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1 | 1 | Atoms in Motion | 1 | Introduction | This two-year course in physics is presented from the point of view that you, the reader, are going to be a physicist. This is not necessarily the case of course, but that is what every professor in every subject assumes! If you are going to be a physicist, you will have a lot to study: two hundred years of the most ra... | |
1 | 2 | Basic Physics | 1 | Introduction | In this chapter, we shall examine the most fundamental ideas that we have about physics—the nature of things as we see them at the present time. We shall not discuss the history of how we know that all these ideas are true; you will learn these details in due time. The things with which we concern ourselves in science ... | |
1 | 2 | Basic Physics | 2 | Physics before 1920 | It is a little difficult to begin at once with the present view, so we shall first see how things looked in about 1920 and then take a few things out of that picture. Before 1920, our world picture was something like this: The “stage” on which the universe goes is the three-dimensional space of geometry, as described b... | |
1 | 3 | The Relation of Physics to Other Sciences | 1 | Introduction | Physics is the most fundamental and all-inclusive of the sciences, and has had a profound effect on all scientific development. In fact, physics is the present-day equivalent of what used to be called natural philosophy, from which most of our modern sciences arose. Students of many fields find themselves studying phys... | |
1 | 3 | The Relation of Physics to Other Sciences | 2 | Chemistry | The science which is perhaps the most deeply affected by physics is chemistry. Historically, the early days of chemistry dealt almost entirely with what we now call inorganic chemistry, the chemistry of substances which are not associated with living things. Considerable analysis was required to discover the existence ... | |
1 | 3 | The Relation of Physics to Other Sciences | 3 | Biology | Thus we come to the science of biology, which is the study of living things. In the early days of biology, the biologists had to deal with the purely descriptive problem of finding out what living things there were, and so they just had to count such things as the hairs of the limbs of fleas. After these matters were w... | |
1 | 4 | Conservation of Energy | 1 | What is energy? | In this chapter, we begin our more detailed study of the different aspects of physics, having finished our description of things in general. To illustrate the ideas and the kind of reasoning that might be used in theoretical physics, we shall now examine one of the most basic laws of physics, the conservation of energy... | |
1 | 4 | Conservation of Energy | 2 | Gravitational potential energy | Conservation of energy can be understood only if we have the formula for all of its forms. I wish to discuss the formula for gravitational energy near the surface of the Earth, and I wish to derive this formula in a way which has nothing to do with history but is simply a line of reasoning invented for this particular ... | |
1 | 4 | Conservation of Energy | 3 | Kinetic energy | To illustrate another type of energy we consider a pendulum (Fig. 4–7). If we pull the mass aside and release it, it swings back and forth. In its motion, it loses height in going from either end to the center. Where does the potential energy go? Gravitational energy disappears when it is down at the bottom; neverthele... | |
1 | 4 | Conservation of Energy | 4 | Other forms of energy | We can continue in this way to illustrate the existence of energy in other forms. First, consider elastic energy. If we pull down on a spring, we must do some work, for when we have it down, we can lift weights with it. Therefore in its stretched condition it has a possibility of doing some work. If we were to evaluate... | |
1 | 5 | Time and Distance | 1 | Motion | In this chapter we shall consider some aspects of the concepts of time and distance. It has been emphasized earlier that physics, as do all the sciences, depends on observation. One might also say that the development of the physical sciences to their present form has depended to a large extent on the emphasis which ha... | |
1 | 5 | Time and Distance | 2 | Time | Let us consider first what we mean by time. What is time? It would be nice if we could find a good definition of time. Webster defines “a time” as “a period,” and the latter as “a time,” which doesn’t seem to be very useful. Perhaps we should say: “Time is what happens when nothing else happens.” Which also doesn’t get... | |
1 | 5 | Time and Distance | 3 | Short times | We should now notice that in the process of checking on the reproducibility of the day, we have received an important by-product. We have found a way of measuring, more accurately, fractions of a day. We have found a way of counting time in smaller pieces. Can we carry the process further, and learn to measure even sma... | |
1 | 5 | Time and Distance | 4 | Long times | Let us now consider times longer than one day. Measurement of longer times is easy; we just count the days—so long as there is someone around to do the counting. First we find that there is another natural periodicity: the year, about $365$ days. We have also discovered that nature has sometimes provided a counter for ... | |
