on the car.

But what's keeping the car going in a circle? Actually, let's just do air resistance for fun. The air resistance, the force of the air on the car, that's going to be pushing in the direction opposite from the velocity of the car. So we could call that, let's just call that the force of air. You can't read that? Let me do this. So, the force of the air— that would be its magnitude.

And then that's being counteracted by—and this is a little bit counterintuitive—and this will actually give us a clue on the centripetal force. That is, this component that's going to be counteracted by this component of the friction. So, the force of friction in the direction that the car is going. Think about it. If you didn't have—if you did, if this was on ice, if the wheels didn't have traction, no matter how hard the engine went, and no matter how fast the wheels sped, it wouldn't be able to overcome the air resistance, and then the car would decelerate.

But these are all the forces that are not acting in a radial direction—that aren't keeping the car on the road, so to speak—are keeping it going in that circular motion around the curve. Once again, there is the force of friction. So this is another, I guess you could say, another component of the force of friction, and that's all happening where the tires—in other words, literally the rubber meets the road. But this right over here, you have the force of friction that is keeping—and maybe I'll call it force of friction radially, radially put in parentheses—force of friction radially that is keeping us going in a circular direction.

In this situation, that is our centripetal force. Let's do another example, and let's keep going with the theme of cars now. So let's say a scenario where we are on a loop-de-loop, which is always fun and kind of scary. I have dreams where I have to drive on a loop-de-loop for some reason, and I find it intimidating. But let's think about the car at different points of the loop-de-loop and think about what is the centripetal force at different points.

So let's first think about this point right over here, and once again, we assume that we are dealing on a— we're on a planet. So you have your force of gravity right over here, force of gravity, and then you also have your normal force. I'm going to draw it a little bit larger because in order to be moved—I guess you could say upwards to stay on the loop-de-loop—the normal force has to be larger. You have to have a net force inward.

So this is our normal force, and so in this situation, the magnitude—the magnitude of our centripetal force—let me just in a different color. The magnitude of our centripetal force is going to be the net radial inward force, or the magnitude of the net radial inward force. So this would be equal to the magnitude of our normal force minus the magnitude of the force of gravity.

If this wasn't net inward right over here, then you would not—this car would not be able to move in a circle. It would just, if this netted out to zero, it would go in a straight line that way. If this netted out so that it was negative, it would accelerate downwards. So let's go at this point right over here, and we could also think about things like air resistance and friction, where air resistance is pushing back on the car and then the friction is overcoming it. But we're going to focus just on the things that are driving us centripetally inward or outward right now.

Now, what about this point for the car? Well, we still have the force of gravity—you still have the force of gravity—and actually, I'll make this a little bit bigger. We could, let me put the air resistance there just to be complete. So this would be the air resistance, force of the air, and that's being counteracted by the force of friction—the traction that the car has of the road over here.

This orange vector would now be the combination of the force of gravity, and actually, you could even consider it the force of gravity plus the force of the air, plus the force of the air pushing back on the car—the pressure of the air. That is being counteracted by the force of friction. So the force of friction of the tires pushing— or I guess the force of friction of the tire between the tire and the road— but neither of these are acting centripetally, acting radially inward.

So what's that going to be? Well, here you have the normal force of the track. The track is what's keeping this car going in this circular direction. So you have the inward force, which is the normal force, F normal. So in this situation, our centripetal force, the magnitude of our centripetal force, is equal to the magnitude of our normal force. These actually are even going to be the same, the exact same vectors.

Now last, let's now consider one last scenario when we are at the top of the loop-de-loop. Pause the video and see if you can figure that out. Well, once again, we can do things like we could say, "Hey, look, there's probably some air resistance that is keeping us—that is trying to decelerate us," so that and then that's being netted out by the force of friction.

But let's think about what was going on in the vertical direction. So here, pushing down this way, you're going to have potentially several forces, and I want this to be actually at the top of the loop-de-loop, although it doesn't look quite like that. But actually, let's just assume it is.

We're at the top of the loop-de-loop. Pushing down, you're going to have the force of gravity. But what else are you going to have? Assuming you're going fast enough, the track is also pushing down— the force of gravity plus the normal force. The magnitude of this vector would be the sum of the magnitudes of the gravitational force and the normal force, and that is what's providing your centripetal force there.

So in this scenario, we would say the magnitude of our centripetal force is equal to the magnitude of our gravitational force plus the magnitude of our normal force. Or we could even think about it as vectors. We could say, "Hey, look, if we just add up these vectors, these two vectors, you’re going to get your centripetal force vector." That's what keeps the car going in that circular motion.

Now, let's just do one last scenario just for fun. Let's imagine that we have an object in orbit. So, this is our planet, or any planet, really. You have an object in orbit—some type of a satellite. I'll draw what we normally associate with as a satellite, but this could be even a natural satellite, a moon for the planet. What I'm about to say applies to the moon as well.

So here, we don't have air; we have very minimal air resistance. There might be a few air molecules every here and there, but for the most part, this is in a vacuum and it's in orbit. So what keeps—so it's in uniform circular motion—it’s moving in a circular orbit around the planet. What keeps it from going off in a straight line? Pause the video and think about it.

Well, here you have the force of gravity. You have the force of gravity of the planet. So right there, you have the force of gravity. At first, people say, "Wait, gravity? You know, I see these pictures of astronauts floating when they're in orbit." Well, that's just because they're in free fall. But the gravity at that point, if you're a few hundred miles above the surface of the Earth, is not that different than the gravity on the surface of the Earth. You just don't have air there. And if you are in orbit, you're in constant free fall; so it feels to you like there is no gravity.

But it's gravity that is keeping you on the orbital path, on that circular path, and keeps you from just going in a straight line out into space.