 Okay, so let's see. I'm going to try to go over chapter one and two just in case you forgot everything. I'm going to go really quick and then after this I'll post some videos, a couple of worked out examples. Hopefully that will help. So I put some notes right here just so I won't forget. I'm just going to go basic. Okay. Okay, so chapter one was really about, it was about forces and the nature of forces, but really it got to that more in chapter two. So primarily chapter one was about two things. It was about the definition of average velocity. Okay, so this says that the velocity is just a change in position over the change in time. Change is important. It's not position over time. It's a change in position over time. Don't fall into this trap of saying v equals distance over time. That's just a special case. There's so many places where that doesn't work. So be careful with that. Also, v is a vector and the position is a vector and the change in position is a vector. So these are all vector quantities. So from this also we get the very important position update formula. So if the velocity is constant then I could say r2 just by solving this equals r1 plus v average or v delta t. Okay, that's the other, that's the position update formula. So if I know where it was and I know the velocity, I multiply the velocity by the time interval and I can find the new position. Okay, that's it. The last thing in chapter one, and that looks not very much. It's not very much. It did talk about vectors and what is a vector. I'm not going to cover that. The last thing in there was momentum. So the real momentum definition is this. P equals mass times velocity over the square root of 1 minus the magnitude of the velocity squared over c squared. Where c is the speed of light and it's about 3 times 10 to the 8 meters per second. That's momentum. Now for a lot of cases, let's take something super fast like a bullet. A bullet fired from a gun is maybe let's say 300 meters per second, which is really fast. 300 meters per second squared over 3 times 10 to the 8 squared is very, very, very, very, very close to zero. So this just becomes, for low speeds, P is approximately equal to, that should be approximately, mv, because that whole thing's 1. It's still a vector. So if you're dealing with things going closest, be light, use this, otherwise use this. How close does closest be light have to be? Well, it depends on how good you want your answer to be. If you are, I don't think it matters in any case for a bullet, but if you have something going a tenth of the speed of light, 3 times 10 to the 7th meters per second, you could get away with this formula. If you wanted it to be a better answer, you'd use this formula. So it just depends. Okay, that's chapter 1. Chapter 2. Chapter 2 is primarily about the momentum principle. We could write it like several ways, but if I write f net, net equals delta P over delta T. So this tells us what the fundamental nature of forces does. The forces change the momentum, and change is very important. You're going to fall into the trap of saying this, force is proportional to momentum. That is wrong. That's what a lot of people like to say. They say, oh, if it has a constant force, it's going at a constant motion. But no, the most important thing here is this delta symbol, which means change. Force is related to the change in momentum, and since momentum is proportional to the velocity for low speeds, we can say force is related to the change in motion. Change is key. Okay. But just like before, and this is the net force, the vector sum of all the forces acting on that object. Not all the forces in that situation, just on that object. Just like with the velocity, we can get the momentum update formula. If you just play around with this, you get P2 equals P1 plus F net delta T. So that's the momentum update formula. Now I think this might be above the video. If that's the case, I'm going to free write this. F net is delta P over delta T. That's the momentum principle. And this is the same thing, exactly the same thing, except I put delta P as P2 minus P1 and solve for P2. So here if I know the net force and the time and the momentum, I can find the new momentum. This assumes the net force is constant. If the net force is not constant, this doesn't work unless you cheat. And the way to cheat is to say, if delta T is super small, then F net, even if it is changing, is almost not changing. And you can get a very good value for this. And that's what I talked about in class. I talked about this with the numerical calculations. Just a couple of other things that we looked at in chapter two, the gravitational force. We have F, I'll call it G, is MG. This is near the surface of the earth. The earth pulls on things. The force is proportional to G. G is called the gravitational field. And it has a value of zero, negative 9.8, zero newtons per kilogram. Now, that's not true if you get far away from the earth or if you're on a different planet. The other force we looked at was the force due to spring, F spring. It's going to be the book worded as negative KSSL hat, where S is equal to L minus L naught. So KS is called the spring constant. And it is a measure of how stiff that spring is. S is how far that spring has stretched. So L is a vector if I have a typical spring with a mass on the end of it. L is the vector from the place where it's attached to the place where it ends. And L naught is the length of the spring if it weren't stretched or compressed. So this gives you how much it's compressed. L hat is a unit vector in the direction of the spring. That makes this a vector. One last thing, and I'll derive this I think I already did. In the case of a velocity that changes linearly with time. So constant acceleration. Then we can get something like this. I'll write it as a vector. R2 equals R1 plus V1 delta t plus 1 half F net over M delta t squared. This is just not super important, but it is useful. You've probably seen this as a kinematic equation if you've had physics before. The final position is initial plus the initial velocity times delta t plus 1 half. That's like F over M is like the acceleration t squared. It's not too hard to derive. You just need to use V average is V1 plus V2 over 2. That is true if the velocity changes linearly with time. If the object has a constant acceleration. Okay, I think that's it for chapter 1 and 2. Did my thing turn off? Okay, so I'll stop there.