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Identifying force vectors for pendulum: Worked example

A worked example finding all force vectors acting on a pendulum moving in a horizontal circle.

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Video transcript

- [Lecturer] 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. So this ball is attached to the string, and it's currently hanging down, and I think it's fair to say that we are on some type of a planet. And so, if we're on some type of planet, you're definitely gonna have the force of gravity acting on the ball, so let me draw that vector. So 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? And 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. And so, we could say the force of the tension, so it might look something like this, the force, 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 is one downwards, and then there is one going in the direction of the string, and if you look at these choices here, you would say it is that one right over there. Now some of you might say, "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 off? "And then isn't there some type of force "that counteracts the actual force of gravity?" And the answer to the question is yes, there is but those are really just components of the tension. And 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 Tx, that is our centripetal force, or that its magnitude of the X component of tension is the same thing as the magnitude of our centripetal force. 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 Ty, and F sub Ty, 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.