12. Rotational Kinematics

More Connect Wheels (Bicycles)

# Bicycle Problems (Moving)

Patrick Ford

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Hey, guys, we're not gonna look into bicycle problems where the bike is actually free to move. So the wheels air touching the floor. So as they spin it also caused the bike to move sideways. Check it out. Um, so movie bikes. Yea. But first, I want to remind you what happens if the bike doesn't move. If it's not free to move sideways. Okay, if the bike doesn't move when the wheel spin, you have what's what we call a fixed access or fixed wheel. Andi, this means that the velocity of the center of mass off the wheel will be zero. Okay, neither wills or will spend. Additionally, the both of a loss in the front wheel and the omega in the front wheel will be zero. Remember the omega in the back wheel? The back wheel could be spinning because you could lift the bike and move the pedals, and then that caused the back to spend. But the front wouldn't spend unless you spend the front yourself. Okay. All right. Now, if the bike is moving, we have a free access, which is a situation where you have both Omega and the Omega Envy. So It's sort of the toilet paper that's rolling around the floor. Okay, in this case, because the bike is one unit, the back wheel in the front wheel are moving sideways together. They don't become farther apart, they move together. What that means is that this velocity here, the loss of center mass here when I clean it up. So it's not a mass in the velocity center mass here are actually the same. Okay. And that's what typically ah, problem would call the velocity the bike If the problem says the bike moves the 10 m per second. This means that this moves with 10. And this moves with 10. This way. Okay, let's clean it up so we don't make a huge mess. All right, Now, remember, for free access, which is this situation here we have that This velocity right here we have the velocity center mass is, um, our omega. Where are the race of the wheel? So this relationship here can be rewritten if V C. M is our omega, then v c m equals V. C. M is gonna be our omega equals are omega. Now, in this case, I'm gonna write front front back back. Okay. So we can write those two now for most bikes. Um, the front wheel on the back wheel are supposed to have the same radios, same diameter. Now, the reason I say most is because you could get a physics problem that doesn't have it that way. That's not really supposed to be like that, but they could give you one of those. Um, And if that's the case, we can say that's Omega. So basically, what happens is if these two are there the same, these two guys with cancel, Right? Okay, So if our front equals are back, the ours would cancel. Then you have that Omega front equals Omega back. So not only do they have the same V, but they have the same w. So let's sort of recap Here. You have pedal one sprocket too back, sprocket Three back. Well, four front wheel five. And the relationships are that these two guys spinning the same access. So the omega is the same. Omega equals omega, too. Um, these two guys spend the same access, so omega three equals omega four. The chain that connects Thies too. Make it so that's their V's are the same. So I can say that V two equals V three. And what this means that I can write that are to Omega two equals R three omega three. Okay. And this is really, um, the important one. Is this one here? That's the useful one. Okay, the first this is just to get to that. All right. Boom. And then the last relationship here, which this is old stuff, by the way, Um, the new thing here is that there's also relationship between front wheel and back wheel, which is this right here. Okay, so I'm going to write that are four omega four equals R five omega five. And obviously, if the art of the same they canceled. So Omega four is Omega five becomes the same. Cool. So this is how a moving wheel works theme on Lee New thing. If the wheels moving is this, I'm gonna put a little plus here to indicate that this is what's new. Okay, back and put a little new here. Um, and then obviously that this guy would actually move. Okay, This is now actually touching the floor. Let's do an example. So it says here the wheels on your bike have radius 62 both 66. Both of them. Okay, so let's draw both wheels. Um And then it says if you ride with 15 so that's the bike equals 15. Calculate the linear speeds, the center of mass of both wheels and the angular speed of both wheels. So we're not talking about pedals or sprockets or anything. Just these two wheels. I'm gonna call this just for the sake of simplicity. I only have two things, So I'm gonna do R one and R two. Now I'm giving the radius years. That's good. 0.66 0.66. And we want to know what is the linear speed of the center of mass. So I wanna know what is V. C. M. One and what is V c m. Two v c m of any wheel that moves while rolling is our omega. So V C M one is our one omega one. Um, and V C m two is our to Omega too. But the key thing to remember here, there's two things to remember. These two wheels move together, so these numbers are actually the same. Okay, also, they're also both 15. Okay, remember if the bike moves of 15 to the right, both wheels move with 15 to the right. So what I'm gonna do is I'm gonna do this. I'm gonna say this equals 15 and this equals 15. Okay? And that's the answer to part A Is that both of these guys equal 15 now for part B, I want to know what is Omega one and what is Omega Shoe? Well, if you look at this equation, I can use this here to solve, okay? And so it's just basically plugging into the equations. Let's do that. So Omega one will be 15 divided by R one or divided by 150.66. And the answer to that is 20 to radiance per second. Second, we will have the same omega because it's the same numbers. So I've Omega two equals 15 divided by r. Two arches, the same 20.66. So the answer is also 22.7 radiance per second. Okay, so that's the answer for parts. Be now just to recap again. What happened here? I told you the velocity bike was 15. So automatically you would know that the boss of the wheels. The linear velocity. The wheels at the center of mass in the middle of them is 15 as well. Once you know that this is 15 and you have the radius of both wheels. You could just plug it into that equation, um, in solve for w Very straightforward. Cool. That's it for this one. Lets the next example.

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