 So far we have been describing motion as a linear motion along one, two, or three axis. But now we're going to be adding in rotational motion is the possibility to turn around one, two, or three of those axes. Let's first have a look what we used in the linear case to describe motion. What we are trying to describe is position displacement, we had velocity and acceleration. And the variables we used were S, or X, or Y, or Z. Displacement being the delta S in the difference between a final and initial position. Velocity V and acceleration A. Now in the rotational case we're going to try to give the exact same things. Position, displacement, velocity, and acceleration, but in this case as rotation around an axis. So the position instead of giving it as a distance traveled is an angle traveled. The displacement is simply the change in the position of an angle. Velocity for the rotational case is going to be omega and the acceleration we're going to be calling alpha. Note that they're really the same things. The only thing that might look a bit difficult is that we're using Greek characters. As a general rule when we explain rotational entities we're using Greek characters. It makes it look very fancy, very complicated, but actually at the end of the day it's exactly the same thing as we had it linear. So if you don't like Greek characters, replace those letters by anything else that you want, it will still get the job done. Now what are the SI units that we are using? In the linear case we are used meters for position and displacement. We used meters per second for velocity and we used meters per second square for acceleration. In the rotational case we're going to give the angle in rats radians. So the displacement also in radians. The angular velocity is going to be given in radians per second and the acceleration in radians per second square. Now if an object is traveling around the circular path it can give its position either in linear variables like position S as how far has the object traveled along the path. Or we can give it in angular rotational variables. There is a link between those two which is quite simple. The position is the radius times the angle in rats. If you think about it the angle is given in rats so a full circle would be 2 pi. If I multiply the full circle with R, what I get is the circumference which would be the linear displacement along the circumference of the circle. As we had it for position we're going to get the same thing for displacement. Placement is delta S is R times delta theta. For velocity linear velocity gives us R times omega. And for linear acceleration if I follow the same pattern A equals R times alpha. Now wait a minute in my last video I talked about something like centripetal acceleration that comes into place. In that video I figured out that I have a centripetal acceleration which is R omega square. So then what is my R times alpha? Well it's very simple. My R times alpha is the component of the acceleration that goes along the circle. So this is my A I would call it tangential. While the A centripetal is an acceleration that goes towards the center and then together they actually form my total acceleration. So I have my A tangential and I have my centripetal acceleration which together will form my total amount of acceleration.