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Torque & Acceleration of a Point Mass

Patrick Ford
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Hey, guys. So in this video, I want to talk about a torque producing an acceleration on a point mass. So you may remember that in all these rotation questions, we can have either point masses, which are tiny objects with no radius and no volume. Or we can have rigid bodies or shapes that have radius have a volume. Eso Let's check out how torques and acceleration works for point masses so real quick. I want to point out that most heart problems are actually going to involve, uh, shapes or rigid bodies. Um, but I want to quickly just do one with point masses because it works just the same. Most of the time you're gonna be here, but this works just the same. Cool. So quick Example you spin a small rock. Small rock is on indication that this is going to be a point mass because they say it's small and I don't give you the shape of the rock. The masses 2 kg at the end. You do this at the end of a light string of length three. If you spin a rock or any object at the end of a string, um, the length of the string will be the distance to the center. Okay, so it will be your little are so little r equals length of the string, which is 3 m and the masses kg. Okay. We want to know what net torque is needed to give the rock and acceleration of four. So if you wanna have an acceleration of four, what is the torque you need? And I want to remind you that net torque is the same thing as some of all torques. Okay, so check this out. I am asking for some of all torques, and I'm giving you Alfa. So I hope that you immediately thought of using, uh, immediate thought of using some of all torques equals I Alfa. And this is what we're looking for. Okay, Now, to calculate this, we just have to figure out these two guys remember point masses have a moment of inertia. Theme, Moment of inertia of point masses is given by M R Square. Where are is a distance to the center. Okay, so we're gonna replace this with m R squared Alfa and we have all of these numbers. The masses to the R is the distance, which is going to be three. And we have to square that. And then Alfa is four. Okay? And if you multiply all of this, you get 72 Newton meters. Remember, Torque is has units of Newton meter. That said four part A Got that done. Um, for part B, it's asking us to find the tangential acceleration while it has that speed. Remember, the tangential acceleration 8 10 is related is related to Alfa. By this equation, 8 10 equals R Alfa. So all we gotta do is multiply. Um, R is the distance here, which is three, and Alfa is a four. So that means that at that point, when you have an Alfa of Four, your tangential acceleration is 12. This is an acceleration A. It's a linear acceleration. So it's going to be 12 m per second square. Cool. Thes two are somewhat unrelated. Um, this is new stuff. This is just plugging it back, um, into a different kind of acceleration. Some old stuff bringing that back, putting it all together. All right, so that's it for this one. Let me know if you have any questions and let's keep going