 Now we can talk about angular position and displacement. It's a quick reminder we've got our coordinate systems, and we had two that we've been working with. Rectangular, sometimes called Cartesian, and polar. In rectangular coordinate systems, we primarily used the coordinates x and y. In polar, we used r and theta. When it comes to angular positions, we really want to use the polar theta coordinate. So if I've got a object somewhere on a circle, I can measure the angle theta, and we typically measure that up from the positive x axis. In this case, it's about 36 degrees, but remember you can use any angular unit here. Degrees, revolutions, or radians. We'll see examples of all of these in this presentation. A couple other things to know about angular positions. They can wrap around. So for example, if I have an object, and it goes around but it keeps going around, you can have something like 1.5 revolutions. You can also have negative positions if it wraps around the other direction. So this one would be negative 0.5 revolutions. Now notice both of these particles look like they're at the same position, so we have to be a little careful with our angular positions and take into account the motion, which leads us to the concept of angular displacement. And that's a change in angular position. And like any of our changes, we can use our delta notation. Delta theta is the change in angular position, and it's the difference between the final and the initial positions. On a circle here, you've got a starting position, and you'd measure that, as we typically do, giving us our initial theta. And in this case, that's about 0.75 radians. We then move the object, so we now have a new position called our final angular position, or theta f. And it's about 1.4 radians for this particular example. Now our delta theta looks at where it started to where it went, and so that change is our delta theta. Mathematically, it's just the subtraction of these, giving us 0.65 radians, 1.4 minus 0.75. Now when it comes to displacement, we have to care about the sign. So positive represents a counterclockwise motion, and negative represents a clockwise motion. So we got some of those negative positions when we went in a negative displacement. Now if we think about distance versus displacement, and we did this in regular 1D kinematics quite a while ago, we have to consider the path. So here's another example. I'm going to go part way around the circle, 270 degrees, or 3 fourths of a revolution, but then I'm going to backtrack a little bit. And so I've got a displacement of negative 90, because I was going in the clockwise negative direction. If I look at my net displacement, it's just 180 degrees. But if I look at my distance, it's 360. How'd I get to 360? Well, I had the 270 and the 90. Remember, distance doesn't care about which direction I go, so I don't care about that negative on that second displacement. So this is a basic introduction to angular position and displacement so that we can start using these quantities in other equations.