Subtitles section Play video Print subtitles Prof: So, I've got to start by telling you the syllabus for this term--not the detailed one, just the big game plan. The game plan is: we will do electromagnetic theory. Electromagnetism is a new force that I will introduce to you and go through all the details. And I will do optics, and optics is part of electromagnetism. And then near the end we will do quantum mechanics. Now, quantum mechanics is not like a new force. It's a whole different ball game. It's not about what forces are acting on this or that object that make it move, or change its path. The question there is: should we be even thinking about trajectories? Should we be even thinking about particles going on any trajectory? Forget about what the right trajectory is. And you will find out that most of the cherished ideas get destroyed. But the good news is that you need quantum mechanics only to study very tiny things like atoms or molecules. Of course the big question is, you know, where do you draw the line? How small is small? Some people even ask me, "Do you need quantum mechanics to describe the human brain?" And the answer is, "Yes, if it is small enough." So, I've gone to parties where after a few minutes of talking to a person I'm thinking, "Okay, this person's brain needs a fully quantum mechanical treatment." But most of the time everything macroscopic you can describe the way you do with Newtonian mechanics, electrodynamics. You don't need quantum theory. All right, so now we'll start with the brand new force of electromagnetism. But before doing the force, I've got to remind you people of certain things I expect you all to understand about the dynamics between force, and mass, and acceleration that you must have learned last term. I don't want to take any chances. I'm going to start by reminding you how we use this famous equation of Newton. So you've seen this equation, probably, in high school, but it's a lot more subtle than you think, certainly a lot more subtle than I thought when I first learned it. So I will tell you what I figured out over these years on different ways to look at F = ma. In other words, if you have the equation what's it good for? The only thing anybody knows right away is a stands for acceleration, and we all know how to measure it. By the way, anytime I write any symbol on the board you should be able to tell me how you'd measure it, otherwise you don't know what you're talking about as a physicist. Acceleration, I think I won't spend too much time on how you measure it. You should know what instruments you will need. So I will remind you that if you have a meter stick, or many meter sticks and clocks you can follow the body as it moves. You can find its position now, its position later, take the difference, divide by the time, you get velocity. Then find the velocity now, find the velocity later, take the difference, divide by time, you've got acceleration. So acceleration really requires three measurements, two for each velocity, but we talk of acceleration right now because you can make those three measurements arbitrarily near each other, and in the limit in which the time difference between them goes to zero you can talk about the velocity right now and acceleration right now. But in your car, the needle points at 60 that's your velocity right now. It's an instantaneous quantity. And if you step on the gas you feel this push. That's your acceleration right now. That's a property of that instant. So we know acceleration, but the question is can I use the equation to find the mass of anything. Now, very often when I pose the question the answer given is, you know, go to a scale, a weighing machine, and find the mass. And as you know, that's not the correct answer because the weight of an object is related to being near the earth due to gravity, but the mass of an object is defined anywhere. So here's one way you can do it. Now you might say, "Well, take a known force and find the acceleration it produces," but we haven't talked about how to measure the force either. All you have is this equation. The correct thing to do is to buy yourself a spring and go to the Bureau of Standards and tell them to loan you a block of some material, I forgot what it is. That's called a kilogram. That is a kilogram by definition. There is no God-given way to define mass. You pick a random entity and say that's a kilogram. So that's not right and that's not wrong. That's what a kilogram is. So you bring that kilogram, you hook it up on the spring, and you pull it by some amount, maybe to that position, and you release it. You notice the acceleration of the 1 kilogram, and the mass of the thing is just one. Then you detach that mass. Then you ask--Then the person says, "What's the mass of something else?" I don't know what the something else is. Let's say a potato. And you take the potato or anything, elephant. Here's a potato. You pull that guy by the same distance, and you release that, and you find its acceleration. Since you pulled it by the same amount, the force is the same, whatever it is. We don't know what it is, but it's the same. Therefore we know the acceleration of 1 kilogram times 1 kilogram is equal to the unknown mass times the acceleration of the unknown mass. That's how by measuring this you can find what the mass is. In principle you can find the mass of everything. So imagine masses of all objects have been determined by this process. Then you can also use F = ma to find out what forces are acting on bodies in different situations, because if you don't know what force is acting on a body you cannot predict anything. So you can go back to the spring and say, "I want to know what force the spring exerts when it's pulled by various amounts. Well, you pull it by some amount x. You attach it to a non-mass and you find the acceleration, and that's the force. And if you plot it, you'll find F as a function of x will be roughly a straight line and it will take the form F = -kx, and that k is called a force constant. So this is an example of your finding out the left hand side of Newton's law. You've got to understand the distinction between F = -kx and F = ma. What's the difference? This says if you know the force I can tell you the acceleration, but it's your job to go find out every time what forces might be acting on a body. If it's connected to a spring, and you pull the spring and it exerts a force, someone's got to make this measurement to find out what the force will be. All right, so that's one kind of force. Another force that you can find is if you're near the surface of the earth, if you drop something, it seems to accelerate towards the ground, and everything accelerates by the same amount g. Well, according to Newton's laws if anything is going to accelerate, it's because there's a force on it. The force on any mass m must be mg, because if I divide by m I've got to get g. So the force on masses near the earth is mg. That's another force. Something interesting about that force is that unlike the spring force where the spring is touching the mass, you can see it's pulling it, or when I push this chair you can see I'm doing it, the pull of gravity is a bit strange, because there is no real contact between the earth and the object that's falling.