Physics and
Astronomy Glossary

Technical terms of science have very specific meanings. Standard dictionaries are not always the best source of useful and correct definitions of them.This glossary is not intended to be complete. It focuses on those terms which give students particular difficulties. Some words have subtle and intricate meanings which cannot be encapsulated in a short definition. That's why textbooks exist. A good glossary for elementary physics may be found in Appendix G-1 of Kirkpatrick & Wheeler, Physics, A World View, Saunders, 1992.

This document is continually under development and may never be finished.

Glossary

Accurate.Conforming closely to some standard. Having very small error of any kind. See: Uncertainty. Compare: precise.

Absolute uncertainty.The uncertainty in a measured quantity is due to inherent variations in the measurement process itself. The uncertainty in a result is due to the combined and accumulated effects of these measurement uncertainties which were used in the calculation of that result. When these uncertainties are expressed in the same units as the quantity itself they are calledabsolute uncertainties. Uncertainty values are usually attached to the quoted value of an experimental measurement or result, one common format being: (quantity) ± (absolute uncertainty in that quantity).Compare: relative uncertainty.

Action.This technical term 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 calledPlanck's quantum of action. Pairs of measurable quantities whose product has dimensions of energy×time are calledconjugate quantitiesin quantum mechanics, and have a special relation to each other, expressed in Heisenberg's uncertainty principle. Unfortunately the wordactionpersists in textbooks in meaningless statements of Newton's third law: "Action equals reaction." This statement is useless to the modern student, who hasn't the foggiest idea what action is. See: Newton's 3rd law for a useful definition. Also see Heisenberg's uncertainty principle.

Avogadro's constant.Avogadro's constant has the unitmoleIt is^{-1}.notmerely a number, and shouldnotbe calledAvogadro's number.Itisok to say that the number of particlesina gram-mole is 6.02 x 10^{23}. Some older books call this valueAvogadro'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

mustspecify 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 simplymol. The unit name for a kilogram-mole iskmol. When the kilogram-mole is used, Avogadro's constant should be written: 6.02252 x 10^{26}kmol^{-1}. The fact that Avogadro's constant has units further convinces us that it isnot"merely a number."

Though it seems inconsistent, the SI base unit is the gram-mole. As Mario Iona reminds me, SI isnotan MKS system. Some textbooks still prefer to use use the kilogram-mole, or worse, use itandthe 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 which say "You could have a mole of stars, grains of sand, or people." In science wedouse entities which arejustnumbers, such as , e, 3, 100, etc. Though these areusedin science, their definitions areindependent of science. No experiment of science can ever determine their value, except approximately. Avogadro’s constant, however,mustbe determined experimentally, for example bycountingthe number of atoms in a crystal. The value of Avogadro's number found in handbooks is anexperimentallydetermined 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.The reciprocal of Avogadro's constant is numerically equal to the unified atomic mass unit, u, that is, 1/12 the mass of the carbon 12 atom.

1 u = 1.66043 x 10

^{-27}kg = 1/6.02252 x 10^{23}mole^{-1}.

Because.Here's a word best avoided in physics. Whenever it appears one can be almost certain that it's afillerword in a sentence which says nothing worth saying, or a word used when one can't think of a good or specific reason. While the use of the wordbecauseas 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 which is meant. See: why.

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 mountain-top 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!"Capacitance.Thecapacitanceof a capacitor is measured by this procedure: Put equal and opposite charges on its plates and then measure the potential between the plates. Then C = |Q/V|, where Q is the charge ononeof 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

chargingthe capacitor, which is misleading because it suggests adding charge to the capacitor. In fact, this process usually consists of moving charge from one plate to the other. The capacity of a single object, say an isolated sphere, is determined by considering theother plateto 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 potentialof the objectis the potential between the object and the infinite sphere.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 the 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

notby itself thedefinitionof capacitance, but merely a formula which allows us to relate the capacitance to the charge and potentialwhenthe capacitor plates have equal and opposite charge on them.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 equal and opposite charge. It is wrong because the maximum charge one may put on a capacitor plate is determined by the potential at which dielectric breakdown occurs. Compare: capacity.

