 So now we're looking at angular units. Degrees is one of the really commonly used units for measuring angles. And you're probably all familiar with this. You can have some small angles. You can have some bigger angles. And you don't have to measure these angles with one of the lines being horizontal. At anything, you can have two different lines in different directions and measure the angles in between them. For degrees, we've got a couple of special measurements. We just want to make sure we've got here, which is if I go all the way around a circle, that's going to be 360 degrees. And what I call a right angle is 90 degrees. That's a quarter of the way around the circle. And that brings us to revolutions. Revolutions is defined so that once around the circle is one revolution. And if I'm doing my right angle, which is a quarter of the way around the circle, that's 0.25 revolutions. So you could measure angles in revolutions as well as in degrees. One thing to keep in mind with revolutions is you can go around more than once. So for example, I could go all the way around completely once, but keep going. And I'd have 1.5 revolutions or any amount of revolutions. Then we get to radians. Radiant is another unit that we can use for angular measurements, but it's a little bit different. It's defined by the ratio of the arc length to the radius. In particular, one radian is the angle where the arc length equals the radius. And this is going to need a diagram to explain. So we start off with a circle, and we can define the radius of that circle. Then I start moving along that circle. And when I have gone a distance so that the distance along that arc is equal to the radius, that angle I'm measuring out is 1 radian. So it's the ratio between the arc length and the radius. Because it's defined by a ratio, the unit symbol's not always listed. So sometimes you'll have things where the angle is listed as a number without a unit symbol after that. And if there is no unit symbol after the number, but it's an angle, it's got to be in radians. Now coming back to the ones we've been using sort of as our comparison then, if I look at a full circle, the distance all the way around the circle is 2 pi r, the circumference. So 2 pi radians is my full distance around a circle. If I were going to look at a right angle, that's pi over 2 radians. So this is how I end up having radians come in. Now in physics, we're gonna have problems that might specify more than one. And so we're gonna have to do unit conversions. And we use our full circle as sort of our guide. So one revolution equals 360 degrees because both of those represent going once around a circle. Similarly, one revolution is 2 pi radians. Or I could use 2 pi radians equals 360 degrees. So these are our unit conversion factors if I have to do some unit conversions. So those are the basic angular units we're gonna be using in physics. You'll need to do some more practice with them.