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Angular speeds of moving bicyle

Patrick Ford
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Alright. So here you have the wheels on your bike with radius 70. Both of them. So let's draw that real quick. Yeah, and e got the middle BRAC sprockets. I'm giving the radio, I hear so little guy, middle guy this and then you got the pedals here. Okay, if you read the question, doesn't actually mention the paddles that I put it here just so that we get in the habit of doing this one. The middle sprocket to back sprocket three back we or four. And this is five. Okay, the wheels have radius. So r four equals R five, which is 50.70 the middle sprocket in the back sprocket middle and back or 15 and eight. So middle is to r two equals 20.15 and r three equals points 08 Okay, if you ride with 20 this means that the bike equals 20. Let's say you're going that way, which means that V center of mass five equals 20. Let's get this out of the way on. I'm gonna draw this, um e just drive here. I'm gonna write it up here. That the center of mass of four, which is the back wheel. He's going to equal 20 as well. Remember, if you move in 20 the center mass of the wheels Are you gonna move with 20 as well? Okay, so we want to calculate the angular speed omega of the front wheel. Front wheel is five. Okay. How do we get this? Well, I know the radius, and I know the V c m. Okay. Remember when you have a wheel that's free. Um, you have that. The c m of that wheel is our omega here. We're talking about five. So I'm gonna put five year, five year, five year, and I wanna find Omega five. So, omega five, I have these two numbers, so it's just a matter of plugging it in V C. M is 20 and the radius is 0.7. Okay. And if you do this, the answer is 28 0. radiance per second. All right, B, what about the back wheel? Well, back. Well, what's gonna be the same exact thing? Because the numbers are the same. So what is Omega four? Well, omega V C m four equals R four omega four. The radius and the V C. M are the same, right? It's moving 20 and the radius 200.7. Which means Omega four will be the same 28.6. If you calculate you get the same number. Okay. For part C, can you get it out of the way for part C? We want to know what is, um the English speed of the back sprocket. Remember, the back sprocket has the same angular speed is the back wheel. So we've already calculated this. Basically, Omega three is the same as Omega Four. So it's also 28.6 radiance per second. So so far, these first three things all have the same Omega, then for party. What about the middle sprocket? Let's let's give ourselves a little bit more room here. Sorry about that. I'm gonna sort of go backwards here. I wanna know what is Omega to? Well, I just found 32 is connected to three. Using this equation are to Omega two equals R three, omega three. So if I want to find this, I just have to move things around. So our three omega three divided by r. Two are three is 0.8 right here. Omega three is 28. and R two is 0 15. And if you calculate everything here, multiply this whole thing, you get 15.3 radiance per second. All right, so that's what this one hopefully makes sense very similar to the static bike. Uh, you just have this additional thing where the wheels now both have center of mass velocity, center of mass. And there's this new equation. Um, you know, we have to take care of All right, that's it for this. Well, I mean, if you guys have any questions