Discussion

the spectrum of mechanics

The general study of the relationships between motion, forces, and energy is called mechanics. It is a large field and its study is essential to the understanding of physics, which is why these chapters appear first. Mechanics can be divided into sub disciplines by combining and recombining its different aspects. Three of these are given special names.

The study of motion without regard to the forces or energies that may be involved is called kinematics. It is the simplest branch of mechanics. In contrast, the study of forces in the absence of changes in motion or energy is called statics. Lastly, the branch of mechanics that deals with both motion and forces together is called dynamics.

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Prior to the Seventeenth Century, the most significant works on mechanics were written in the Fourth Century BCE by the Greek philosopher Aristotle a.k.a. Αριστοτέλης (384-322 BCE) — these were (in English) Mechanics, On the Heavens, and The Nature. Although the first section of every general physics textbook is about mechanics, Aristotle's Mechanics (Μηχανικά - "Mekhanika") probably wasn't written by him and won't be discussed here. On the Heavens (Περί Ουρανού - "Peri Uranu") will be discussed later in this book.

The Nature is the work by Aristotle that people think of when they think of physics. That's because it's the origin of the word physics. The full name of this work is Φυσική Ακρόασις (Fysike Akroasis), which translates literally to "Lesson on Nature" but more accurately should be called "Lesson on the Nature of Things". It acquired great stature in the Western world and was identified almost reverently by academics as Τὰ Φυσικά (Ta Fysika) — in English, The Nature or The Physics. In this book Aristotle discusses such subjects as space, time, and motion as elements in a larger philosophy of the natural world. Consequently people who studied "the nature of things" were often known as "natural philosophers". The term "physicist" was not widely used until probably the late Nineteenth Century. Since "the nature of things" is such a broad phrase, the Greek root word also was applied to medical doctors (physicians) who studied the nature of the human body (or when referring to its general state of development, its physique).

Aristotle professed many things about the physical world and certainly was a great thinker for his time, but unfortunately he never tested to see if any of his notions were correct. He was a philosopher, not a scientist. He never once made a measurement (no doubt because there were few measuring devices to be had) and balked at the application of mathematics to the natural world. This resulted in some seriously wrong statements on his part. A particularly famous error can be found in Aristotle's History of Animals,

Ἔχουσι δὲ πλείους οἱ ἄρρενες τῶν θηλειῶν ὀδόντας καὶ ἐν ἀνθρώποις καὶ ἐπὶ προβάτων καὶ αἰγῶν καὶ ὑῶν· ἐπὶ δὲ τῶν ἄλλων οὐ τεθεώρηταί πω.   Males have more teeth than females in the case of men, sheep, goats, and swine; in the case of other animals observations have not yet been made.

Bertrand Russell (1872-1970)

Aristotle, in spite of his reputation, is full of absurdities. He says that children should be conceived in the Winter, when the wind is in the North, and that if people marry too young the children will be female. He tells us that the blood of females is blacker then that of males; that the pig is the only animal liable to measles; that an elephant suffering from insomnia should have its shoulders rubbed with salt, olive-oil, and warm water; that women have fewer teeth than men, and so on. Nevertheless, he is considered by the great majority of philosophers a paragon of wisdom.   …   If the matter is one that can be settled by observation, make the observation yourself. Aristotle could have avoided the mistake of thinking that women have fewer teeth than men, by the simple device of asking Mrs. Aristotle to keep her mouth open while he counted. He did not do so because he thought he knew. Thinking that you know when in fact you don't is a fatal mistake, to which we are all prone. I believe myself that hedgehogs eat black beetles, because I have been told that they do; but if I were writing a book on the habits of hedgehogs, I should not commit myself until I had seen one enjoying this unappetizing diet. Aristotle, however, was less cautious. Ancient and medieval authors knew all about unicorns and salamanders; not one of them thought it necessary to avoid dogmatic statements about them because he had never seen one of them.

This sorry state of affairs persisted for roughly a millennium and half until Galileo Galilei (1564-1642) came along and taught the world how to see. Prior to the Seventeenth Century, most science was done as if it were mathematics; statements of "fact" were made like mathematical postulates, the rules of logic were applied, and conclusions were drawn. Galileo added two additional steps to this chain of reasoning that made all the difference in the universe. He performed experiments to test his conclusions and then modified some part of the theory until it agreed with observation.

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and then took off in the Eighteenth Century with Isaac Newton (1642-1727). We will deal with the accomplishments of these two great scientists throughout this book, but especially in the first several chapters.

Newton also invented the branch of mathematics we now call calculus in order to solve difficult mathematical problems. Since it was invented to make physics easier, physics and calculus are often thought of as inseparable. Still it is possible to learn a great deal of physics without ever having taken calculus. In fact, it's possible for a typical person to learn all the physics they ever need without any math at all. However, your understanding of the subject will be enhanced through the use of mathematics. The more math you know, the more physics you can learn.

Energy is an abstract physical quantity that is not easily perceived by humans. It can exist in many forms simultaneously and only acquires meaning through calculation. When the total of all the different forms of energy is determined, we find that it remains constant in systems that are isolated from their surroundings. This statement is known as the law of conservation of energy and is one of the really big concepts in all of physics, not just mechanics. It was first hypothesized by Julius Mayer (1814 - 1878), a German ship's physician; was first measured quantitatively by James Joule (1818-1889), an English brewer; and was first stated formally by Hermann Helmholtz (1821-1894), a German professor of anatomy and physiology (and later of physics and mathematics).

