Identifying force vectors for pendulum: Worked example | AP Physics 1 | Khan Academy

We're told that a ball attached to a string swings in a horizontal circle at constant speed. As shown below, the string makes an angle theta with the horizontal. Which arrows show all the forces on the ball? So pause this video and see if you can figure that out.

Okay, so let's work through this together. This ball is attached to the string, and it's clearly hanging down. I think it's fair to say that we are on some type of a planet. If we're on some type of a planet, you're definitely going to have the force of gravity acting on the ball. So let me draw that vector. The force of gravity, I'll do in orange; let's say it looks something like that. Its magnitude I'll denote as capital F with a sub g right over here.

Now, what's keeping that ball from accelerating downwards? And also, what's keeping that ball in this uniform circular motion? The answer to both of those questions is the tension in the rope. Remember, tension is a pulling force; the rope is pulling on this ball. So we could say the force of the tension; it might look something like this: the force of the tension.

Now, just with that, we have constructed a free-body diagram, and we can immediately answer their question: what are the forces that are acting on the ball? Which arrows show it? So there's one downward, and then there's one going in the direction of the string. If you look at these choices here, you would say it is that one right over there.

Now, some of you might be saying, "Wait, hold on a second! Isn't there some type of a centripetal force that keeps the ball going in a circle? That keeps it from just going straight away, straight off?" And then, "Isn't there some type of force that counteracts the actual force of gravity?" The answer to the question is yes, there is. But those are really just components of the tension.

So if you look at the x component of the tension, I'll do that in a blue color right over here. This x component of the tension, so I'll call that F sub t x, that is our centripetal force, or its magnitude of the x component of tension is the same thing as the magnitude of our centripetal force.

And if we look at the y component of our tension, the y component of our tension, that's what counteracts the force of gravity. So this right over here, its magnitude is F sub t y, and F sub t y, this magnitude is going to be the same thing as the magnitude of the force of gravity. But we already answered our question, and we just got a little bit more intuition of what's going on right over here.