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16. Angular Momentum

Angular Momentum of Objects in Linear Motion


Angular Momentum of Objects in Linear Motion

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Hey, what's up, guys? So in this video, we're gonna talk about calculating the angular momentum. L often object that has linear motion. Now, remember, angular momentum is the mo mentum oven object that rotates eso. It might seem weird they would find the angular momentum oven object that is moving in a straight line that is not rotating. Let's check this out. So says here in some problems, an object movie in a straight line will collide against an object that is fixed in a rotating axis. So here, for example, I have these sort of like a rotating door that's fixed about this axis. Um, this object here will collide here, and it will cause this door to spend this way. Let's say right, so it is in a situation like this that the angular momentum off this guy so the l of that object will make sense to be used. Okay, so you may remember that we use linear momentum to solve collision problems well, to solve linear collision problems. So if you have a problem where both objects have linear velocity as they collide, then we're gonna solve this. We're gonna solve with linear momentum with conservation of linear momentum. But if we have a situation where one object has a V and another object has an Omega like here, this object moves with a V. But then, after the collision, the doors will have in Omega. Then we're not going to use P to do this. We're going to use l. Okay, so I'm gonna right here. We're going to solve this with l. Now, if I have to objects with Omega, So if you have two discs and they're both spinning and you push them against each other, that is an angular collision. I have an omega meeting up with another Omega, and therefore we're going to use not linear momentum, but angular momentum. Okay, these two here are probably obvious. Um, if you have to learn your motions, you usually your momentum if you have to, Um, angular momentum to angular motion to use angular momentum. What's interesting is the middle one, which is when you have one of each. Um, el takes over. So what matters is the l, not the P. We're gonna do some collision questions later, and you see this happen. So when we're trying to figure this out in this case here, we need to first find the objects angular momentum L and knots. It's lean your momentum because of what I just said here. Thes questions would be solved with L. So I don't care what this guy's P is. I care what l is. Okay, But the question is, how do we get the angular momentum? How do you get an angular momentum, Often object that's moving in a straight line? This object isn't even rotating. How do I find it's rotating momentum? Well, a knob checked in straight line has angular momentum relative toe on unrelated axis of rotation. What do I mean is you can actually find the angular momentum of this guy relative to this access, even though they haven't really collided yet, Right? So it's an unrelated access, So hey, that acts is over there. Let's find an angular momentum relative to it, and we use the equation. L equals M V R. Okay. And notice that this is the same equation that we used for the England momentum of a point mats. Angular momentum of a point mass. Okay, so let's do an example and see what the deal is here. so to rotating dollars each 6 m long are fixed to the same central axis of rotation has shown above. This is a top view, which means you are looking down into the doors and you see them from the top. Okay, so we've got those two. They're andan. Suppose a bird. 4 kg birds. So the mass of this guy here for kilograms, the bird moves with a velocity of 20 Um, or 30. Actually, it's It's 30 horizontal. It's about to collide against the door. So your top view, you see the bird going like this, um, is about to collide against the door at a 0.50 centimeters from one end. Now it says here that has two doors, which means we're talking about one to and the door's air 6 m long. Okay, which means each each one of these points here is 3 m long. So you can think of this is a half a door. Okay, so it means that this whole thing here is 3 m now. The bird is colliding at 50 centimeters from one end. So the bird is colliding 57 m from one end. Obviously, we're talking about this end and not this end. Okay, so this is 0.5 m, which means that this distance here is 2. meters. 0.5 hands, 2.5. Okay, we wanna know the birds. Angular momentum about the access to the center off the door just before hitting the door. So, again, the angular momentum often object in linear motion is given by l equals M V. R. Mass is four v is 30. Those air Just plug. Just plug into the equation. And R is the distance from the axis of rotation to the point where it will touch. Okay, So, just like a bunch of the other little ours that we've drives or that we've used, it's just a distance from, um, the axis of rotation to the point where the point of interest, which is the point of collision, that distance is 2.5. Okay, so this is very straightforward. Um, this is 0.5. So we're gonna use this distance here because it collides here. So it's 2.5, so 2.5 goes right there. We multiply this whole thing, and we have that This is kilograms meters per meters square per second. Okay, that's it. Just straightforward. Plug it in. Um, here. Just warning you that this is going to come back later. It's gonna make a return when we fully solve these problems. Thes types of rotational collision. So later on this is gonna collide. The door is gonna spin, and we're gonna actually be able to calculate how fast the door spits, but not yet. So contain your excitement and let's keep going. Let me know if you have any questions.