Our first quantity and rotational motion is the angular displacement. So we're not going to define it. Let's just point something out about it. It depends on the object, both on its shape and which direction it's pointing, but it depends on the object and the axis of rotation. Just like translational motion, you have to define an axis before you can really describe anything. So the same thing is true for rotational motion. So we're going to think about this with my favorite object. In all of my courses, this is my Teflon rod. So if you've taken 102x, my electricity magnetism course, which I highly recommend, you know how much I love to play with the Teflon rod. So now we're going to use it to think about orientation and angular displacement. So first, we'll define an axis along the back. That's we're going to think about it rotating about an axis perpendicular to one face of the object. So I'll try to draw it in 3D so you can see the axis, axis like this. And we'll start with the rod down here like that. So there's the rod right there. And we'll say for this, this is the rotation axis here. And we'll say that this direction, in addition to defining the axis, you have to define the origin. So we're going to say flat is theta equals 0. Now we know that the rotation we want is goes around the axis. So if my finger is the axis, it's going to go up and down like that. So in the drawing, it's going to go higher like this. So we could change the orientation and get it to go like that. Say, and then say what's its direction now? And you could say theta equals, it looks like maybe 20 degrees. So that's a displacement. We're from one position, one angular position, to another angular position. But that 20 degrees describes this kind of emotion about this axis. We could define another axis. We could do an axis going straight through the middle and rotate like this. So we can draw that real quick. So if the axis is down, then we can draw, I just flatten like this and call that 0. So there's theta equals 0 degrees. And then if we just turn it in and out of the page a little bit, I'll kind of tilt it so you can see it. It could go kind of like that, like that. And then this theta maybe is 20 degrees. Well, we're just turning it in and out like that. So you can see in both cases, it moved 20 degrees. But it's completely different motions because it was around. Those motions were around different axes. So picking the axis is the most important thing. In some problems, it'll be chosen for you. In some problems, its natural free motion will define the axis. Don't worry about where to get it for now. So let's look at the quantities we use. We talked about theta, which is the angular position. But that's not the displacement. Remember, displacement is always a change. So delta theta is theta, final minus theta, initial. So since our initial theta is here, are both 0, the displacements are also both 20 degrees. So delta theta here is 20 degrees, final minus initial. Delta theta here is 20 degrees, final minus initial. There's one more thing. The angular displacement is a vector. Remember how the translational displacement delta x is always a vector because it's in a direction along the x axis. Angular coordinates are also vectors. The direction is the tricky part. We'll talk about how to get it in a minute. For now, I'm just going to tell you, this direction is along the rotation axis. The direction is always along the rotation axis of the vector. So even though it's pointing away from the rotation axis, it's pointing perpendicular to the rotation axis. And the motion is in this perpendicular plane. The formal mathematical vector is actually along the axis in that case. Here, we went from here to here, the delta theta vector, the angular displacement is that way. The only question remaining is, what is the direction? So we'll get to that in the next one. And one more little thing. Remember, eventually, in translational motion, we acknowledge that even the position was a vector, because the position is the displacement from the origin. So technically, these are also vectors, because they are the displacement from the origin. So when you're here, the vector length is 0. But when you're at 20, technically, that's a position displaced from 0. So the same as the displacement in this case. So everything is always vectors, really. We'll look at that more next.