12. Rotational Kinematics

More Connect Wheels (Bicycles)

# Bicycle Problems (Static)

Patrick Ford

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Hey, guys. We're now gonna talk about bicycle problems, which are special type of connected wheel problems that we've seen, however, bike problems a little bit more complicated. Let's check it out. So it says your bike problems a bit more complicated. That's because they have more parts. They have five in total. In fact, um, in the simplest example we've covered so far, you have two cylinders or two wheels connected to each other. So that's two parts, by case, as many as five. Now, the reason I say as many as five is because most bike problems I'm going to talk about all the five parts. Uh, they may talk about two or three, but we don't know which ones. Someone to cover all of them. Okay, so let's check it out. What we're gonna do is we're gonna see some relationships between the pieces. So the pedals number one, um, the pedals. We're gonna draw them over here. Um, number one. The pedals caused the middle sprocket to spin middle sprocket. Is this green? Over here. This'll is the This is the front of the bike over here. Just to be clear, um, this is the middle sprocket, which is the gear like thing that your pedals air connected to. Okay, um, I'm gonna go in disorder. I'm gonna go pedals first called one, and then I'm gonna go middle sprockets second, because you interact directly with the pedal. That's the first thing you touch. The first thing that starts spinning and it causes the other one to spin. Now, these two things are spinning on the same axis of rotation. They're both spinning around the same central points on day one causes the other to spend. So we're gonna say that w of one has to equal w of the other. Okay, so I'm gonna say w one equals W two. Okay, Um, that's the first one I'm gonna put it here is Well, w one equals W two. So it's more visual. The chain there's a chain that connects both sprockets. I'm gonna draw a little chain here with green check and export sprockets. What that does that means that any point here is going to have the same linear velocity. A Xeni point here. Okay, so if I write this, I get that, um, let's call this number three over here again. Going sequential order number one, cause number two Just spin, which caused number three to spin. Um, points two and three over here have the same tangential velocity at the edge of the sprocket. So I can write that VT one. I'm sorry. VT two equals VT three. But remember, the tangential velocity at the edge of a circle is a potential lawsuit. The edge of a circle is VT. But over here, bt is our omega. If you are a distance, are okay. In this case, you're always going to be a distance. Are will be the radius because in bicycles, the chain is always on the very outside on the very edge off the circle. So our little are will always be the radius. So I'm gonna write Big are to Omega two equals big are three omega three. That's the second relationship you need to know. The third thing that happens is the back sprocket Number three over here is connected to the back wheel back wheels. The blue one. It's called it a four. And again it follows the sequence Number one cause number two to spin, which caused number three to spin, which causes number four to spin. Okay. Now, these two guys here have a similar relationship as these two guys. Okay, one and two are on top of each other. One causes to to spin. They spend together on the same central access. It's the same thing that happens here between three. And four. Okay, so I'm gonna say that Omega of three, which is the back sprocket, equals omega four, which is the back wheel. Okay, let me also add here that the these two points here are related. And Aiken, right? So what I wrote over here are to Omega two equals R three, omega three. I wanna have them in the diagram here, so it's nice to see, but I also wanna have him here. It's a little bit more organized. So here, we're gonna write that Omega three equals Omega form. Cool. So these are the three relationships you have, um, and bikes. Um, Now, the last thing we want to talk about is if the bike is not free to move on, but it wouldn't be free to move if the wheels are not touching the ground. Right. So if you lift your bike, for example, that we don't touch the ground. So if you spend the pedal, the back, the back tire, the back wheel will spin. But the front wheels not gonna spend because there's nothing connected to it. Okay, so in this case, the front wheel doesn't spin. So this is a special situation, which is when you have bicycles that are static. Okay, that's what we're looking into right here. Static bikes. You could lift the bike or you could flip it upside down. There's nothing connecting to the front wheel. The front wheel really only spins. If you are touching the floor, um, you rotate this pedals which make the metal sprocket rotate, which make the bottom of the back sprocket rotate, which in terms makes the back we rotate. And because, um, that causes the bike to go forward, which means that this will spin as well. So this is actually the last thing that happens. The front well, basically just spends because the back is already moving and you're touching the floor over here. All right, so that's it for that. Let's quickly do an example and see what we get here. So you turn your bike upside down for maintenance. This means that the bike won't move. So I'm already thinking. Okay, Bike doesn't really move. So v front in omega front, which, if you remember, we number that number five will make a five are both going to be zero. The middle and back sprockets have diameter 16 and 10. You spend the pedals at eight. You wanna know the angular velocity, which is w for all of these guys. So here it's talking about the middle sprocket, the back sprocket, the back wheel, the front wheel and the pedal. So this problems actual, including all five elements again, usually won't see that. But we're doing this here for just for completion. The back sprocket is always smaller. The middle sprocket is bigger. But then obviously the tire that we on the back is even bigger. So I got the little petals here. Okay, Pedals, one sprockets too. Three and wheel four in sequence. Okay, these guys are connected. You don't necessarily gonna do the whole thing, But I wanna do it just to get in the habit. The front wheel doesn't matter. It's not part of this thing. It's not gonna do anything. Okay, So I know that the the pedals spin a eight radios per second. Radiance per second is Omega. So this means that omega one is eight. That's given. Okay. Part eggs. Asking for the middle sprocket metal sprocket is Omega too, Remember, one and two are they go together. In fact, it's the same number for Omega. Okay, so I'm just gonna put here that omega two is eight as well because they rotate together very easy for part B. What about the back sprocket? Well, I wanna know Omega three. And what I know about Omega three is there's a way to connect, uh, back sprocket to the middle Sprocket by using this equation right here. Okay, so that's what we're gonna do. Um, are to w two equals R three W three. Okay, so w three becomes are two w two. So are too. W two divided by r three. Before we plugging numbers notice that we were given diameters instead of radio, So we're just gonna convert the to remember, in physics, you're always gonna use radius and not diameters. So we were given that the middle has a diameter so d to of 16 which means are too is 0.8 and then the back sprocket over here D three is 10. So are three is 0.5 now, Technically, if you plugged in diameters, right, if you did this D and D, it would have worked because they would have canceled. Um, but just to develop the habit of always switching to radius, just in case you can't really switch, you can't really use diameter. So we're gonna do that. All right. So even though we would have worked So this is gonna be 0. w two we just found here is eight. And then this divides by 0. All right. And if you do this, you get 12. 12.8 regions per second for part C. We want to know the back wheel. So we want to know what is w four eso. What do you think w four would be what's special about four. And how does four connect to three? They're on top of the same thing. They spin together. So w four is the same as W three. So it's 12.8, and lastly, the front wheel doesn't spin it all. So I hope you thought Do Omega is zero. Okay, that's it for this one. Let's see the next one

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