by Donald E. Simanek

"Lest you think that I am quibbling over minor points of language, I note that in my experience many of the misconceptions people harbor have their origins in imprecise language... Precise language is needed in science, not to please pedants but to avoid absorbing nonsense that will take years, if ever, to purge from our minds." - Dr. Craig F. Bohren, from his "Clouds in a Glass of Beer: Simple experiments in atmospheric physics"

"...(language) becomes ugly and inaccurate because our thoughts are foolish, but the slovenliness of our language makes it easier for us to have foolish thoughts." - George Orwell

"The search for the mot juste is not a pedantic fad but a vital necessity. Words are our precision tools. Imprecision engenders ambiguity and hours are wasted in removing verbal misunderstandings before the argument of substance can begin." - Anonymous civil servant (from Roget's Thesaurus Webpage)

"Many errors, of a truth, consist merely in the application of the wrong names of things." -Spinoza


Sometimes it seems a losing battle to combat the decline of the English language. As the language deteriorates into imprecise flabbiness, so does our ability to express ideas. This is bad enough in everyday life, but disastrous in the sciences, for science requires precision of thought and expression.

Physics, for example, is hard enough to learn without having to surmount semantic roadblocks. While we claim physics is a "precise science" in the sense that it strives for the greatest possible precision of measurement, physicists, as a class, are notoriously less precise when speaking and writing about the subject. When they speak to each other they frequently adopt a conversational mode so abbreviated, with so many details left out, that anyone not working in that particular field finds it incomprehensible. They must do this, of course, or they would spend hours explaining things that are, to them, trivial. They communicate effectively with each other through a common base of knowledge and agreed-upon verbal conventions, which are seldom ever written down. They play a very good "mind-reading" game in which each hears what the other means, not what he says. And it works! But outsiders are baffled.

The Physics teacher's dilemma.
Many physicists have extreme difficulty when they try to explain physics to outsiders. They are not used to spelling out everything, and impatient at having to do so. It seems to be something like trying to explain economics to a four-year-old. Some have said that, for this reason, physics is the worst taught subject. It may be so. But those who can learn physics in spite of these difficulties, and become physicists, often can't understand why others find it so hard.

Some of these difficulties are unavoidable. But there is no excuse for some of the imprecise and misleading expressions we sometimes find in textbooks, and often find in the physics classroom. There is little excuse for a proliferation of words that all mean the same thing. There is no excuse for using a vague or imprecise word when a perfectly good precise one is available.

I list below a few modest proposals toward this end.


The dictionary reminds us that one should only use the word "ratio" when comparing two "like" things. "Pi" (p), the ratio of the circumference to diameter of a circle, is fine, since both circumference and diameter are lengths. But we shouldn't speak of the ratio of the circle's area to its radius and we shouldn't speak of a ratio of mass to volume, for we'd be comparing different physical quantities. These are simply quotients.


Even textbooks commit this language sin. "Density is mass per unit volume." "Electric field strength is force per unit charge." I note with satisfaction that many scientists are now being more careful about this, saying instead: "Density is mass divided by volume", or "Density is the quotient of mass to volume." The point here is that the definition does not necessarily require one unit of the quantity in the denominator. In the case of the definition of electric field as force/charge, in the MKS system, we certainly would not want to use a charge of one unit, a Coulomb, for such a large charge would very likely disturb the situation we are trying to measure. [In fact, the proper definition of electric field is "the limit of force/charge as the charge size goes to zero".]


These words are entrenched in the informal language of science, but they are entirely unnecessary. We have perfectly good technical words for these measurable quantities: current, potential, and power. Physics textbooks set a good example when describing current and power; the good ones hardly ever use "amperage" or "wattage". Then why do they persist in using "voltage"? This seems inconsistent, doesn't it?


The worst sinners here are the people in the news media. How often have you heard, "He was traveling at a high rate of speed"? Speed is already a rate of change of position. A "rate of speed" is either redundant, or incorrectly implies an acceleration, which is not what is meant. Simply say "a high speed".


This ubiquitous phrase pops up frequently in textbooks, as in a statement of Newton's third law: "Interacting bodies exert equal and opposite forces on each other." What is really meant is that they exert forces of equal magnitude and opposite sign on each other. How can any two nonzero vectors be "equal" and also "opposite"?

[Thanks to Paul Lee for bringing this one to my attention, after I'd committed the error myself.]


A moment of inertia.
Rare is the physics book that doesn't say something like "The net force on a body at rest is zero" in the chapters about statics. Then, in the dynamics chapters we may see "A body thrown straight upward is momentarily at rest at the highest point of its motion". The student then logically concludes that at that point the net force on the body is zero and therefore its acceleration at that point is zero. This is the "at rest = zero net force = equilibrium = zero acceleration" fallacy. We can't exactly blame students for taking textbooks at their word.

