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Anderson Video - Cartesian Coordinates

Professor Anderson
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>> Hello class, Professor Anderson here. Let's talk a little bit about coordinate systems and how we can think about motion in our universe or more locally here on earth. So when we think about coordinate systems, what do we think about? Well, let me ask you guys a question, how many variables do we really need to localize a point or an object? If you want to say oh this object is in a particular location, how many variables do we need? Four. We need x, y, z and time. If the object is moving along x, y, z, tells where it is in coordinate space, t tells us as time progresses where it is in that coordinate space. Alright so let's start with this idea of x, y, z, and everybody have probably seen this sort of picture over and over and over again. x, y, z, where they're all at right angles is to each other, this is of course called a Cartesian coordinate system, and it's named after Descartes and when you're looking at a Cartesian coordinate system, make sure you draw it like this. This is something called a right-handed Cartesian coordinate system. The x and the y at the particular orientation relative to the z. If I switch these, if I made this the y, and this one the x, then that is in fact called a Left-handed coordinate system. And typically in physics, we always use Right-handed coordinate systems, okay. So anytime you see that, just switch it, make it look like this. When we get a little further on and we start talking about cross products, then you'll see what we mean by a Right-handed coordinate system. Okay, so x, y, z not too bad right? If I have some position here and I think about the position of that object, I can say "oh it has some has some particular x value, it has some particular y value and it has some particular z value." Okay when I drop the projection of this down unto the plane, this right here is the particular x value. This sign is the y value and then of course how far up you go on the z axis, that is the z coordinate. Okay, so that would localize this thing in space. Now, when we think about x, y, z coordinates, they're very useful because x is always pointing in the x, y is always pointing in the y and z is always pointing in the z. And so when we start talking about unit vectors, it turns out to be a very convenient system because the unit vectors will always point in the same direction.