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

Capacity.This word is used in names of quantities which express therelativeamount of some quantity with respect to a 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, orcapacitanceis another example: C = |dQ/dV|, where Q is the magnitude of charge on each capacitor plate and V is the potential diference between the plates.

Centrifugal force.When a non-inertial rotating coordinate system is used to analyze motion, Newton's lawF= maisnotcorrect unless one adds to the real forces afictitious forcecalled thecentrifugal force. The centrifugal force required in the non-inertial system is equal and opposite to thecentripetal forcecalculated in the inertial system. Since the centrifugal and centripetal forces are concepts used intwo differentformulations of the problem, they can not in any sense be considered a pair of reaction forces. Also, they act on the same body, not different bodies. See: centripetal force, action, and inertial systems.

Centripetal force.Thecentripetal forceis the radial component of the net force acting on a body when the problem is analyzed in an inertial system. The force is inward toward the instantaneous center of curvature of the path of the body. The size of the force is mv^{2}/r, where r is the instantaneous radius of curvature. See: centrifugal force.

cgs.The system of units based upon the fundamental metric units: centimeter, gram and second.

Classical physics.The physics developed before about 1900, before we knew about relativity and quantum mechanics. See: modern physics.

Closed system. A physical system on which no outside influences act; closed so that nothing gets in or out of the system and nothing from outside can influence the system's observable behavior or properties.Obviously we could never make measurements on a closed system unless we were in it

^{†}, for no information about it could get out of it! In practice we loosen up the condition a bit, and only insist that there be no interactions with the outside world which would affect those properties of the system which are being studied.† Besides, when the experimenter is a part of the system, all sorts of other problems arise. This is a dilemma physicists must deal with: the fact that if we take measurements, we are a part of the system, and must be very certain that we carry out experiments so that fact doesn't distort or prejudice the results.Conserved.A quantity is said to beconservedif under specified conditions it's value does not change with time.

Example: In a closed system, the charge, mass, total energy, linear momentum and angular momentum of the system are conserved. (Relativity theory allows that mass can be converted to energy and vice-versa, so we modify this to say that the mass-energy is conserved.)Current.The time rate at which charge passes through a circuit element or through a fixed place in a conducting wire, I = dq/dt.

Misuse alert.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 either redundant, misleading, or wrong. This expression should be purged from our vocabulary. Compare a similar mistake: "The velocity moves West."

Data.The worddatais the plural ofdatum. Examples of correct usage:

"The data are reasonable, considering the…"

"The data were taken over a period of three days."

"How well do the data confirm the theory?"

Derive.To derive a result or conclusion is to show, using logic and mathematics, how a conclusion follows logically from certain given facts and principles.

Dimensions.The fundamental measurables of a unit system in physics—those which are defined through operational definitions. All other measurable quantities in physics are defined through mathematical relations to the fundamental quantities. Therefore any physical measurable may be expressed as a mathematical combination of the dimensions. See: operational definitions.

Example: In the MKSA (meter-kilogram-second-ampere) system of units, length, mass, time and current are the fundamental measurables, symbolically represented by L, M, T, and I. Therefore we say that velocity has the dimensions LT^{-1}. Energy has the dimensions ML^{2}T^{-2}.

Discrepancy.(1) Any deviation or departure from the expected. (2) A difference between two measurements or results. (3) A difference between an experimental determination of a quantity and its standard or accepted value, usually called theexperimental discrepancy.

Empirical law.A law strictly based on experiment, which may lack theoretical foundation.

Electricity.This word names a branch or subdivision of physics, just as other subdivisions are named ‘mechanics’, ‘thermodynamics’, ‘optics’, etc.

