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.
Motion is the action of changing location or position. 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. The branch of mechanics that deals with both motion and forces together is called dynamics and the study of forces in the absence of changes in motion or energy is called statics.
The term energy refers an abstract physical quantity that is not easily perceived by humans. It can exist in many forms simultaneously and only acquires meaning through calculation. A system possesses energy if it has the ability to do work. The energy of motion is called kinetic energy
Whenever a system is affected by an outside agent, its total energy changes. In general, a force is anything that causes a change (like a change in energy or motion or shape). 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 called the work-energy theorem.
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.
The first few chapters of this book are basically about these topics in this order…
- motion (kinematics)
- forces (dynamics and statics)
types of motion
Motion may be divided into three basic types — translational, rotational, and oscillatory. The sections on mechanics in this book are basically arranged in that order. The fourth type of motion — random — is dealt with in another book I wrote.
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 (22 km each way for a total of 44 km) or I've gone nowhere (22 km each way for a total of 0 km). The first answer invokes translational motion while the second invokes oscillatory motion.
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.
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 a while.
Random motion occurs for one of two reasons.
Some motion is predictable in theory but unpredictable in practice, which makes it appear random. For example, a single molecule in a gas will move freely until it strikes another molecule or one of the walls containing it. The direction the molecule travels after a collision like this is completely predictable according to current theories of classical mechanics. Every measurement has uncertainty associated with it. Every calculation made using the results of a measurement will carry that uncertainty along. Now imagine that you are trying to predict the motion of a billion gas atoms in a container. (That's a small amount, by the way.) After measuring the position and velocity of each one as accurately as possible, you enter the data into a monstrous computer and let it do the calculations for you. Since the measurements associated with each molecule 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. The molecule could be anywhere within the container. This type of randomness is called chaos.
Some motion is unpredictable in theory and is truly random. For example, the motion of the electron in an atom is fundamentally unpredictable because of a weird conspiracy of nature described by quantum mechanics. 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. This is fundamental quality of small objects like electrons and there is no way around it. Although the electron is often said to "orbit" the nucleus of an atom, strictly speaking, this isn't true. The probability of finding the electron at any particular point in space is predictable, but how it got from the first place you observed it to the second is actually a meaningless question. There is no name for this kind of motion because the concept of motion doesn't even apply.
Prior to the Renaissance, the most significant works in mechanics were those written in the Fourth Century BCE by the Greek philosopher Aristotle of Stagira (384–322 BCE) — these were Mechanics, On the Heavens, and The Nature or in Greek Μηχανικά (Mekhanika), Περί Ουρανού (Peri Uranu), and Φυσική Ακρόασις (Fysike Akroasis). Although the first section of every general physics textbook is about mechanics, Aristotle's Mechanics probably wasn't written by him and won't be discussed here. On the Heavens will be discussed later in this book.
The Nature is Aristotle's work that's most relevant to this book. That's because it's the origin of the word physics. The full name Φυσική Ακρόασις (Fysike Akroasis) translates literally to "Lesson on Nature" but "The Lesson on the Nature of Things" is probably more faithful. The Nature acquired great stature in the Western world and was identified almost reverently by academics as Τὰ Φυσικά (Ta Fysika) — The Physics. In this book Aristotle introduced the concepts of space, time, and motion as elements in a larger philosophy of the natural world. Consequently, a person who studied the nature of things was called a "natural philosopher" or "physicist" and the subject they studied was called "natural philosophy" or "physics". Incidentally, this is also the origin of the words "physician" (one who studies the nature of the human body) and "physique" (the nature or state of the human body).
Aristotle professed many things about the physical world and certainly was a great thinker for his time. Unfortunately his scientific statements are usually wrong — sometimes comically. The English philosopher Bertrand Russell (1872–1970) compiled a list of Aristotle's worst offenses in his 1943 essay An Outline of Intellectual Rubbish.
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.
Bertrand Russell, 1943
Aristotle was a philosopher, not a scientist, He is sometimes credited as the inventor of logic. ("Invent" may be too strong a word here. Certainly without Aristotle, logic would have evolved differently.) And logic and reasoning are central to science, so it seems logical and reasonable to assume that Aristotle could have been one of the first scientists. Unfortunately, that's not the way it went. Russell said it best.
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.
Bertrand Russell, 1943
Science is different from other human activities. It doesn't matter what you reason yourself into logically (all swans are white), what you feel emotionally (dogs are better than cats), or what is accepted culturally (there ain't no room for sheep in cattle country). In the end, it all comes down to observation.
The statement "women have fewer teeth than men" is famous now, not because Aristotle said it, but because Russell said Aristotle said it. The original quote came from Aristotle's History of Animals, which I managed to find in both the original Greek and an English translation.
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 Αριστοτέλης, σ.μ. 350 πΚΧ Aristotle, ca. 350 BCE
How astoundingly ironic.
This sorry state of affairs persisted in the Western world for roughly a millennium and half. It took an Italian from Pisa — Galileo Galilei — to show the world how to see.