There's something about tangential and radio acceleration that causes a lot of concern. So let's talk about them. AR-radial acceleration, AT-tangential acceleration. Basically when you speed up around a circle, so when you normally just go around a circle all we have is some tripletal acceleration, what if we speed up? Or really, therefore anytime you're moving in any kind of a curved path, whether it's a circle or not, you might have radio and tangential acceleration. So let's look at it for a few cases. Let's look first at one you're familiar with, uniform circular motion. What if we had just a little bit of an xy path and we had uniform circular motion going around the origin? It would look kind of like this. And if I were to try to make it clear that it's uniform by putting dots for the position at various times, not look like that. Well you know what the acceleration is in this case, you think of it as centripetal. You think of it as AC. Well really, in this case, that is the only acceleration, but we call it radial. And usually we define the radial direction as out, not in. That's what we say here, the radial acceleration is just the negative of this centripetal acceleration. If you calculated v squared over r, it would just be negative of the value v squared over r. Because we still wait just because we define positive is out. There's no real big physical reason for that negative sign. If you wanted the tangential acceleration, well that would be zero for uniform circular motion. Because tangential is how much it's speeding up along the curve and uniform circular motion means the speed is constant. So we don't worry about it. Let's look at another one. What if you had accelerating circular? Say you had the same kind of thing, x and y, and it's the circular path. But what if you sort of started and again, these think of these as uniform displacements in time? You're going faster as you go around. Well, if you picked a point in time, say right here, you would still have a radial component to the acceleration. I'm not going to label it centripetal because we're no longer doing uniform circular motion. You would still have an ar because the velocity vector is changing direction. And that's really where the radial part comes from. The velocity is changing direction. But you also now have the speed increasing. So now you also have a t. So the tangential acceleration is along the curve radial acceleration and proportionally curve. And if you were told to find them, in this case, ar, it's still v squared over r. Whatever the velocity is at some point, take the magnitude, the speed squared, put it over r. That'll always give you a positive number. Well, it depends on how you're doing it. Like if your positive number and radial is out and the vector points in, you'd probably put a negative sign in front of it. If you're asked for the, which are right out as a vector. If you wanted the tangential acceleration, you would just look at how the speed changes with time. How much is it speeding up along that path? So you could write it that way, dv, dt, where it's the magnitude of the v. So you could find it there. So finally, let's, what if you just had any arbitrary path? Arbitrary path that's curve any time you have some motion, even if it's not curved in the x and the y. So say you're talking about right here. Here you can see there's curvature. So the a r would be there and there's tangential a t would be there. And in some problems you might have to get that in terms of x and y components. Maybe it gives you the acceleration in x and y and you would just have to convert it. So here maybe you know it in x and y and you just have to do a little bit of trig to get it in terms of r and t. And I'll be showing you problems of these various ways to get a r and a t. But let's just review then. The a r is radial acceleration. And the main thing I wanted to say is it is the component perpendicular perpendicular to the path. And tangential a t is tangential acceleration. And the main thing is it is along the path. Along the path. How you get them depends on what kind of a problem it is. Maybe you'll be given enough information to get them this way. Maybe you'll do it this way. So you just have to look at the problem and look at the examples I'm going to show.