What do "at rest" and "momentarily at rest" mean, and are they different? Most people understand a body at rest to be unmoving for some period of time. Can a body even be "momentarily" at rest? One reader suggested "at rest at a point in time." I fear that compounds the problem, for the definition of velocity involves a limiting process of calculus starting with a finite time interval.

Rather than resolve this sticky semantics issue, the cure is simple. When describing a situation where the body's velocity changes sign and therefore must pass through a value of v = 0, just say "the velocity is momentarily zero" at that point. This happens at the top of a trajectory, at the extremes of pendulum motion, and can happen at some point during the collision of two bodies. Avoiding use of the phrase "momentarily at rest" derails this logical fallacy before it begins, putting it to rest for good.

One reader suggests "instantaneously zero" as preferable to "momentarily zero".


Rick Glaser reminded me of this common misconception. Most textbooks avoid this trap, but students fall into it anyway, becoming confused about whether "deceleration" means the same as "negative acceleration". Rick suggests: "Deceleration" is not actually a term in physics. It is only an English word used in common speech, meaning "a decrease in speed." The problem with this word is that some students mistake it to mean the same as negative acceleration. But since the negative sign just defines a direction in a particular problem, relative to a chosen axis, an object's speed would actually INCREASE if it has a negative velocity as well as a negative acceleration.

So how do we avoid this dilemma? I find it interesting as an example of how we think about motion. Compare how we speak of speed compared how we speak of acceleration:

  • We almost never speak of negative speed, even colloquially. Most students recognize that speed is a positive quantity, the magnitude of the velocity. We have no colloquial word for velocity in a negative direction.
  • We often speak colloquially of deceleration to mean reducing the size of the acceleration, whatever the direction of the acceleration. We have no colloquial word for acceleration in a negative direction.
  • The magnitude of a velocity is the speed.
  • There is no single word for the magnitude of an acceleration, niether a colloquial or technical one.
So when we speak of an automobile moving along a straight road, we can speak of its speed, which might be a negative or positive velocity. When we speak of its acceleration, it could be a negative or positive acceleration. And whether it is speeding up or slowing down, we can also correctly call it an acceleration. See how screwed up our language is on these matters? The word "acceleration" can mean three distinct things.

When doing physics problems in a coordinate system, we should refrain from using the word "deceleration", for, in fact, the colloqual concept it names is not one we use often in discussing motion mathematically. When we do need the concept we should say "the acceleration is in the negative direction". "Speed" should be only used for "the magnitude of the velocity". There is seldom any need to name the "magnitude of the acceleration"

I might add that these confusions arise in cases of two-dimensional motion along a straight line. When a body is moving in a curved or convoluted path we deal with the forces, displacements, velocities and accelerations by vector math, and "positive" or "negative" are insufficient descriptors anyway.

I don't wish to minimize the extreme grief this gives to many students, and I'd welcome input from teachers about how they deal with this.


Many conceptual difficulties arise when key words are left out. The phrase "friction force" suggests to the student that friction is a kind of force, or that friction is a physical "thing" that is capable of exerting a force on other things. This confuses a process with a consequence of that process. Friction is a process that occurs at contact interfaces of material bodies. Friction gives rise to two forces, an action/reaction pair in accordance with Newton's third law: Body A exerts a force on body B and B exerts a force of equal magnitude and opposite direction on A, due to the process of friction at their interface or contact points. Due to elastic compression of the bodies, they also exert force normal to (perpendicular to) the surface of contact. Little confusion arises from the label "normal force" for no student is likely to think it a "force due to the normal". (However some might wonder what an "abnormal" force might be.) The normal force and the force due to friction constitute components of a force that we simply call the "reaction force" on the body, due its contact with the other body. To avoid misconceptions, it's better to speak of a "force due to friction". Some readers suggest "frictional force", on the grounds that the suffix "-al" suggests "due to" and will warn students that it's something other than a "friction force". I doubt that students would pick up on that.


If we speak of the "acceleration of the automobile" we certainly mean that the automobile is the thing that's accelerating. Now consider "acceleration of gravity." Is this saying that gravity is accelerating? The little preposition "of" must mean different things in these similar sentences.