The range of personalities involved in its origins ought to give you some notion of the scope of energy in the sciences. The conservation of energy is a concept that overlaps several of the principal branches of physics — namely mechanics (the study of motion, forces, and energy) and thermodynamics (the study of internal energy and external work). The former law is known as the conservation of mechanical energy and deals with the energies of motion, while the latter is called the first law of thermodynamics and deals with the macroscopic appearance of microscopic energy.

The total energy of a system is constant only in isolated systems. Whenever a system is affected by an outside agent, its total energy changes and the the law of conservation of energy no longer holds. The quantity exerted by the outside agent that causes this change is called a force. (In general, a force is anything that causes a change: like a change in energy or motion or shape, for example.) When a force causes a change in the energy of a system, physicists say that work has been done. The mathematical statement that relates forces to changes in energy is therefore called the work-energy theorem.

The law of conservation of energy suffers from an ironic dilemma. Whenever one system interacts with another the total energy of either system may change, so the law doesn't hold. (Another, and possibly better, definition of a force is as an interaction between systems that results in a change in both systems.) If we examine these changes, however, we always find that the change in one system is precisely equal and opposite the change in the other. That is, when one system loses a certain amount of energy the other gains energy in exactly the same amount. Individually the systems don't obey the law, but together they do — as long as they aren't affected by an outside agent. But of course we can fix this by just including the outside agent into our system; which would fix the law as long as this system wasn't acted upon by an outside agent. And so we could keep going until we increase our system to include anything that might affect anything until our system includes everything. Thus, nothing obeys the law of conservation of energy, but everything does! The conservation of energy really only holds for the entire universe. That's why it's important to the whole of science — not just mechanics, not just physics.

The chapters of this book devoted to mechanics appear more or less in the following order …

1. kinematics
2. dynamics and statics
3. energy

types of motion

There are many elementary questions in kinematics, but the one we will use to start this discussion is, "How many different ways can an object move?" There are many ways to answer this question, but for purposes of this book there are basically four types of motion.

1. Translational motion results in a change of location. This category may seem ridiculous at first as motion implies a change in location, but an object can be moving and yet not go anywhere. I get up in the morning and go to work (an obvious change in location), but by evening I'm back at home (back in the very same bed where I started the day). Is this translational motion? Well, it depends. If the problem at hand is to determine how far I travel in a day, then there are two possible answers: either I've gone to work and back (thirteen miles each way for a total of 26 miles) or I've gone nowhere (thirteen miles each way for a total of zero miles). The first answer invokes translational motion while the second invokes oscillatory motion.
2. Oscillatory motion is repetitive and fluctuates between two locations. In the previous example of going from home to work to home to work I am moving, but in the end I haven't gone anywhere. This second type of motion is seen in pendulums (like those found in grandfather clocks), vibrating strings (a guitar string moves but goes nowhere), and drawers (open, close, open, close — all that motion and nothing to show for it). Oscillatory motion is interesting in that it often takes a fixed amount of time for an oscillation to occur. This kind of motion is said to be periodic and the time for one complete oscillation (or one cycle) is called a period. Periodic motion is important in the study of sound, light, and other waves. Large chunks of physics are devoted to this kind repetitive motion. Doing the same thing over and over and going nowhere is pretty important; which brings us to our next type of motion.
3. Rotational motion occurs when an object spins. The earth is in a constant state of motion, but where does that motion take it? Every twenty-four hours it makes one complete rotation about its axis. (Actually, it's a bit less than that, but let's not get bogged down in details.) The sun does the same thing, but in about twenty-four days. So do all the planets, asteroids, and comets; each with its own period. (Note that rotational motion too is often periodic.) On a more mundane level, bocce balls, CDs, and wheels also rotate. That should be enough examples to keep us busy for awhile.

The chapters of this book devoted to mechanics appear more or less in the following order …

1. translational
2. rotational
3. oscillatory

Are there additional types of motion? Well, it depends on whom you ask and when you ask them. All motion is basically translational to some extent; that is to say, you can't be moving unless you (or a part of you) moves from one place to another. There is possibly a fourth type of motion that goes nowhere in the long run (not intentionally, anyway) and yet does not require that the object ever return to a particular location.

4. Chaotic motion is predictable in theory but unpredictable in practice, which makes it appear random.
   
   I don't like how this sounds.
   
   We now know that atoms move. For example, an atom in a gas is free to bounce around within its container. This motion appears random, but is completely predictable according to current theories of classical mechanics. In practice, however, there is no way to do this with any degree of accuracy for an extended period of time. Every measurement has error associated with it. Now imagine that you were trying to predict the motion of a billion gas atoms in a container. After measuring the position and velocity of each one as accurately as possible, you enter the data in a monstrous computer and let it do the calculations for you. Since the measurements associated with each atom are a little off, the first round of computation will be a little wrong. Those wrong numbers will then be used in the next round of calculation and the results will be a little more wrong. After a billion calculations, the compounded error would render the results useless. This is chaos.
   
   The motion of the electron in an atom is fundamentally unpredictable. That is, there is no known method to measure the position and velocity of an electron simultaneously without some uncertainty. The harder you try to locate the electron, the less you know about its velocity. The harder you try to measure its velocity, the less you know about its location. According to current theories of quantum mechanics, there is no way around this. Although the electron is often said to "orbit" the nucleus of an atom, nothing can actually be determined about the path of its motion. It is impossible to say where an electron in an atom is going. This is uncertain motion.