Misuse alert:Sometimes the wordelectricityis 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 beavoided!In all such cases there's available a more specific or precise word, such as "The capacitor storeselectrical energy," "The resistor is heated by the electriccurrent," and "The utility company charges me for theelectric energyI use." (I am not being charged based on thepower, so these companies shouldn't call themselvesPowercompanies. Some already have changed their names to something like "... Energy")Energy.Energy is a property of a body, not a material substance. When bodies interact, the energy of one may increase at the expense of the other, and this is sometimes called atransfer of energy. This doesnotmean 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 auroras—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 aurorae.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.

In certain quack theories of oriental medicine, such as

qi gong(pronouncedchee gung) something calledqiis believed to circulate through the body on specific, mappable pathways called meridians. This idea pervades the contrived explanations/rationalizations of acupuncture, and theqiis generally translated into English asenergy. No one has ever found this so-called "energy", nor confirmed the uniqueness of its meridian pathways, nor verified, through proper double-blind tests, that any therapy or treatment based on the theory actually works. The proponents ofqican't say whether it is a fluid, gas, charge, current, or something else, and their theory requires that it doesn't obey any of the physics of known carriers of energy. But, as soon as we hear someone talking about it as if it were athingwe know they are not talking science, but quackery.The statement "Energy is a property of a body" needs clarification. As with many things in physics, the size of the energy depends on the coordinate system. A body moving with speed V in one coordinate system has kinetic energy½mV. 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 ..."^{2}

Equal.[Not all "equals" are equal.] The wordequaland the symbol "=" have manydifferentuses. The dictionary warns that equal things are "alike or in agreement in a specified sense with respect to specified properties." This we must be careful about the specified sense and specified properties.The meaning of the the mathematical symbol, "=" depends upon what stands on either side of it. When it stands between vectors it symbolizes that the vectors are equal in both size

anddirection.In algebra the equal sign stands between two algebraic expressions and indicates that two expressions are related by a reflexive, symmetric and transitive relation. The mathematical expressions on either side of the "=" sign are mathematically identical and interchangeable in equations.

When the equal sign stands between two mathematical expressions with physical meaning, it means something quite different. In physics we may correctly write 12 inches = 1 foot, but to write 12 = 1 is simply wrong. In the first case, the equation tells us about physically equivalent measurements. It has physical meaning, and the units are an indispensable part of the quantity.

When we write

a =dv/dt, we aredefiningthe acceleration in terms of the time rate of change of velocity. One does not verify a definition by experiment. Experiment can, however, show that in certain cases (such as a freely falling body) the acceleration of the body is constant.The three-lined equal sign,When we write=, is often used to mean "defined equal to". Unfortunately this symbol is not part of the HTML character set, so in this document we use an underlined equal sign instead.F =ma, we are expressing a relation between measurable quantities, one which holds under specified conditions, qualifications and limitations. There's more to it than the equation. One must, for example, specify that all measurements are made in an inertial frame, for if they aren't, this relation isn't correct as it stands, and must be modified. Many physical laws, including this one, also include definitions. This equation may be considered a definition of force, if m and a are previously defined. But if F was previously defined, this may be taken as a definition of mass. But the fact that this relation can be experimentally tested, and possibly be shown to be false (under certain conditions) demonstrates that it ismorethan a mere definition.Additional discussion of these points may be found in Arnold Arons' book

A Guide to Introductory Physics Teaching, section 3.23, listed in the references at the end of this document.Usage note:Whenreadingequations aloud we often say, "F equals m a". This, of course, says that the two things are mathematically equal in equations, and that one may replace the other. It isnotsaying that Fisphysically the same thing as ma. Perhaps equations were not meant to be read aloud, for the spoken word does not have the subtleties of meaning necessary for the task. At least we should realize that spoken equations are at best a shorthand approximation to the meaning; a verbal description of the symbols. If we were to try to speak the physical meaning, it would be something like: "Newton's law tells us that the net vector force acting on a body of mass m is mathematically equal to the product of its mass and its vector acceleration." In a textbook, words like that would appear in the text near the equation, at least on the first appearance of the equation.Error.In colloquial usage, "a mistake". In technical usageerroris a synonym for theexperimental uncertaintyin a measurement or result. See: uncertainty.