English teachers tell me that elementary students find prepositions the single part of speech most difficult to master. Clearly physicists who invent these names for physical concepts never overcame that difficulty. If they'd check a dictionary, they would find that "of" can mean:

Tom O'Haver may have doubted that this is a problem. He used Google to search the web to find out what language is being used. He found that "acceleration of gravity" is used about 13,000 times while "acceleration due to gravity" does win out, at over 20,000 hits. He says, "There is still a long way to go." The term, "force of friction" gave about 4000 hits and force due to friction" only 300.

owing to
away from
separated from
composed or made from
associated with
adhering to
belong to or connected to
possessing, having (as in "a person of honor")
containing or carrying
specified as

Now I ask you, does the phrase "acceleration of gravity" meet any of these criteria precisely? Does the list of meanings of "of" include "due to", "caused by" or "the result of"? The closest matches are "associated with", "from" and  "owing to". "Associated with" is weak, and could cover a whole range of associative relations.

We shouldn't speak of "the force of gravity" but say "the gravitational force" or even better, "the force due to (resulting from)" gravity. We don't want to suggest that gravity is a "thing" on an equal status with planets and bricks.

But the important thing is what students interpret "of" to mean in such contexts. I have asked students this question over many years, and the results are:

contained in, composed of (as in "United States of America")
possessed by (as in "assets of the bank")
caused by, generated by (as in "consequences of education", "wages of sin")
made from (as in "milk of magnesia")
about (as in "Of mice and men")

You can easily imagine the conceptual difficulties that can arise from these interpretations if applied to physics concepts.

Prepositions in English indicate relations between things. Physics is very much concerned with precise relations between things. But the prepositions available: "at", "by", "to", "from", and "with", are blunt instruments at best. The trouble with prepositions is that they have such a wide spectrum of incompatible meanings that it's very easy to interpret them in a way not intended by the writer or speaker. The cure: substitute other words conveying more precision and clarity, even if that requires lengthier statements.

The little word "of" also muddies the conceptual waters in other cases. I illustrate:

Force of friction. Better: Force due to friction.
Force of gravity. Better: Gravitational force. Force due to gravity.
Mechanical equivalent of heat. Better: Joule's constant.

Could we just throw out some of these pesky prepositions? See how it works in my document P-prime.


A very common mistake found in textbooks is to speak of "flow of current". Current itself is a flow of charge; what, then, could "flow of current" mean? It is redundant, misleading, or wrong. This expression should be purged from our vocabulary. Compare a similar mistake: "The velocity moves west."


Sometimes the word electricity is colloquially misused as if it named a physical quantity, such as "The capacitor stores electricity," or "Electricity in a resistor produces heat." Such usage should be avoided! In all such cases there's available a more specific or precise word, such as "The capacitor stores electrical energy," "The resistor is heated by the electric current," and "The utility company charges me for the electric energy I use." (I am not being charged based on the power, so these companies shouldn't call themselves Power companies. Some already have changed their names to something like "Acme Energy")


The term "electromotive force" is defined at the potential across the terminals of a chemical cell or other electrical power source under conditions of no load (zero current). It used to be abbreviated "E.M.F.", but then such abbreviations were simplified to "EMF" (usually accompanied by an explanation that it stands for "electromotive force", and finally, today, you see it written in textbooks as "emf" (without any explanation). It has evolved from an abbreviation to a word. Its historical origins have been swept under the rug, and maybe that's a good thing, for the old name caused much confusion for modern students.

The word originated when "force" had a broader technical meaning, to describe "that which can cause something to happen". So "electromotive force" meant, "That which can cause electrical charges to move". Nowadays we have narrowed and restricted the concept of force, so in the modern sense, emf isn't a force, it is an electrical potential. They are quite different concepts, with different units and dimensions. Also, force is a vector, while potential is a scalar. Lots of dissonant concepts clash here.


Older dictionaries suggested that percentage be used when a non-quantitative statement is being made: "The percentage growth of the economy was encouraging." But use percent when specifying a numerical value: "The gross national product increased by 2 percent last year."

One other use of "percentage" is proper, however. When comparing a percent measure that changes, it's common to express that change in "percentage points." For example, if the unemployment rate is 5% one month, and 6% the next, we say, "Unemployment increased by one percentage point". The absolute change in unemployment was, however, an increase of 20 percent. The average person hearing such figures seldom stops to think what the words mean, and many people think that "percent" and "percentage point" are synonyms. They are not. This is one more reason to avoid using the word "percentage" when expressing percent measures. The term "percentage point" is almost never used in the sciences. (Unless you consider economics a science.)

Students in the sciences, unaware of this distinction will sometimes say, "The experimental percentage uncertainty in our result was 9%." Perhaps they are trying to "sound profound". In view of the above discussion, this isn't what the student meant. The student should have simply said: "The experimental uncertainty in our result was 9%."


