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. Some 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. Informally, 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 study of how energy changes forms and location during physical processes is called energetics, but the word is used more by scientists in fields outside of physics than inside.
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
- Motion that results in a change of location is said to be translational. 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
- Motion that is repetitive and fluctuates between two locations is said to be oscillatory. 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 or Big Ben), 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
- Motion that occurs when an object spins is said to be rotational. 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, boccie balls, phonograph records, and wheels also rotate. That should be enough examples to keep us busy for a while.
- Random motion
- Random motion occurs for one of two reasons.
- Chaos theory
- 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.
- Quantum theory
- 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 a 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.
- Physics is the study of the fundamental nature of all things.
- Prior to the Renaissance, the most significant works in mechanics were those written in the 4th 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 Φυσικῆς ἀκροάσεως (Fysikes 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 Φυσικής ακρόασις (Fysikes 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).
mechanics, dynamics, statics, kinematics
The words mechanics, dynamics, statics, and kinematics are used throughout this book and heavily in the first third. Each refers to a discipline or branch of physics, thus the common suffix -ics. Each word can also be changed from a noun to an adjective. This gives us words like dynamic, static, kinematic, mechanical, dynamical, and physical. We can also make adverbs like dynamically and physically. Here are the relevant nouns, each followed by brief definition and a semi-long-winded story about its origin. For many readers, the brief definitions will be good enough.
- The branch of physics dealing with motion and forces.
- The word's origin can be traced back to the ancient Greek words for machine, μηχανή (mekhane), a clever device for doing work; and mechanic, μηχανικός (mekhanikos), a person skilled with machines. The word mechanics did not acquire its current meaning until sometime in the 17th century — probably by the Irish chemist Robert Boyle (1627–1691).
- Mechanics can be divided into the subdisciplines of kinematics, statics, and dynamics. Historically statics came first (antiquity), then kinematics (1638 for the subject, 1834 for the word), then mechanics (1663 as a word), and finally dynamics (1690s as a word). Conceptually mechanics contains dynamics, which overlaps with statics and kinematics.
- The study of motion and forces together. (That sounds a little too informal.) The study of the effect that forces have on the motion of objects. (That's better.)
- The word dynamics was invented in the late 17th century just to be a word that meant the opposite of the word statics. Credit goes to the German mathematician and philosopher Gottfried Leibniz (1646–1716). Leibniz is mostly known as the co-creator of calculus with the English scientist and mathematician Isaac Newton (1642–1727). Leibniz and Newton may have argued about priority, but more of Leibniz lives on in calculus than does Newton. The lowercase d (d) for derivative and the crazy long s (∫) for integral were Leibniz's ideas. He also coined the term coordinate axes and named the axes abscissa and ordinate. Leibniz adapted the word dynamics from the Greek word for force, strength, or power — δύναμης (dynamis) — which in turn comes from the Greek word meaning "I can" or "I am able" — δύναμαι (dynamai). The word did not immediately jump into the English language because Leibniz thought in German, wrote in French and Latin, and wrote for a Continental European audience.
- The study of forces without regard to motion. Technically, statics is the study of forces in the absence of acceleration. One way to not be accelerating is to not move. In that special case, both velocity and acceleration are zero. Since there is no way to distinguish between motion at a constant velocity (v ≠ 0, a = 0) and being in a state of rest (v = 0, a = 0), statics covers both situations.
- The origin of the word goes back to ancient Greek phrase τέχνη στατική (tekhne statike), which now literally means "static art" but at the time meant something more like "the art of weighing". Basically, the phrase describes the skills that a structural engineer would need. A knowledge of the way the weight of a building or bridge or tower is distributed so that it stays standing in place. Although originally all about weight, statics as a branch of mechanics now covers all forces and statics as a part of structural engineering includes subjects like wind loads on tall buildings and buoyant forces from groundwater on basements. Statics and structural engineering are about more than just weight.
- The study of motion without regard to the forces affecting it.
- The concepts of distance, displacement, and time are ancient if not primitive. The concepts of speed, velocity, and acceleration seem like they should be as well, but any formal definitions prior to the 16th century do not seem to exist. Pretty much all credit for this goes to the Italian scientist Galileo Galilei (1564–1642) and his groundbreaking work on the subject, known in English by the short name of Two New Sciences. Galileo wrote in dialog form (and brilliantly so) with no equations. This was partly because mathematical notation didn't exist like we know it now, but mostly because he wanted to make his book approachable. Just three learned gents passing the time talking about the latest advances in science.
