 Let's look at centripetal acceleration. When we talked about circular motion, one of the things that we noticed was that the direction of motion is always changing. In particular here, if we look at a circle, notice that as I go around, my velocity keeps changing direction. So even if I'm going in uniform circular motion at the same speed, I still have a change in direction. And that means the velocity vector is changing. And a changing velocity vector means there is an acceleration. So let's see if we can figure out a few other things about this acceleration. So let's start by looking at the direction of the acceleration. I'm going to start with a circle here. And I'm going to look at the velocity at two different points that are pretty close to each other. Here and here. So these are my two velocities. Now, I'm going to copy those velocities over here real quick. And I've got my initial and final velocities. Well, since the acceleration is related to that change in velocity, that means my acceleration is given by this little blue vector here. Copying that back over to my circle, what I find is that I've got it in the general direction, kind of pointing in. Now, I can repeat the same procedure for another two velocity points. They appear at the top and slightly further on. Copying those over, looking at the change in velocity and copying that back shows me that again, I'm pointing in towards the center of the circle. As a matter of fact, I could do this at any different point inside that circle no matter where I am. And I'm always going to find that that acceleration points towards the center of the circle. So we're going to call this our centripetal acceleration. Now, this is the acceleration needed in order to keep something moving in circular motion. And it must point towards the center of the circle. That's the direction part we found. And actually, that's where the word centripetal comes from. Centripetal means center seeking. So the center seeking acceleration helps keep something in circular motion. Beyond just the direction of the centripetal acceleration, though, I can think about how much acceleration I need. And it's going to depend on two things. First, it's going to depend on how fast you're moving. And second, it's going to depend on how tight of a turn you've got. Now, the equation that we're going to have for centripetal acceleration is this one shown right here. So A with the subscript of C stands for our centripetal acceleration. I've got my dependence on my velocity and my dependence on the radius. And so my centripetal acceleration is equal to v squared over r. Now notice, as I've got a higher speed, that means I've got a higher acceleration. I need more acceleration to keep it staying on that circular path. Also, if I've got a smaller radius, then because the radius is on the bottom, a smaller radius on the bottom means higher acceleration. Again, more acceleration is needed if I want to make a tight turn. Now, if I want to look at the units for centripetal acceleration, I can start with the same equation that the centripetal acceleration is v squared over r. And note that my velocity has units of meters per second in that squared. And my radius has units of meters. Now, the other way I can write this here is to list my meters per second squared and then my 1 over meters as separate quantities. And then it's really easy to see that one of those meters cancel, leaving me with just meters per second squared. And that's the same sort of units that I have for any other acceleration that I've been working with. So whether it's a centripetal acceleration or a linear acceleration, it's still meters per second squared. So that introduces you to centripetal acceleration. We'll work some more problems in other videos.