This is another misguided attempt at profundity: "Government spending took a quantum jump this year." The dictionary meaning of "quantum" is "a quantity or amount". So the quoted use of the word is empty or redundant, for any change would he a quantum amount. In physics the word takes a more specific meaning: a quantum "jump" is a change from one allowed state of a system to another; and this is used only to describe systems where the allowed states have discrete, measurably different, values. Government spending is hardly quantized in this sense, unless you consider the quantum unit to be the penny, a unit too small to be recognized by government spenders. In physics, quantum jumps of energy are usually quite small compared to the full range of energies the system can have. Colloquial misuse of this word treats it as if it always meant "very large".


Textbooks often speak of "overcoming friction". What can this possibly mean? Most likely the intended meaning was to say that the component of net applied force in the plane of contact between two bodies was equal or greater than the maximum force that could arise from static friction in this case.

The word "overcome" has no specific technical meaning. It's a slippery word capable of many misinterpretations. Consider another abuse of the word: "When a force overcomes the inertia of a body at rest, the body begins to move." Yes, I've actually seen such absurd statements in textbooks and heard them in classrooms. Force and inertia are two quite different things, and cannot be mathematically equated. Inertia is simply mass, no more, no less. How do you "overcome" mass? Destroy it?


Teachers and textbooks try to "colloquialize" physics in various ways, hoping to relate concepts to everyday life and everyday language. This usually backfires, creating misconceptions. For example, a textbook says, "Force is a push or a pull." That seems innocent enough, but the colloquial concept of pushing and pulling is something you do that necessarily causes motion, an Aristotelian physics notion. The student thinks of "pushing an automobile" or "pulling a wagon", producing motion. So when tides are discussed in textbooks, we sometimes see "Tides are caused because the moon pulls more strongly on the near side of the earth, less on the body of the earth, and still less on the far side. Therefore the water on the near side is pulled a greater distance toward the moon, the earth is pulled less, and the water on the far side moves least, therefore making the ocean profile oblate, and raising tides on both the near and opposite sides of the earth." That's a completely false view of what happens. See my document Tidal Misconceptions.


The technical term action is a historic relic of the 17th century, before energy and momentum were understood. In modern terminology, action has the dimensions of energy×time. Planck's constant has those dimensions, and is therefore sometimes called Planck's quantum of action. Pairs of measurable quantities whose product has dimensions of energy×time are called conjugate quantities in quantum mechanics, and have a special relation to each other, expressed in Heisenberg's uncertainty principle.

Unfortunately the word action persists in elementary textbooks in meaningless statements of Newton's third law: "Action equals reaction." This memorized slogan is useless to the modern student, who hasn't the foggiest idea what action is. Ask the student who has memorized this slogan to define "action" and "reaction". If you can't define something, you can't use it intelligently. The most useful statement of Newton's third law is simply this: "If body A exerts a force on body B, then body B exerts and equal size but oppositely directed force on A."

The use of the terms "action" and "reaction" also give the false impression that "action" has some sort of primary status and "reaction" is a secondary "effect" resulting from the action force. This misconception is a consequence of "cause and effect" thinking (see elsewhere in this document). The two forces of an action and reaction pair have completely equal status, and neither should be thought of as the cause, or the effect, of the other. They are both consequences of the physical phenomena that give rise to forces, such as the elastic properties of materials, gravitational attraction, electric or magnetic interactions, etc.

Weighing a mole.


Avogadro's constant has the unit mole-1. It is not merely a number, and should not be called Avogadro's number. It is ok to say that the number of particles in a gram-mole is 6.02252 x 1023. Some older books call this value Avogadro's number, and when that is done, no units are attached to it. This can be confusing and misleading to students who are conscientiously trying to learn how to balance units in equations.

One must specify whether the value of Avogadro's constant is expressed for a gram-mole or a kilogram-mole. A few books prefer a kilogram-mole. The unit name for a gram-mole is simply mol. The unit name for a kilogram-mole is kmol. When the kilogram-mole is used, Avogadro's constant should be written: 6.02252 x 1026 kmol-1. The fact that Avogadro's constant has units further convinces us that it is not "merely a number."

Though it seems inconsistent, the SI base unit is the gram-mole. As Mario Iona reminds me, SI is not an MKS system. Some textbooks still prefer to use the kilogram-mole, or worse, use it and the gram-mole. This affects their quoted values for the universal gas constant and the Faraday Constant.

Is Avogadro's constant just a number? What about those textbooks that say "You could have a mole of stars, grains of sand, or people"? In science we do use entities that are just numbers, such as p and e (the base of natural logarithms). Though these are used in science, their definitions are independent of science. No experiment of science can ever determine their value, except approximately. Avogadro’s constant, however, must be determined experimentally, for example by counting the number of atoms in a crystal. The value of Avogadro's number found in handbooks is an experimentally determined number. You won't discover its value experimentally by counting stars, grains of sand, or people. You find it only by counting atoms or molecules in something of known relative molecular mass. And you won't find it playing any role in any equation or theory about stars, sand, or people.