Error analysis.The mathematical analysis done to show quantitatively how uncertainties in data produce uncertainty in calculated results, and to find the sizes of the uncertainty in the results. [In mathematics the wordanalysisis synonymous withcalculus, or "a method for mathematical calculation." Calculus courses used to be namedAnalysis.]See: uncertainty

Extensive property.A measurable property of a thermodynamic system is extensive if, when two identical systems are combined into one, the value of that property of the combined system is double its original value in each system. Examples: mass, volume, number of moles. See: intensive variable and specific.

Experimental error.The uncertainty in the value of a quantity. This may be found from (1) statistical analysis of the scatter of data, or (2) mathematical analysis showing how data uncertainties affect the uncertainty of calculated results.

Misuse alert:In elementary lab manuals one often sees: experimental error = |your value - book value| /book value. Thisshouldbe called theexperimental discrepancy.See: discrepancy.Factor.One of several things multiplied together.

Misuse alert:Be careful that the reader does not confuse this with the colloquial usage: "One factor in the success of this experiment was…"

Fictitious force.See: inertial frames.Focal point.The focal point of a lens is defined by considering a parallel bundle or beam of light incident upon the lens, parallel to the optic (symmetry) axis of the lens. The focal point is that point to which the rays converge or from which they diverge. The first case is that of aconverging(positive) lens. The second case is that of adiverging(negative) lens. It’s easy to tell which kind of lens you have, for converging lenses are thicker at their center than at the edges, and diverging lenses are thinner at the center than at the edges.

FPS.The system of units based on the fundamental units of the ‘English system’: foot, pound and second.

Heat.Heat, like work, is a measure of the amount of energytransferredfrom one body to another because of the temperature difference between those bodies. Heat isnotenergypossessedby a body. We shouldnotspeak of the "heatina body." The energy a body possesses due to its temperature is a different thing, calledinternal thermal energy. The misuse of this word probably dates back to the 18th century when it was still thought that bodies undergoing thermal processes exchanged a substance, calledcaloricorphlogiston, a substance later calledheat. 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. See: work.

Heisenberg's Uncertainty Principle.Pairs of measurable quantities whose product has dimensions of energy×time are calledconjugate quantitiesin quantum mechanics, and have a special relation to each other, expressed in Heisenberg's uncertainty principle. It says that the product of the uncertainties of the two quantities is no smaller than h/2. Thus if you improve the measurement precision of one quantity the precision of the other gets worse.

Misuse alert:Folks who don't pay attention to details of science, are heard to say "Heisenberg showed that you can't be certain about anything." We also hear some folk justifying belief in esp or psychic phenomena by appeal to the Heisenberg principle. This is wrong on several counts. (1) The precision ofanymeasurement is never perfectly certain, and we knew that before Heisenberg. (2) The Heisenberg uncertainty principle tells us we can measure anything with arbitrarily small precision, but in the process someothermeasurement gets worse. (3) The uncertainties involved here affect only microscopic (atomic and molecular level phenomena) and have no applicability to the macroscopic phenomena of everyday life.

Hypothesis.An untested statement about nature; a scientific conjecture, or educated guess. Formally, a hypothesis is made prior to doing experiments designed to test it. Compare: law and theory.

Ideal-lens equation.1/p + 1/q = 1/f, where p is the distance from object to lens, q is the distance from lens to image, and f is the focal length of the lens. This equation has important limitations, being only valid forthinlenses, and forparaxial rays.Thin lenses have thickness small compared to p, q, and f. Paraxial rays are those which make angles small enough with the optic axis that the approximation(angle in radian measure) = sin(angle)may be used. See: optical sign conventions, and image.

