12/10/2023 0 Comments Rotational motion![]() ![]() Just traces out a distance that's equal to however far it rolled. ![]() Now let's say, I give thatīaseball a roll forward, well what are we gonna see on the ground? We're gonna see that it This outside with paint, so there's a bunch of paint here. On the ground, right? Roll it without slipping. We coat the outside of our baseball with paint. The center mass velocity is proportional to the angular velocity? Well imagine this, imagine So, how do we prove that? How do we prove that That these two velocities, this center mass velocityĪnd this angular velocity are also proportional. Two kinetic energies right here, are proportional, and moreover, it implies Why is this a big deal? I'll show you why it's a big deal. Respect to the ground, which means it's stuckįor just a split second. This point up here is goingĬrazy fast on your tire, relative to the ground, but the point that's touching the ground, unless you're driving a little unsafely, you shouldn't be skidding here, if all is working as it should, under normal operating conditions, the bottom part of your tire should not be skidding across the ground and that means thatīottom point on your tire isn't actually moving with The point that doesn't move, and then, it gets rotatedĪround that point, and then, a new point is The tire can push itself around that point, and then a new point becomes So that point kinda sticks there for just a brief, split second. It's just, the rest of the tire that rotates around that point. So this is weird, zero velocity, and what's weirder, that's means when you'reĭriving down the freeway, at a high speed, no matter how fast you're driving, the bottom of your tire Right here on the baseball has zero velocity. Here isn't actually moving with respect to the ground because otherwise, it'd be slipping or sliding across the ground, but this point right here, that's in contact with the ground, isn't actually skidding across the ground and that means this point There's gonna be no sliding motion at this bottom surface here, which means, at any given moment, this is a little weird to think about, at any given moment, this baseball rolling across the ground, has zero velocity at the very bottom. Gonna be moving forward, but it's not gonna be Motion just keeps up so that the surfaces never skid across each other. This ball moves forward, it rolls, and that rolling Like leather against concrete, it's gonna be grippy enough, grippy enough that as Would stop really quick because it would start rolling and that rolling motion would just keep up with the motion forward. Skid across the ground or even if it did, that ![]() I mean, unless you reallyĬhucked this baseball hard or the ground was really icy, it's probably not gonna ![]() At least that's what thisīaseball's most likely gonna do. Something that we call, rolling without slipping. What's it gonna do? It's gonna rotate as it moves forward, and so, it's gonna do So, say we take this baseball and we just roll it across the concrete. Pitching this baseball, we roll the baseball across the concrete. Gonna talk about today and that comes up in this case. A really common type of problem where these are proportional. Translational kinetic energy isn't necessarily related to the amount of rotational kinetic energy. So we saw last time that there's two types of kinetic energy, translational and rotational, but these kinetic energies aren't necessarily ![]()
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