1 | 5 | Time and Distance | 5 | Units and standards of time | We have implied that it is convenient if we start with some standard unit of time, say a day or a second, and refer all other times to some multiple or fraction of this unit. What shall we take as our basic standard of time? Shall we take the human pulse? If we compare pulses, we find that they seem to vary a lot. On c... | |
1 | 6 | Probability | 1 | Chance and likelihood | “Chance” is a word which is in common use in everyday living. The radio reports speaking of tomorrow’s weather may say: “There is a sixty percent chance of rain.” You might say: “There is a small chance that I shall live to be one hundred years old.” Scientists also use the word chance. A seismologist may be interested... | |
1 | 6 | Probability | 2 | Fluctuations | We would like now to use our ideas about probability to consider in some greater detail the question: “How many heads do I really expect to get if I toss a coin $N$ times?” Before answering the question, however, let us look at what does happen in such an “experiment.” Figure 6–1 shows the results obtained in the first... | |
1 | 6 | Probability | 3 | The random walk | There is another interesting problem in which the idea of probability is required. It is the problem of the “random walk.” In its simplest version, we imagine a “game” in which a “player” starts at the point $x=0$ and at each “move” is required to take a step either forward (toward $+x$) or backward (toward $-x$). The ... | |
1 | 6 | Probability | 4 | A probability distribution | Let us return now to the random walk and consider a modification of it. Suppose that in addition to a random choice of the direction ($+$ or $-$) of each step, the length of each step also varied in some unpredictable way, the only condition being that on the average the step length was one unit. This case is more repr... | |
1 | 6 | Probability | 5 | The uncertainty principle | The ideas of probability are certainly useful in describing the behavior of the $10^{22}$ or so molecules in a sample of a gas, for it is clearly impractical even to attempt to write down the position or velocity of each molecule. When probability was first applied to such problems, it was considered to be a convenienc... | |
1 | 7 | The Theory of Gravitation | 1 | Planetary motions | In this chapter we shall discuss one of the most far-reaching generalizations of the human mind. While we are admiring the human mind, we should take some time off to stand in awe of a nature that could follow with such completeness and generality such an elegantly simple principle as the law of gravitation. What is th... | |
1 | 7 | The Theory of Gravitation | 2 | Kepler’s laws | First of all, Kepler found that each planet goes around the sun in a curve called an ellipse, with the sun at a focus of the ellipse. An ellipse is not just an oval, but is a very specific and precise curve that can be obtained by using two tacks, one at each focus, a loop of string, and a pencil; more mathematically, ... | |
1 | 7 | The Theory of Gravitation | 3 | Development of dynamics | While Kepler was discovering these laws, Galileo was studying the laws of motion. The problem was, what makes the planets go around? (In those days, one of the theories proposed was that the planets went around because behind them were invisible angels, beating their wings and driving the planets forward. You will see ... | |
1 | 7 | The Theory of Gravitation | 4 | Newton’s law of gravitation | From his better understanding of the theory of motion, Newton appreciated that the sun could be the seat or organization of forces that govern the motion of the planets. Newton proved to himself (and perhaps we shall be able to prove it soon) that the very fact that equal areas are swept out in equal times is a pre... | |
1 | 7 | The Theory of Gravitation | 5 | Universal gravitation | What else can we understand when we understand gravity? Everyone knows the earth is round. Why is the earth round? That is easy; it is due to gravitation. The earth can be understood to be round merely because everything attracts everything else and so it has attracted itself together as far as it can! If we go even fu... | |
1 | 7 | The Theory of Gravitation | 6 | Cavendish’s experiment | Gravitation, therefore, extends over enormous distances. But if there is a force between any pair of objects, we ought to be able to measure the force between our own objects. Instead of having to watch the stars go around each other, why can we not take a ball of lead and a marble and watch the marble go toward the ba... | |
1 | 7 | The Theory of Gravitation | 7 | What is gravity? | But is this such a simple law? What about the machinery of it? All we have done is to describe how the earth moves around the sun, but we have not said what makes it go. Newton made no hypotheses about this; he was satisfied to find what it did without getting into the machinery of it. No one has since given any machin... | |
1 | 8 | Motion | 1 | Description of motion | In order to find the laws governing the various changes that take place in bodies as time goes on, we must be able to describe the changes and have some way to record them. The simplest change to observe in a body is the apparent change in its position with time, which we call motion. Let us consider some solid object ... | |
1 | 8 | Motion | 2 | Speed | Even though we know roughly what “speed” means, there are still some rather deep subtleties; consider that the learned Greeks were never able to adequately describe problems involving velocity. The subtlety comes when we try to comprehend exactly what is meant by “speed.” The Greeks got very confused about this, and a ... |
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