InertiaA descriptive term for that property of a body which resists change in its motion. Two kinds of changes of motion are recognized: changes in translational motion, and changes in rotational motion.In modern usage, the measure of translational inertia is mass. Newton's first law of motion is sometimes called the "Law of Inertia", a label which adds nothing to the meaning of the first law. Newton's first and second laws together are required for a full description of the consequences of a body's inertia.

The measure of a body's resistance to rotation is its

Moment of Inertia.

Inertial frame.A non-accelerating coordinate system. One in whichholds, whereF =mais the sum of all real forces acting on a body of mass m whose acceleration isF. In classical mechanics, theareal forceson a body are those which are due to the influence of another body. [Or, forces on a part of a body due to other parts of that body.] Contact forces, gravitational, electric, and magnetic forces are real.Fictitious forcesare those which arise solely from formulating a problem in a non-inertial system, in whichma = F + (fictitious force terms)

Intensive variable.A measurable property of a thermodynamic system is intensive if when two identical systems are combined into one, the variable of the combined system is the same as the original value in each system. Examples: temperature, pressure. See: extensive variable, and specific.

Image.(Optics) A surprising number of physics glossaries omit a definition of this! No wonder. It's difficult to put in a few words, and still be comprehensive in scope. Try this.Image:A point mapping of luminous points of an object located in one region of space to points in another region of space, formed by refraction or reflection of light in a manner which causes light from each point of the object to converge to or diverge from a point somewhere else (on the image). The images which are useful generally have the character that adjacent points of the object map to adjacent points of the image without discontinuity, and is a recognizable (though perhaps somewhat distorted) mapping of the object. See: real image and virtual image.

Law.A statement, usually mathematical, which describes some physical phenomena. Compare: hypothesis and theory.

Lens.A transparent object with two refracting surfaces. Usually the surfaces are flat or spherical (spherical lenses). Sometimes, to improve image quality. Lenses are deliberately made with surfaces which depart slightly from spherical (aspheric lenses).

Kinetic energy.The energy a body has by virtue of its motion. The kinetic energy is the work done by an external force to bring the body from rest to a particular state of motion. See: work.

Common misconception:Many students think that kinetic energy isdefinedby½mv. It is not. That happens to be approximately the kinetic energy of objects moving slowly, at small fractions of the speed of light. If the body is moving at relativistic speeds, its kinetic energy is^{2}mc, which can be expressed as^{2}½mv.^{2}+ an infinite series of terms, where^{2}= 1/(1-(v/c)^{2})cis the speed of light in a vacuum.

Macro-.A prefix meaning ‘large’. See: micro-

Macroscopic.A physical entity or process of large scale, the scale of ordinary human experience. Specifically, any phenomena in which the individual molecules and atoms are neither measured, nor explicitly considered in the description of the phenomena. See: microscopic.

Magnification.Two kinds of magnification are useful to describe optical systems and they must not be confused, since they aren't synonymous. Any optical system which produces a real image from a real object is described by its

linear magnification. Any system which one looks through to view a virtual image is described by itsangular magnification. These have different definitions, and are based on fundamentally different concepts.

Linear Magnificationis the ratio of the size of the object to the size of the image.

Angular Magnificationis the ratio of the angular size of the object as seen through the instrument to the angular size of the object as seenwith the 'naked eye'. The 'naked eye' view iswithoutuse of the optical instrument, but under optimal viewing conditions.Certain 'gotchas' lurk here. What are 'optimal' conditions? Usually this means the conditions in which the object's details can be seen most clearly. For a small object held in the hand, this would be when the object is brought as close as possible and still seen clearly, that it, to the near point of the eye, about 25 cm for normal eyesight. For a distant mountain, one can't bring it close, so when determining the magnification of a telescope, we assume the object is very distant, or at infinity.

And what is the 'optimal' position of the image? For the simple magnifier, in which the magnification depends strongly on the image position, the image is best seen at the near point of the eye, 25 cm. For the telescope, the image size doesn't change much as you fiddle with the focus, so you likely will put the image at infinite distance for relaxed viewing. The microscope is an intermediate case. Always striving for greater resolution, the user may pull the image close, to the near point, even though that doesn't increase its size very much. But usually, users will place the image farther away, at the distance of a meter or two, or even at infinity. But, because the object is very near the focal point, the magnification is only weakly dependent on image position.