Because is a word best avoided in physics. Whenever it appears one can be almost certain that it's a filler word in a sentence that says nothing worth saying, or a word used when one can't think of a good or specific reason. While the use of the word because as a link in a chain of logical steps is benign, one should still replace it with words more specifically indicative of the type of link that is meant.

Illustrative fable: The seeker after truth sought wisdom from a Guru who lived as a hermit on top of a Himalayan mountain. After a long and arduous climb to the mountaintop the seeker was granted an audience. Sitting at the feet of the great Guru, the seeker humbly said: "Please, answer for me the eternal question: Why?" The Guru raised his eyes to the sky, meditated for a bit, then looked the seeker straight in the eye and answered, with an air of sagacious profundity, "Because!"


Many have the notion that some "law of cause and effect" is a very important principle in science. Philosophers of science have thoroughly demolished that naive notion. But teachers still ask ambiguous questions such as "What is the force that causes the forward acceleration of an automobile." One valid answer would be "The force the foot exerts on the accelerator pedal."

Students still think that "Every effect has a cause", and "The cause precedes the effect" are profound statements. Now it is true that some events are physically connected such that one always precedes the other. We like to call an earlier set of events the cause of the later events. But in fact, statements about cause and effect are only made "after the fact", after the specific details of the connectedness of events are found and understood. The "cause" and "effect" labeling is of no value at all for learning anything about nature, and of no use in constructing logical arguments about nature. We lose nothing by purging these words from scientific discussions. Avoiding these words forces us to express ourselves in clearer and more precise language, and that's a good thing.

Such language does little harm when we are speaking of events within the observable universe. But when one tries to invoke this as a philosophical/physical principle, nonsense results. One example of the muddled thinking resulting from cause and effect language is this silly argument still bandied about:

Everything that happens in the universe has an identifiable cause. We know no exceptions. Therefore the universe itself must have had a cause, and that cause was God.
The remarkable thing is that folks who say this, or accept it as an "argument" seem to think it is valid and profound. It is neither. Even if, for the sake of argument, we accept the premise, it's an unwarranted extrapolation from observations of things within the universe to something "outside" of the universe, independent of the universe and presumably not bound by the same laws that operate within the universe. Yet I've heard folks with Ph.D.s (who ought to know better) present this argument as if it carried great weight. The final phrase is a logical leap, for even if we could establish that the universe had a cause, we are only giving that cause a name if we assert it was "God" (or any other invented name). The cause might be something else for all we know, and we have no way to know.

There's another deficiency in this fraudulent pseudo-logic. It is an extrapolation from our imperfect and possibly fallible science to a conclusion that the person making the argument treats as an absolute and infallible truth. This objection also demolishes all of the arguments I've seen made by the so-called "scientific creationists" and "intelligent design" advocates.

It gets worse. Within the universe, causes always precede effects in time. When this is applied to the theo-illogical argument, and if the universe had a "cause", then everything in the universe and everything that goes on in the universe are "effects". Space, time, matter, superstrings, black holes and everything are "effects" of this hypothesized "cause". Time itself is an effect of that cause. Since causal connectivity requires two things to occur at different times, how can a cause (or an effect) have any meaning outside of time? This needless confusion has pervaded discussions of "origins" and generated incredible volumes of wasted words on meaningless questions.


Reification means, "to make real." The word is used in philosophy to describe the process by which we treat certain of our mental constructs as if they were as real as rocks, water, and trees. We speak of "love" and "patriotism", "good", "evil" and "soul" as if they were something one could determine by medical examination. What is the definition of "real"? That's slippery, too. Whole books have been written on that question.

Without getting into deep philosophy, we will simply point out some of the dangers of reification in physics teaching. Some things are real in a sense nearly everyone (except a perversely argumentative person) would agree really are "real". These are concepts directly accessible to our sensory apparatus, and part of our common experience. Rocks, water, and trees qualify. They are also accessible to direct and precise measurement, using measuring instruments or apparatus. Perhaps somewhat less "real" are force and temperature. Our sensory perception of these is crude at best, and indirect—highly subject to conditioning and environmental variables. Measuring instruments and measuring methods give consistent results, so we treat these as real in physics, but we do not trust our unaided senses for precise information about them.

One may also make a distinction between material concepts and properties of materials. Mass, distance and time are generally considered so basic as to qualify as "things" of nature (but I could easily dispute that). However, color, temperature, and hardness are properties of materials, not "things" in themselves.

