It's time for angular momentum. Now, there's two ways to do angular momentum. You can do the easier, let's just think about large objects rotating about their symmetry axis and calculate the angular momentum and thinking about the fact that it's conserved, that's fine. You can also do a more difficult mathematically sophisticated process, where you compare angular and translational momentum and there's lots of cross-products. We're going to do both. I'm just telling you about the different approaches because whatever book or class you're following, might do one or the other or both or different orders, I don't know. We're going to do the first unit on the more intuitive approach and the second unit on the more mathematical approach. To get started then, I'm going to give you the Tina Turner definition of angular momentum and that is big wheel keep on turning. Basically, if we spin a big object like this aluminum wheel that we use on our rotational motion, it doesn't stop spinning, it keeps turning, because just like we have translational momentum, things that are in motion tend to stay in motion. When something is rotating, it tends to keep rotating. Let's look at this mathematically a little bit. Oh yes, at this point, oh god, I have five Tina Turner angular momentum jokes and I forgot to pick one, teaching is so hard. I think I'll just do all five, let's just go through them one at a time here. So of all the celebrities we could possibly listen to about angular momentum, we have to go with Tina Turner because she has the perfect name [inaudible] Tina herself had quite a bit of angular momentum on stage, if you ever saw her sing and dance, there's a lot of angular momentum going on. The big wheel she refers to, is actually the paddle wheel on a steamboat because the song is about a steamboat and technically though that wheel isn't continuing to turn because it's conserving angular momentum, the wheel paddles are going into the water, it's very damped and that's what's pushing the boat forward. So really, the engine had to turn the wheel constantly, it wasn't an isolated system and this is what Tina and I used to argue about a lot, led to some of the disagreements there. We know that Tina was a physicist because she was famous for never, ever doing nothing nice and easy, so clearly, she would have been a great physicist. Finally, in fact, the way I've set this up, where we do the easy unit and the hard unit, is exactly what Tina would've done because she likes to start something out easy and then she does the end rough. That's how she always did everything. So here we go, this is the Tina Turner, well not memorial, she's still with us fortunately, this is the Tina Turner approach to angular momentum. Where were we? We were talking about the big wheel, now, we're going to draw the big wheel like this, down like that and I'd like to note that all five and I didn't even get to thunderdome, clearly, there's some thunderdome material available here. Let's see, so here's the wheel and we know any wheel like this, it hasn't big radius R, it has a mass M, and we're turning it and it keeps on turning. The Omega, of course, we should really draw here because we know that Omega is a vector like that, as it goes around. Let's see, if we want to define then the angular momentum, this is the straightforward approach, we're just going to define it and we can think to all the similarities between angular, rotational and translational, translational momentum P equals mass times velocity. So this is just the rotational version of that, it's the moment of inertia of the wheel times its angular velocity. So L is angular momentum and it equals I Omega, just like P equals MV. If we want the direction by the right-hand rule, so we use right-hand rule a lot. This is one of the cases where we're talking about something curving and something straight. So clearly the disk is spinning, that's the curving part, we're looking for the L vector, that's the straight part. So you curve your fingers with the rotation and your thumb is along the straight part, which is the angular momentum. If we take this disk and see it's going around like this, use your right hand and you get that way. You see the angular momentum is the same direction as the angular velocity. You can also see that here, this is a positive constant, so L is the same direction as Omega. Let's just calculate an L for the aluminum disk at one revolution per second. So come back to the disk here, it's going to go around about a revolution per second, 1,000, 2,000, something like that. Lets calculate its L. Let's see. So we'll just do magnitudes because we know the direction and in this case is, let's get the direction, right-hand rule, in this case we're doing the L vector it's pointing in to the plate, it's pointing that way. I is one half MR squared for a disk, one half, the mass of the disk I estimated it's about two kilograms. I just used the volume of it and the density of aluminum and IR squared, so the radius of the disc was 18 centimeters, so 0.18 meters squared and then omega, we did revolution, one revolution per second, but if you want to turn that into Omega, it's going around two pi radians per one second, so you multiply all those and you get 0.2 kilogram meters squared per second is the unit of angular momentum. It's not what it's real meaningful units, it has a nickname, we just put kilogram meter squared per seconds. That's the very basics, that's what angular momentum is and roughly that's how you calculate it for this geometry.