Some texts express angular magnification as the ratio of the angles, some express it as the ratio of the tangents of the angles. If all of the angles are small, there's negligible difference between these two definitions. However, if you examine the derivation of the formula these books give for the magnification of a telescope

, you realize that they must have been using the tangents. The tangent form of the definition is the traditionally correct one, the one used in science and industry, for nearly all optical instruments which are designed to produce images which preserve the linear geometry of the object.f_{o}/f_{e}

Micro-.A prefix meaning ‘small’, as in ‘microscope’, ‘micrometer’, ‘micrograph’. Also, a metric prefix meaning 10^{-6}. See: macro-

Microscopic.A physical entity or process of small scale, too small to directly experience with our senses. Specifically, any phenomena on the molecular and atomic scale, or smaller. See: macroscopic.

MKSA.The system of physical units based on the fundamental metric units: meter kilogram, second and ampere.

Modern physics.The physics developed since about 1900, which includes relativity and quantum mechanics. See: classical physics.

Mole.The termmoleis short for the namegram-molar-weight; it isnota shortened form of the wordmolecule. (However, the wordmoleculedoes also derive from the wordmolar.) See: Avogadro’s constant.

Misuse alert:Many books emphasize that the mole is "just a number," a measure of the number of particles in a collection. They say that one can have a mole ofanykind of particles, baseballs, atoms, stars, grains of sand, etc. It doesn't have to be molecules. This is misleading.To say that the mole is "just a number" is simply wrong, from physical, pedagogical, philosophical and historical points of view. There's no physical significance to a mole of stars or a mole of grains of sand, or a mole of people. The physical significance of the mole as a measure of quantity arises

onlywhen dealing with physical laws about matter on the molecular scale. The only physical and chemicallawswhich use the mole are those dealing with gases, or systems behaving like gases.

Molecular mass.Themolecular massof something is the mass ofone moleof it (in cgs units), orone kilomoleof it (in MKS units). The units of molecular mass are gram and kilogram, respectively. The cgs and MKS values of molecular mass are numerically equal. The molecular mass isnotthe mass of one molecule. Some books still call this themolecular weight.One dictionary definition of

molaris "Pertaining to a body of matter as a whole: contrasted withmolecularandatomic." The mole is a measure appropriate for amacroscopic amount of material, as contrasted with amicroscopic amount (a few atoms or molecules). See: mole, Avogadro's constant, microscopic, macroscopic.

Newton's first and second laws of motion.F= d(mv)/dt.

is theFnet(total) force acting on the body of mass m. The individual forces acting on m must be summed vectorially. In the special case where the mass is constant, this becomes.F= ma

Newton's third law of motion.When body A exerts a force on body B, then B exerts and equal and opposite force on A. The two forces related by this law act ondifferent bodies. The forces need not benetforces.

Ohm's law.V = IR, whereVis the potential across a circuit element,Iis the current through it, andRis its resistance. This isnota generally applicable definition of resistance. It is only applicable toohmicresistors, those whose resistanceRis constant over the range of interest and V obeys a strictly linear relation toI.Materials are said to be

ohmicwhenVdepends linearly onR. Metals are ohmic so long as one holds their temperature constant. But changing the temperature of a metal changesRslightly. Therefore such a device as an electric light bulb increases its temperature as it warms up, which is why it glows slightly brighter for a very brief time just after it is turned on.For non-ohmic resistors,

Ris a function of current and the definitionR = dV/dIis far more useful. This is sometimes called thedynamic resistance. Solid state devices such as thermistors are non-ohmic, and non-linear. A thermistor's resistance decreases as it warms up, so its dynamic resistance is negative. Tunnel diodes and some electrochemical processes have a complicatedI-Vcurve with a negative resistance region of operation.The dependence of resistance on current is partly due to the change in the device's temperature with increasing current, but other subtle processes also contribute to change in resistance in solid state devices.

