We have spent the first half of this class lost in translation but it is now time to move on to rotational motion. Let me hit you with one of my simple definitions. Changing the direction an extended object points. Lots of keywords in there, extended object. I want to start though by really stressing something very important. We have already talked about circular motion in 2D kinematics. Circular motion is, and I'm already using caps, I don't know what to do, not rotational motion. They use similar symbols and concepts but they are not the same thing. To make this contrast very clear because I think it's helpful, let's go back and take ourselves back to LS2 unit 3. It's hanging from the ceiling like a pendulum but if we move it like this, it's essentially going in uniform circular motion in the x, y plane. This plane here. There we go. That's right. We were talking about an object on a string, string radius R, the length of the string gives you the radius of the circle. We have got an object mass, m and we had a mass, m spins with string radius R. It was something like this. Here we are, string radius R. The object is the tennis ball mass, m and we spun it around like this. Let's think about the physics that we got out of that. We say well, if I spin it around with a uniform speed like that, that's V and we talked about how that is a changing direction of the velocity vector, so we have an acceleration that is centripetal acceleration like that. We also talked about the tension you would need in the string would have to be m times that centripetal acceleration if it's uniform circular motion. Then we also talked about the magnitude of that centripetal acceleration, was the speed squared over big R. All that stuff. Beautiful, uniform circular motion, beautiful 2D translational kinematics has nothing to do with rotational motion and the reason is we treated this thing as a point mass. It was not an extended object, it was a point mass. Now, we're going to do what we're doing here in LS6 unit 1. That's here, rotational motion. Let's see, what are we doing? Now, we're going to spin something like this. An extended object, a block on the same radius. I'm going to spin it. It's probably going to break, approximately uniform. I don't want to break the string. That's going around and I'm telling you that that is entirely different. Let's look at how it's entirely different. I've got my string and now I've got my block like this and the string is the same length going around at R, I'm spinning it around. Let's say it's the same speed, V. Now we have an extended mass on a string length R, so extended rather than point. Extended mass, m spins on string length R. Let's see what is the same? What is different? Let's do a few bullets here. Let's say, notice it's the same v, the same speed but most of the mass has a radius greater than R. This is the fundamental difference. Since it's an extended object, the part of the mass right at the end of the string is going around at R. The hook really, the hook is going around at R, but all this mass in the block is going out at a larger radius. Because it's an extended object, we can't just say the mass is going around the big R. It's going around at all kinds of radii. What's really happening here, it has an element of circular motion. It's not pure rotational. This is actually a combination of circular and rotational motion. If you think about it, you can watch it again. Watch it spin, go around and around and you can imagine that there's two things happening to this block. One is, it is going around in a circle but at the same time it's doing this, isn't it? When you're up here, the hook is on this side, when you're down here, the hook is on this side. It's both going in a circular motion and it's rotating. Now, the reality is, all objects are extended. There are no point masses accept electrons and I can't really spin an electron on a string, this is smaller than an electron. Even this object really was doing both. In all the translational mechanics, we approximated everything as a point mass and really none of it was a point mass. If I put a little piece of tape around the top, that helps us visually identify the fact that this tennis ball is not a point mass. The top and the bottom are different. If I spin this one around, now we know of course it's going in a circle. We can tell it's going in a circle but at the same time, it's going under rotational motion. Over here the red tape was on the bottom side and down here it's on the top, so it's also rotating. I stress this point because I know most of you have already done this and you've thought about this and you think, ''I know about rotation.'' It's totally different.
