Anderson Video - 2D Motion and Displacement

Professor Anderson
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Hello class, Professor Anderson here. Welcome to another installation of the looking glass physics lectures. Today we're going to talk a little bit more about 2D motion, projectile motion and how we deal with all this stuff mathematically. So let's talk a little bit about 2D motion. Do we really care about moving in two dimensions? Should we just worry about one dimension? Or do we really need three dimensions? And to think about this for a second, let's say we do the following: Let's say we drive from San Diego to LA. Okay, you guys have probably all done this drive. It's roughly 110 miles from San Diego to LA. What is the trajectory that you take? Once you get on the road, how do you get from here to LA? If you have a thought, raise your hand. What freeway do you take? Yeah >> Take the five. >> Take the five. And the five, is it a straight line from San Diego to LA? >> Not really. >> Not really. What is it? It's kind of squiggly, and in particular it is pretty curved. It sort of squiggles around a bit but, it curves to the left. Why does it curve to the left? Why wouldn't we just go in a straight line from San Diego to LA? >> The ocean is in the way? >> Because the ocean's in the way, right. This is the curve of California between San Diego and LA and so we can't go in a straight line because the ocean's in the way. If you fly in an airplane of course it's much straighter. And if you've ever done that, you know that you go over the ocean. So, this is two dimensional motion. Okay when you're driving around on the surface of the Earth and you don't drive very far – you're not driving all the way across the country – it is essentially 2d motion. We know of course the earth is a sphere and so it's really three-dimensional motion but for the a good approximation we can just say it is two-dimensional motion. And in fact a lot of what we observe in the world is two-dimensional motion. When i throw an object– a projectile– it follows two dimensional motion, not three dimensional motion. You really only have to worry about the x horizontal position and the y vertical position. You don't have to worry about the other one which is towards you or away from you. All right so let's review a little bit. Let's say I have an x y coordinate system If I have an x y coordinate system and I start at that point right there, I can label that with a vector, right. That is my position vector for the starting position. Position vectors always start at the origin and go to the point of interest. Now, let's say I follow some complicated trajectory And I end up over there. Do I have to worry about that path? Well it depends on what you mean by worry. If we're worried about how much energy you exerted due to friction along the way, then yes, you do have to worry about that. But if you're just worried about the displacement, then you don't. We draw our final vector rf and that describes the position of our final location and so usually when you're interested in physical quantities, you are interested in the difference between those two. And the displacement vector delta r which is "where did you go?" It is r final minus r initial. Okay, there's our our final. That was our r initial. So, how do we figure this out graphically? Well remember, any time you have two vectors and you want to add them, you do the tip to tail method but we're not adding them, we're subtracting them. What we know is that this is exactly the same as rf plus negative ri. And if this is ri, we can do the negative of that very easily. We just flip the direction of it. So rf is there, ri is going to look like this. The negative of ri will look like that. Okay and now where is our delta r? Delta r is right there Okay, where is it on our picture? If I move this over, it's exactly the same as that right there. Okay, that is your displacement vector. Start at the end of the ri, go to the end of the rf All right, what about velocity? We talked about position and displacement but what about velocity? How does that figure in?
Hello class, Professor Anderson here. Welcome to another installation of the looking glass physics lectures. Today we're going to talk a little bit more about 2D motion, projectile motion and how we deal with all this stuff mathematically. So let's talk a little bit about 2D motion. Do we really care about moving in two dimensions? Should we just worry about one dimension? Or do we really need three dimensions? And to think about this for a second, let's say we do the following: Let's say we drive from San Diego to LA. Okay, you guys have probably all done this drive. It's roughly 110 miles from San Diego to LA. What is the trajectory that you take? Once you get on the road, how do you get from here to LA? If you have a thought, raise your hand. What freeway do you take? Yeah >> Take the five. >> Take the five. And the five, is it a straight line from San Diego to LA? >> Not really. >> Not really. What is it? It's kind of squiggly, and in particular it is pretty curved. It sort of squiggles around a bit but, it curves to the left. Why does it curve to the left? Why wouldn't we just go in a straight line from San Diego to LA? >> The ocean is in the way? >> Because the ocean's in the way, right. This is the curve of California between San Diego and LA and so we can't go in a straight line because the ocean's in the way. If you fly in an airplane of course it's much straighter. And if you've ever done that, you know that you go over the ocean. So, this is two dimensional motion. Okay when you're driving around on the surface of the Earth and you don't drive very far – you're not driving all the way across the country – it is essentially 2d motion. We know of course the earth is a sphere and so it's really three-dimensional motion but for the a good approximation we can just say it is two-dimensional motion. And in fact a lot of what we observe in the world is two-dimensional motion. When i throw an object– a projectile– it follows two dimensional motion, not three dimensional motion. You really only have to worry about the x horizontal position and the y vertical position. You don't have to worry about the other one which is towards you or away from you. All right so let's review a little bit. Let's say I have an x y coordinate system If I have an x y coordinate system and I start at that point right there, I can label that with a vector, right. That is my position vector for the starting position. Position vectors always start at the origin and go to the point of interest. Now, let's say I follow some complicated trajectory And I end up over there. Do I have to worry about that path? Well it depends on what you mean by worry. If we're worried about how much energy you exerted due to friction along the way, then yes, you do have to worry about that. But if you're just worried about the displacement, then you don't. We draw our final vector rf and that describes the position of our final location and so usually when you're interested in physical quantities, you are interested in the difference between those two. And the displacement vector delta r which is "where did you go?" It is r final minus r initial. Okay, there's our our final. That was our r initial. So, how do we figure this out graphically? Well remember, any time you have two vectors and you want to add them, you do the tip to tail method but we're not adding them, we're subtracting them. What we know is that this is exactly the same as rf plus negative ri. And if this is ri, we can do the negative of that very easily. We just flip the direction of it. So rf is there, ri is going to look like this. The negative of ri will look like that. Okay and now where is our delta r? Delta r is right there Okay, where is it on our picture? If I move this over, it's exactly the same as that right there. Okay, that is your displacement vector. Start at the end of the ri, go to the end of the rf All right, what about velocity? We talked about position and displacement but what about velocity? How does that figure in?