Operational definition.A definition which describes anexperimental procedureby which a numeric value of the quantity may be determined. See dimensions.

Example:Length is operationally defined by specifying aprocedurefor subdividing a standard of length into smaller units to make a measuring stick, then laying that stick on the object to be measured, etc..

Veryfew quantities in physics need to be operationally defined. They are thefundamentalquantities, which include length, mass and time. Other quantities are defined from these through mathematical relations.

Optical sign conventions.In introductory (freshman) courses in physics a sign convention is used for objects and images in which the lens equation must be written1/p + 1/q = 1/f. Often the rules for this sign convention are presented in a convoluted manner. A simple and easy to remember rule is this:pis theobject-to-lensdistance.qis thelens to imagedistance. The coordinate axis along the optic axis is in the direction of passage of light through the lens, this defining thepositivedirection. Example: If the axis and the light direction is left-to-right (as is usually done) and the object is to the left of the lens, the object-to-lens distance is positive. if the object is to the right of the lens (virtual object), the object-to-lens distance is negative. It works the same for images.For refractive surfaces, define the surface radius to be the directed distance from a surface to its center of curvature. Thus a surface convex to the incident light is positive, one concave to the incident light is negative. The surface equation is then

n/s + n'/s' = (n'-n)/Rwheresands'are the object and image distances, andnandn'the refractive index of the incident and emergent media, respectively.For mirrors, the equation is usually written

1/s + 1/s' = 2/R = 1/f. A diverging mirror is convex to the incoming light, with negativef. From this fact we conclude thatRis also negative. This form of the equation is consistent with that of the lens equation, and the interpretation of sign of focal length is the same also. But violence is done to the definition ofRwe used above, for refraction. One can say that the mirrorfoldsthe length axis at the mirror, so that emergent rays to a real image at the left represent a positive value ofs'. We are forced also to declare that the mirror also flips the sign of the surface radius. For reflective surfaces, the radius of curvature is defined to be the directed distance from a surface to its center of curvature,measured with respect to the axis used for the emergent light.With this qualification the convention for the signs ofs'andRis the same for mirrors as for refractive surfaces.In advanced optics courses, a

cartesiansign convention is used in which all things to the left of the lens are negative, all those to the right are positive. When this is used, the lens equation must be written1/p + 1/f = 1/q. (The sign of the1/pterm is opposite that in the other sign convention). This is a particularly meaningful version, for1/pis the measure of vergence (convergence or divergence) of the rays as they enter the lens,1/fis the amount the lens changes the vergence, and1/qis the vergence of the emergent rays.

Pascal's Principle of Hydrostatics. Pascal actually has three separate principles of hydrostatics. When a textbook refers toPascal's Principleit should specify which is meant.

Pascal 1: The pressure at any point in a liquid exerts force equally in all directions.This means that an infinitessimal surface area placed at that point will experience the same force due to pressure no matter what its orientation.

Pascal 2: When pressure is changed (increased or decreased) at any point in a homogenous, incompressible fluid, all other points experience the same change of pressure.Except for minor edits and insertion of the words 'homogenous' and 'incompressible', this is the statement of the principle given in John A. Eldridge's textbook

College Physics(McGraw-Hill, 1937). Yet over half of the textbooks I've checked, including recent ones, omit the important word 'changed'. Some textbooks add the qualification 'enclosed fluid'. This gives the false impression that the fluid must be in a closed container, which isn't a necessary condition of Pascal's principle at all.Some of these textbooks do indicate that Pascal's principle applies only to changes in pressure, but do so in the surrounding text, not in the bold, highlighted, and boxed statement of the principle. Students, of course, read the emphasized statement of the principle and not the surrounding text. Few books give any examples of the principle applied to anything other than enclosed liquids. The usual example is the hydraulic press. Too few show that Pascal's principle is derivable in one step from Bernoulli's equation. Therefore students have the false impression that these are independent laws.