Energy and momentum aren't properties specific to a particular material, but are useful concepts we invented that help us describe how things interact. Energy alone has no material existence. You can't put pure energy in a bottle; you can only put material substances that have energy into that bottle.

Then there are concepts such as field lines and light rays. They also have no material existence, but help us describe things we observe. The next few sections discuss dangers of treating them as real.

Cutting field lines.


Some books speak of cutting field lines. This conjures up images of cutting strings with scissors. In fact, in the early 20th century textbooks often spoke of the "number" of field lines emanating from a unit charge, as if they could be counted. [In the cgs system it was 4p field lines from a unit charge, in case you care.] This is a clear case of misleading reification.


A textbook says "Light rays bend at interfaces between media of different refractive index." Here the bending is a discontinuity of direction of a static drawing of light rays. We must remember that these lines are only a geometric construct to help us visualize the direction of propagation of light energy, not something as real as a moving automobile. The Huygens wavelets are another case of reification, since they are only geometric constructs to carry out a calculation process.


Energy is not a material substance. When bodies interact, the energy of one may increase at the expense of the other, and this is sometimes called a transfer of energy. This does not mean that we could intercept this energy in transit and bottle some of it. After the transfer one of the bodies may have higher energy than before, and we speak of it as having "stored energy". But that doesn't mean that the energy is "contained in it" in the same sense as water in a bucket.

Misuse example: "The earth's aurorae 'the northern and southern lights' illustrate how energy from the sun travels to our planet." [Science News, 149, June 1, 1996]. This sentence blurs understanding of the process by which energetic charged particles from the sun interact with the earth's magnetic field and our atmosphere to result in the auroras.

Whenever one hears people speaking of "energy fields", "psychic energy", and other expressions treating energy as a "thing" or "substance", you know they aren't talking physics; they are talking moonshine.

The statement "Energy is a property associated with a body" needs clarification. As with many things in physics, the size of the energy depends on the chosen coordinate system. A body moving with speed V in one coordinate system has kinetic energy ½mV2. The same body has zero kinetic energy in a coordinate system moving along with it at speed V. Since no inertial coordinate system can be considered "special" or "absolute", we shouldn't say, "The kinetic energy of the body is ..." but should say, "The kinetic energy of the body moving in this reference frame is ..."

We shouldn't even call energy or momentum "properties of the body". Such physical concepts are useful ways for doing physics, but the bottom line is that they are just abstractions from the geometry, mass, and motion of the body, or the particles that make up a body.

Torque presents the same difficulty. A torque isn't a unique property of a force, but also depends on the location of an arbitrarily chosen center of torques.


Heat, like work, is a measure of the amount of energy transferred from one body to another because of the temperature difference between those bodies. Heat is not energy possessed by a body. We should not speak of the "heat in a body." The energy a body possesses due to its temperature is a different thing, called internal thermal energy. Thermal energy is internal to the body, and independent of coordinate system. It is the kinetic energy of motion of the microscopic particles that make up the body.

The misuse of the word "heat" probably dates back to the 18th century when it was still thought that bodies undergoing thermal processes exchanged a substance, called caloric or phlogiston, a substance later called heat. We now know that heat is not a substance. Reference: Zemansky, Mark W. The Use and Misuse of the Word "Heat" in Physics Teaching" The Physics Teacher, 8, 6 (Sept 1970) p. 295-300.

RADIOACTIVE (Are you scintillating?)

Radioactivity is a process, not a thing, and not a substance. It is just as incorrect to say, "U-235 emits radioactivity" as it is to say "current flows." A malfunctioning nuclear reactor does not release radioactivity, though it may release radioactive materials into the surrounding environment. A patient being treated by radiation therapy does not absorb radioactivity, but does absorb some of the radiation (alpha, beta, gamma) given off by the radioactive materials being used.

This misuse of the word radioactivity causes many people to incorrectly think of radioactivity as something one can get by being near radioactive materials. There is only one process that behaves anything like that, and it is called artificially induced radioactivity, a process mainly carried out in research laboratories. When some materials are bombarded with protons, neutrons, or other nuclear particles of appropriate energy, their nuclei may be transmuted, creating unstable isotopes that are radioactive.


Cutting off and removing a piece of an object reduces its mass (makes its remaining mass smaller). Adding a resistor in a series string of resistors reduces the current. What's the danger here? Many students think that "reducing the current" means that the current "coming out" of a resistor is smaller than the current "going in". But Kirchoff's current laws assure us that the currents in and out of a component in a DC circuit are equal at any instant. The problem here is partly one of "reifying" the abstract concept of current. The "reduction" is a change observed between two different circuits, one with the extra resistor, one without it. It is not a reduction observed between two points of the same circuit. We have similar problems when speaking of "voltage drop" across a resistor. Calling it a "potential difference" across the resistor is less likely to cause confusion.