- Galileo would not have used the word kinematics, however (or even physics). Credit for inventing that word goes to the French scientist and mathematician André-Marie Ampère (1775–1836). Ampère is best known for his fundamental work in electrodynamics (a word he also invented) and for having the unit of electric current named in his honor. Ampère is almost not at all famous for what I am doing right now — organizing and assigning names to disciplines and subdisciplines in physics. Ampère took this to extremes, however, and attempted the classification of all human knowledge (subdisciplines of subdisciplines of subdisciplines of…). Prior to Ampère's work, there was no name for this branch of mechanics. It might not have even been thought of as a branch in need of a name. Nonetheless, he adapted the Greek word for movement, κίνημα (kinema), into the French word cinématique, which became the English word kinematics. He did not invent the word cinema, since motion picture technology did not evolve into a business until some 60 years after his death — although his work may have inspired the word.
This organizational scheme is incomplete as far as I'm concerned. It's missing one key concept, possibly the most important concept in all of mechanics, possibly in all of physics, possibly in all of science — energy. Because energy arose as a concept after this scheme was created, a name was never assigned to the branch of mechanics dealing with energy. There is a word energetics, but it doesn't seem to be popular in general physics textbooks. The equivalent concept in general physics is called thermodynamics, which started out as the study of work done by thermal processes but expanded into the more general law of conservation of energy.
- The study of the transformation and distribution of energy during processes within systems.
- The word energy in English has been used to represent concepts such as strength, efficacy, persuasiveness, action, resourcefulness, and skill. It didn't acquire its current physical meaning until the 19th century. Its ancient Greek origins are from the prefix εν+ (en+, to endow with a certain quality) and the noun εργον (ergon, work). Think of words like enable (to make possible), enamor (to inspire love), encode (to translate into code), and endanger (to put in danger). Those four examples were all verbs begining with the suffix en+, but energy is a noun. This makes energy then literally something like "the ability to become work". The English scientist Thomas Young (1773–1829) was the first to use the word energy in the modern sense. His definition is almost the same as our current definition of kinetic energy. He was also the first to formally define work as a physical quantity. He also determined that light is a wave.
- The ancient Greek philosopher and scientist Aristotle of Stagira (384–322 BCE) might have invented the word that eventually became energy, but his ἐνέργειά (energeia) was a term of philosophy, not science. Aristotle's sense of the word is often translated as "activity" or "being at work on". This was contrasted with ἕξις (exis), which meant "possession" or "being in the state of". Energeia meant doing. Exis meant having. To ensure happiness, Aristotle argues, positive virtues should be realized through actions and not just held as beliefs. This has nothing to do with its current scientific meaning, however.
- The term energetics is more popular outside of physics than inside. Here are some examples of energetics from other branches of science.
- Chemical energetics
- The study of energy as it relates to chemical reactions. Terms from this field that some of you may be familiar with include endothermic, exothermic, enthalpy, activation energy, and reaction coordinates.
- Biological energetics (bioenergetics)
- The study of energy exchanges within the cell. Processes from this field that some of you may be familiar with include photosynthesis, cellular respiration, membrane transport, protein folding, and signal transduction.
- Physiological energetics (animal bioenergetics)
- The study of the rates of energy expenditure and efficiencies of energy transformations in whole organisms. Some examples of processes dealt with in this field include weight gain, weight loss, growth, healing, and thermoregulation.
- Ecological energetics
- The study of the transfer of energy from one trophic level to another. The study of how energy moves through the food chain, food web, or food cycle from producers to consumers (first herbivores, then carnivores) then on to decomposers and back again.
Here's an oddball word that I don't know how to handle.
- In mechanics, it's an obsolete and redundant word that means the same thing as dynamics. Kinetics is the branch of mechanics that deals with the effect that forces have on motion. The adjectival form kinetic persists in mechanics in the terms kinetic friction and kinetic energy; and in thermodynamics in the terms kinetic theory of heat, kinetic theory of gases, and kinetic molecular theory.
- In chemistry, it's a word that could have been obsoleted, but it wasn't. Kinetics is the branch of chemistry that deals with rates of chemical reactions. For no apparent reason, the word chemical kinetics is favored over chemical dynamics (which is what I think it should be called).
- The noun kinetics and the adjective kinetic are neologisms coined sometime in the 19th century, derived from the Greek word κινητικός (kinetikos), which is a form of the noun for motion, κίνησις (kinesis), with the double suffix -ικ-ός (-ik-os) to make it into a subject of study.