Identifying centripetal force for ball on string | AP Physics 1 | Khan Academy

What we're going to do in this video is try to look at as many scenarios as we can where an object is exhibiting uniform circular motion. It's traveling around in a circle at a constant speed, and what we want to do is think about why it's staying on the circle. What centripetal force is keeping the object from just going off in a straight line?

So in this first scenario, I have some type of a wheel, maybe a ball, attached to a string that is attached to a peg at the center of the table. This wheel is moving in a circle at a constant speed. So it's moving in this circle at a constant speed.

So pause this video, think about all of the forces that are acting on this wheel, and which of those forces, or maybe some combination of those forces, that are actually acting as the centripetal force that are keeping the wheel on the circle.

All right, now let's work through this together. So there's a couple of forces that aren't impacting the wheel's staying on the circle so much, but they're there. For example, you're definitely going to have the force of gravity. We're assuming we're dealing with this wheel on a planet, so that would we denote its magnitude as capital F sub G, and then this is its direction with this orange arrow. So that's the force of gravity, and the reason why the wheel is not accelerating downward is that we have that table there, and so the table is exerting a normal force on the wheel that counteracts the gravitational force.

So the magnitude there would be the force, the normal force, and these are going to be the same magnitude; they're just going to be in different directions. And so let me see if I can draw this arrow a little bit taller. But what else is going on? Well, as you can imagine, if the string wasn't here, the wheel really would go off in a straight line and eventually fall off of the table.

And so the string is providing some inward force that keeps the wheel going in a circle, and that inward force, that pulling force, we would consider that to be the tension force. So I'll just draw it like that, and its magnitude is F sub T. In this situation, it is providing that inward force, so that is the centripetal force.

So we could say the magnitude of the tension, the tension force, the pulling force, is going to be equal to the centripetal force. In this case, they're actually the exact same vector, so I can even write it like this. This is the centripetal force vector; it's the tension in that rope that keeps us going in a circle.

Let's do another example. So this one is similar, but I have a few more dimensions going on here. This is a classic example from physics. I have a string attached to the ceiling, and I have some type of a ball or a pendulum, and it's swinging in a circular motion right over here at a constant speed. So the center of its circle would be right around there.

So once again, pause this video, think about all of the forces on that ball, and we're not going to talk too much about air resistance. Let's assume that these are in vacuum chambers for now, and then think about, well, which of those forces is providing the centripetal force.

Well, just like in the last video, there's definitely some force of gravity, so you have that vector right over there, and so its magnitude is F sub G. You also have the string holding up the ball, and so you're going to have its pulling force on. So this would be the magnitude here, would be F sub T—this is the tension force.

But what's counteracting the gravity, and what's keeping us going in a circle? Well, in this situation, we can think about the different components of the tension because this is going off at an angle. So if we break down that vector in the vertical direction, so if we take the vertical component or the y component of the tension force, it would look something like this.

We could call that F T Y for the y component; this would be its magnitude, and that is what is counteracting the gravity, why the ball is not accelerating downwards. And if we think about the x component of the tension, that would be this right over here. This is the x component of the tension, just to be clear where I'm getting this from.

So this would be F tension in the x direction; that would be its magnitude, and that is what is providing the centripetal force, or that is the centripetal force. So in this situation, the component of our tension in the x direction—and let me just denote that as a vector— that is our centripetal force; that's what keeps the ball from just going straight off in a direction like that.