 So now let's look at radial and tangential accelerations, and we're going to start by remembering something about the relationship between velocity and acceleration. Now velocity has both speed and direction. If the velocity changes, then we have acceleration. Or if we have an acceleration, then the velocity changes. But regardless of which of these two ways you look at it, either we have a change in speed or a change in direction, or both of those. Either one of those changes is a change in velocity, so it should be associated with an acceleration. So then we move to our tangential acceleration. Well, a tangential acceleration is when we have the acceleration along the direction of motion or tangent to the path. So if I've got some sort of curved path over here, at any point along the path, I can define the direction of motion. And if the acceleration is also in that direction, it's a tangential acceleration. Now this kind of acceleration causes a change in the speed. In terms of our equation, that would be the tangential acceleration is the change in the velocity as a rate of time. Now if we've got a radial acceleration, then we've got an acceleration which is perpendicular to the path. So again, I've got a curved path over here, and I can define the direction of motion. If my acceleration is perpendicular to that path, it's a radial acceleration. And this is going to cause a change in direction. Now that change in direction means that the path is going to curve around in an arc. So I could think of myself as fitting a circle to just that segment. It doesn't have to fit the entire curve, but just in that segment, can I fit a circle so that I've got an arc in there? Well, once I've done that, I can define my radius of that particular circle. I know how fast I'm going, that I can relate this back to the centripetal acceleration. So my centripetal acceleration was v squared over r. Now when I talk about my radial acceleration, I'm actually going to use the negative of that. And that's because when I define the radial direction in my standard polar coordinate systems, positive is always pointing out from the center of the circle. But of course, my acceleration is pointing inwards towards the center of the circle. So the radial acceleration is defined as being the negative of my centripetal acceleration, where the negative indicates that it is inward instead of the positive outward direction. Now both these tangential and radial accelerations can go together to form a vector acceleration. That full vector acceleration has two components. But in this case, rather than it being x and y components that we studied earlier in the semester, it's my tangential and radial components. If I take an example again here where I had a tangential acceleration, which was tangent to the curve, and a radial acceleration, which was perpendicular to the curve, those are my two components. So a vector addition is going to give me my full vector acceleration. Now it may be easier to see how this is the vector addition if I go ahead and take my radial and just kind of copy it over here to the side. So that means I've got my regular sort of triangle. Yeah, it's tilted off at a funny angle, but we can still define the magnitude of the acceleration and that angle direction for that full acceleration by looking at my two components, the tangential and the radial accelerations. So that tells you a little bit more about radial and tangential accelerations. We still have to apply those and other problems though.