When we use a pan balance to determine a mass, we call the process "weighing", even though the balance gives answers in mass units. Some balances give answers in weight units, for the two are in proportion in a given laboratory. The term "weighing" is justified because the process depends on the gravitational attraction of the earth on the bodies. We are comparing their weights. Students need to be aware of this. I don't advocate avoiding the term "weighing". Some have proposed the name "massing", which I consider rather ugly.

A live wire
getting juiced.


The capacitance of a capacitor is measured by this procedure: Put charges of equal size and opposite sign on the capacitor plates and then measure the potential between the plates. Then C = |Q/V|, where Q is the charge on one of the plates.

Capacitors for use in circuits consist of two conductors (plates). We speak of a capacitor as "charged" when it has charge Q on one plate, and -Q on the other. Of course the net charge of the entire object is zero; that is, the charged capacitor hasn't had net charge added to it, but has undergone an internal separation of charge. Unfortunately this process is usually called charging the capacitor, which is misleading because it suggests "adding charge to the capacitor". In fact, this process consists only of moving charge from one capacitor plate to the other.

We probably should avoid the phrase "charged capacitor" or "charging a capacitor". Some have suggested the alternative expression "energizing a capacitor" because the process results in the capacitor gaining electrical potential energy by rearranging the charges on it.

The capacitance of a single object, say an isolated sphere, is determined by considering it as one plate of a capacitor and the other plate to be an infinite sphere surrounding it. The object is given charge, by moving charge from the infinite sphere, which acts as an infinite charge reservoir ("ground"). The potential of the object is the potential between the object and the infinite sphere. In practice, the "other plate" is the object's surrounding laboratory environment.

Capacitance depends only on the geometry of the capacitor's physical structure and the dielectric constant of the material medium in which the capacitor's electric field exists. The size of the capacitor's capacitance is the same whatever its charge and potential (assuming the dielectric constant doesn't change). This is true even if the charge on both plates is reduced to zero, and therefore the capacitor's potential is zero. If a capacitor with charge on its plates has a capacitance of, say, 2 microfarad, then its capacitance is also 2 microfarad when the plates have no charge. This should remind us that C = |Q/V|; is not by itself the definition of capacitance, but merely a formula that allows us to relate the capacitance to the charge and potential when the capacitor plates have charges of equal size and opposite sign.


The capacity of a container is how much of something it will hold. This is the colloquial meaning of the word. But as frequently happens, colloquial words are taken over as technical words, with more specific, or altered meaning.

The word capacity is used in names of physical quantities that express the relative amount of one quantity with respect to another quantity upon which it depends. For example, heat capacity is dU/dT, where U is the internal energy and T is the temperature. Electrical capacity (usually called capacitance) is C = |dQ/dV| where Q is the magnitude of charge on each plate, and V is the potential difference between the plates. These are correct technical uses of the word. None of them have anything to do with the maximum amount something will hold.

We usually avoid confusion by referring to C as "capacitance". A common misunderstanding about electrical capacitance is to assume that capacitance represents the maximum amount of charge a capacitor can store. That is misleading because capacitors don't store charge (their total charge being zero) but their plates have charges of equal magnitude and opposite sign. It is wrong because the maximum charge one may put on a capacitor plate is determined by the potential at which dielectric breakdown occurs.

But the same misconceptions can occur with electrical capacitance as with the other uses of the word "capacity" in physics, and we don't have other names for them that might help avoid this. Heat capacity isn't the maximum amount of heat something can have. That would also incorrectly suggest that heat is a "substance", which it isn't.


Do we listen to what we say? Do we think about what we say? Do we really believe what we say? Do students believe it? Maybe they shouldn't. Here's an example to test that.

How many times have we read (or even said) that "Newton showed that when calculating the gravitational attraction between two bodies with the inverse square law, their separation distance must be taken to be the separation of their centers of mass, not the distance between their nearest points." What's wrong with that?

Consider the empty coffee cup of the illustration. If you really believed the statement of the previous paragraph you would analyze it this way. The cup's center of mass is somewhere within the empty part, at point C. Now drop a small object, B, say a pebble or coin, so it falls toward that point. As it nears the point the separation of the centers of mass of cup and pebble becomes very small and the force of attraction between them becomes very large, until it dominates the force of the earth's gravity. The pebble would oscillate about point C, or worse, stop dead at point C (because the 1/r2 force becomes infinite when r = 0). Then the pebble would just hang there suspended, and it would require an infinite force to remove it. Absurd? Of course; because the statement made in the previous paragraph was absurd.

