Our first quantity and rotational motion is the angular displacement. 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 depends on the object, and the axis of rotation. Just like transnationals motion, you have to define an axis before you can describe anything. Same thing is true, for rotational motion. We're going to think about this with my favorite object, in all of my courses. This is my Teflon rod. If you've taken 102X, my electricity, and magnetism course, which I highly recommend I love to play with the Teflon rod. Now we're going to use it to think about orientation and angular displacement. First, we'll define an axis along the back. We're going to think about it rotating, about an axis perpendicular to one face of the object. I'll try to draw it in 3D, so you can see the axis, like this. We'll start with the rod down here, like that. There's the rod right there. We'll say, this is the rotation axis right here. We'll say that this direction, in addition to defining the axis, you'd have to defend the origin. We're going to say flat is theta equals zero. Now we know that the rotation we want, goes around the axis. If my fingers the axis, it's going to go up, and down like that. On the drawing, it's going to go higher like this. We could change the orientation, and get it to go like that. Then say what's its direction now? You could say theta equals, 20 degrees. That's a displacement from one position, one angular position, to another angular position. That 20 degrees describes this motion, or route, this axis. We can define another axis going straight through the middle, and rotate like this. We can draw that real quick. If the axis is down, then we can draw it flat like this, and call that zero. There's theta equals zero degrees. Then if we turn it in, and out of the page, I'll tilt it so you can see it. It can go, like that. Then this theta, maybe it's 20 degrees, or we're turning it around like that. You can see in both cases, it moved 20 degrees, but it's completely different motions, because it was around, different axes. Picking the axis Most important thing. In some problem we chosen for you. In some problems, it's natural free motion will define the axis, so don't worry about where to get it for now. Let's look at the quantities we use. We talked about theta, which is the angular position. That's not the displacement. Remember, displacement is always a change. Delta theta is theta final minus theta initial. Sets are initial thetas here are both zero. The displacements are also both 20 degrees. Delta theta here, it 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, was always a vector, because it's in a direction along the x. Angular coordinates axis 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. Even though it's pointing away from the rotation axis, it's pointing perpendicular to the rotation axis. The motion is in this perpendicular plane. The formal mathematical vector is actually along the axis. In that case, 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? We'll get to that in the next one. More little thing. Remember eventually, in translational motion, we acknowledged that even the position was a vector, because is the displacement from the origin. Technically these are also vectors, because they are the displacement from the origin. When you're here, the vector length is zero. When you're at 20, technically that's a position displaced from zero. It's the same, as the displacement in this case. Everything is always vectors really. We'll look at that more next.