Another one, I just wanted to highlight, because this comes up a lot, is this one. This problem here. Mass over two. We've done everything in class that you need to get these equations of motion. So when we're getting equations of motion from mechanical systems, what type of fundamental properties do we use? Lewis. >> [INAUDIBLE] >> No. Not to get equations of motion. We use conservation of energy if I'm looking for relationships between rates and states. But you can't use conservation of energy to get your second order differential equations. >> [INAUDIBLE] >> Okay. So there's F equals mass times some acceleration vector. Right? When does this hold? >> Mass. >> Okay, mass constant, what else? >> [INAUDIBLE] >> This has to be inertial derivatives, so this r vector has to be taken relative to an inertial point. And you take inertial time derivatives, yeah, when else? >> It's constant? >> Well, yeah mass is constant, yep. Does it apply to this pen? Russell, you're saying yes. >> It's constant mass. >> It's constant mass. So it is good for rigid bodies? >> [INAUDIBLE] >> [LAUGH] >> [LAUGH] >> Okay. >> [INAUDIBLE] >> You're applying what to it? [INAUDIBLE] >> [LAUGH] >> I'm getting wet there's so much back paddling here. Okay. >> [LAUGH] >> So yes to this to what. This is Are made. Come on, how hard is that right? >> What was your question? >> People write whole PhDs on this equation. Anybody doing Orbitz, you can tell your parents that's it. I spent five years working on this equation you know. That's it. F = MA. How hard is it? But it is hard. It gets very quickly hard. So where does it apply to? And I'm saying this pen. Can we use F = MA on this pen? Andre, what do you think? >> Absolutely. >> Okay, good answer. Now second part is what? >> What? >> Why? >> [LAUGH] >> You want to model the trajectory of the pen or something? >> [LAUGH] What part of the pen? I need it more specifically? >> Center of mass. >> Center of mass. Right. What did we call that theorem? >> Super particle theorem? >> Super particle theorem, right? So F= MA holds for the super particle theorem. That's, in fact, how you do your whole Problem, and you just basically ignore the rest of the mass distribution, you say the space station is a point. Which is a decent assumption for some analysis, obviously not a good assumption for other analysis. Depends on what you're doing again. So good, so this could be true for a whole system not just for a point mass. We typically have it written for point masses. If it's a super particle theorem, what is F then it that case? >> External forces? >> A single external force? >> The sum of all. >> The sum of all the external influences that happened on the system, right. So that's important because you can actually use that in this system to argue things about are there any external forces on this dynamical systems? And if you ask what does that mean, and if not, what does that mean under center of mass motion? But that's one of them, so this works for a system, but it also works for a particle. Don't forget the very basics. You can do F=MA on a particle as well, and this also holds, and you have to write this relative to any inertial point, I'm just going to give you the tape, it doesn't have to be some point dot here. There's a much more convenient inertial point in this problem that you could write everything relative to. And now things become very simple. But what's the other equation that we've used? So we have F=MA on particles on the center of math if it's a system. And in this case you could do either. You could do free body diagram and do on that or what else? >> H.=L. >> H.=L. All right. And that also works but if you say H.=L, you're taking points about where? It's like moments talk about which point? >> Well you can pick the point right? But the center of mass is where you're doing it about. [CROSSTALK] >> You can use center of mass. Is there different points you could. It could be an inertial point, right, and either. And you can play with that. And then you write up your momentum. Do this, or you can do these equations. Or you will find maybe combinations of this. You have to have enough, how many degrees of freedom does the system have? Two, the rules of freedom is how many independence states do you need to fully describe the current configuration, right. And the r, there's I think this here has a radius r and then you have some angle theta. So in the end you need differential equations for both of these, right. So you're going to have to use these vector equations and break them up. There's many different ways you can solve this, all right. But this is something where I'm looking for you to apply these very principles. There's lots of easy ways you can do it, but breaking everything down, and sines and cosines galore, I'm giving you a rotating frame for a reason. I want you to use that E theta direction. Write it that way, it'll give you an answer that's actually really, really fast and compact. That's what you're looking for. Once you see how to apply those principles it goes very, very quickly.