A key phrase was left out of our version of the statement about gravitational force and center of mass, as it often is in many textbooks. The principle Newton derived was for spherical bodies with strictly symmetric mass distributions about their centers of mass, and it only applied to separated masses, not contiguous ones.

Sometimes the words we leave out are as important as the ones we put in. The next item illustrates the same error.


The statement "Friction always opposes motion" fails to specify what motion. In more complete form it is: "The force due to friction acts in a direction to oppose slipping at surfaces in contact, and it acts along the tangent plane of surface contact." Or: "Friction opposes the relative motion of two surfaces in contact." Too often students think that the force due to friction acting on a body opposes any motion of that body. Everyday examples show this isn't right. The force due to friction of the road acting on automobile tires is forward, in the direction of the auto's forward motion when the auto is moving at constant speed, or accelerating forward. It prevents tire slippage on the road, which you discover when driving on ice. It is the force that sustains forward motion. Another example: The force due to friction of the floor on your feet is in the direction you are walking.


One danger of treating force as if it were an object is the common textbook blunder of speaking of "the work done by friction". Work done on an object is the product of the distance it moves and the force exerted on it by some other object. If two bodies are in contact, the reaction forces between them have components tangential to the contact surface. It isn't the friction that does the work on each body, but the force exerted on one body by the other body, which may happen to be due to the friction processes at their interface.

Consider a block sliding down a plane. Many textbooks say that the sliding block loses energy due to "the work done on it by friction". But "friction" here is a moving target—the continually changing interface between the body and the plane. Arnold Arons has a long section in his book "A Guide to Introductory Science Teaching" detailing the dangers of this kind of textbook treatment. One obvious problem is how to "isolate the system" in such cases. The portion of the plane where the bodies are in contact can't be "pinned down" and treated as a single physical "thing" during the motion. The usual treatment of textbooks has a very serious deficiency: it is fairly easy to apply and happens to give the right answers to the carefully selected problems the textbook poses. That is, so long as the student doesn't think about it too deeply.


Physicist deflecting forces.
Cartoon by John Holden.

In the language of engineering and martial arts one hears the term "deflected force". This term has many possible misinterpretations, and is best avoided unless one must talk to folks who use it in their specialized field. The clinker is "deflect". Deflect has a clear meaning when applied to a material object. But a force isn't a material object. Does "deflect a force" mean that the force itself is deflected? If so, is the force changed in direction? Does a force bounce off something as an arrow bounces off a suit of armor?

Properly used, in engineering, force deflection refers to a situation where mass loading on an object or system of objects gives rise to reaction forces that maintain the equilibrium of that object. The distributed downward compression forces all along the curve of a classic archway are opposed by more localized forces at the supporting endpoints of the arch. Note that when a force is applied to an object, and another force adjusts its size to maintain the object's equilibrium, the other force is called the "equilibrant" (that which maintains equilibrium). A force and its equilibrant are not reaction forces of each other.

In the martial arts, the term seems to refer to deflection of a blow such as a kick. It's not the force that's deflected, but the motion of the object delivering the blow. Shifting the target, or applying a force to the part of the body delivering the blow, can alter the direction of the impact so that the blow loses a smaller fraction of its momentum and energy to you. Imagine someone punching you, but before the punch lands, you strike your opponent's arm from the side, deflecting his arm. Or you shift your body so instead of punching you directly in the nose, his blow just grazes your shoulder, imparting only a small fraction of its momentum and energy to you. At least that's how it seems these folks use the term. They use "deflected force" to mean, "deflect whatever delivers the blow so that you receive less of its impact (momentum and energy)."

"Deflected force" can also describe a quasi-static situation in which one takes advantage of the limitations of human musculature. When someone is pushing or lifting with an arm, the action can be made less effective if someone else pushes that arm sideways.


Arons, Arnold B. A Guide to Introductory Physics Teaching. Wiley, 1990.

Arons, Arnold B. Teaching Introductory Physics. Wiley, 1997.

Iona, Mario. The Physics Teacher. Regular column titled "Would You believe?" that for 24 years documented and discussed errors and misleading statements in physics textbooks.

Swartz, Clifford and Thomas Miner. Teaching Introductory Physics, A Sourcebook. American Institute of Physics, 1997.

Symbols, Units and Nomenclature in Physics. From Document U.I.P 11 (S.U.N. 65-3) International Union of Pure and Applied Physics. Contained in the Handbook of Chemistry and Physics, The Chemical Rubber Company.

Warren, J. W. The Teaching of Physics. Butterworth's, 1965, 1969.

Text © 1979, 2002, 2008 by Donald E. Simanek.
Cartoon drawings © 1979 by John C. Holden.