 OK, so the momentum principle. This is really one of the biggest ideas in the course. So I didn't want to just leave it alone. I want to go ahead and make sure that I at least give some introduction to it that you can think about. And I may break this into two parts, let's just see. So the first thing is, what is the nature of force and motion? Let me start with an example. Suppose I have a mass, and it's in space or something like that. And I exert, push it with the force. So the question is, what happens? Well, the Greeks thought about this first, and they said the following. They said that if you put a constant force on an object, it's going to move at a constant in a constant motion. Constant force, constant speed. And that idea makes sense even though it's wrong. So they thought that because that's what you experience. If I push something with a constant force, it's probably going to move at a constant speed. And that's because that's not the only force on it. If it's a cart, then there's some frictional force on there too. So the net force would be zero. And so Galileo, I'm skipping a whole bunch of stuff here. But Galileo looked at rolling a ball down a track. And by rolling it down a track and then just really, really fairly tilted track, he could get the ball to roll at a constant speed. And so he kind of made this idealized assumption that, well, if I was able to remove all friction, and all other forces on that ball, then with no forces, it would move at a constant speed. And this is the momentum principle. Let me write it down. It says that the net force on an object is the change in momentum over change in time. That's the best way, I think, to think about forces. What does the force do? The key word here is change. The force is related to the change in momentum. Let me just briefly say, what is momentum? Well, momentum is a vector. And at slow speeds, we can say this. It's the product of the mass times velocity. So this says with the same force, I can change the momentum of another object. But if it has a very large mass, that means it's going to have a small change in velocity. What to say? OK, let me make the connection to Newton's Law of the Motion. Because a lot of times, I like to say this, force related to change momentum. But a lot of textbooks don't. They like to say this. F net is mass and acceleration. It's essentially the same thing. Because if I have an object in which the mass doesn't change, then I can say this is the change in mass times velocity over the change in time. That's equal to the mass times the change in velocity over the change in time. And if the velocity is changing at a constant rate, then this is the acceleration. And sometimes we use it that way. So these two things are saying the same thing, essentially. The other important thing is F net. What does that mean? That means that we have to add up all the forces acting on the object. So the total force is related to the change in momentum over change in time. OK, I'm trying to think of what other important thing I need to say about this. I know it's very important. I was going to talk about the Greeks some more, but I think this is the key thing. I mean, this deals with a lot of stuff that we've been using so far. Because we've been adding vectors. We've been free body diagrams. Momentum, don't worry about that too much right now, other than it is mass and velocity. If we use it this way, we can find the acceleration. And then we can use our kinematics that we've done before in two dimensions. OK, I'll just stop there.