Pascal 3. The hydraulic lever.The hydraulic jack is a problem in fluid equilibrium, just as a pulley system is a problem in mechanical equilibrium (no accelerations involved). It's the static situation in which a small force on a small piston balances a large force on a large piston. No change of pressure need be involved here. A constant force on one piston slowly lifts a different piston with a constant force on it. At all times during this process the fluid is in near-equilibrium. This "principle" is no more than an application of the definition of pressure asF/A, the quotient of net force to the area over which the force acts. However, it also uses the principle that pressure in a fluid is uniform throughout the fluid at all points of the same height.This hydraulic jack lifitng process is done at constant speed. If the two pistons are at different levels, as they usually are in real jacks used for lifting, there's a pressure difference between the two pistons due to height difference

(rho)gh. In textbook examples this is generally considered small enough to neglect and may not even be mentioned.Pascal's own discussion of the principle is not concisely stated and can be misleading if hastily read. See his

On the Equilibrium of Liquids, 1663. He inroduces the principle with the example of a piston as part of an enclosed vessel and considers what happens if a force is applied to that piston. He concludes that each portion of the vessel is pressed in proportion to its area. He does mention parenthetically that he is "excluding the weight of the water..., for I am speaking only of the piston's effect."

Percentage.Older dictionaries suggested thatpercentagebe used when a non-quantitative statement is being made: "The percentage growth of the economy was encouraging." But usepercentwhen specifying a numerical value: "The gross national product increased by 2 percent last year." Though newer dictionaries are more permissive, I find the indiscriminate and unnecessary use of the ugly wordpercentageto be overdone and annoying, as in "The experimental percentage uncertainty was 9%." Much more graceful is: "The experimental uncertainty was 9%."Related note: Students have the strange idea that results are

betterwhen expressed as percents. Some experimental uncertainties mustnotbe expressed as percents. Examples: (1) temperature in Celsius or Fahrenheit measure, (2) index of refraction, (3) dielectric constants. These measurables have arbitrarily chosen ‘fixed points’. Consider a 1 degree uncertainty in a temperature of 99 degrees C. Is the uncertainty 1%? Consider the same error in a measurement of 5 degrees. Is the uncertainty now 20%? Consider how much smaller the percent would be if the temperature were expressed in degrees Kelvin. This shows that percent uncertainty of Celsius and Fahrenheit temperature measurements is meaningless. However, the absolute (Kelvin) temperature scale has a physically meaningful fixed point (absolute zero), rather than an arbitrarily chosen one, and in some situations a percent uncertainty of an absolute temperatureismeaningful.

Per unit.In my opinion this expression is a barbarism best avoided. When a student is told that electric field isforce per unit chargeand in the MKS system one unit of charge is a coulomb (ahugeamount) must we obtain that much charge to measure the field? Certainly not. In fact, one must take the limit ofF/q as q goes to zero. Simply say: "Force divided by charge" or "F over q" or even "force per charge". Unfortunately there is no graceful way to say these things, other than simply writing the equation.

Peris one of those frustrating words in English. TheAmerican Heritage Dictionarydefinition is: "To, for, or by each; for every." Example: "40 cents per gallon." We must put the blame forper unitsquarely on the scientists and engineers.

Precise.Sharply or clearly defined. Having small experimental uncertainty. A precise measurement may still be inaccurate, if there were an unrecognized determinate error in the measurement (for example, a miscalibrated instrument). Compare: accurate.

Proof.A term from logic and mathematics describing an argument from premise to conclusion using strictly logical principles. In mathematics, theorems or propositions are established by logical arguments from a set of axioms, the process of establishing a theorem being called aproof.The colloquial meaning of ‘proof’ causes lots of problems in physics discussion and is best avoided. Since mathematics is such an important part of physics, the mathematician’s meaning of proof should be the only one we use. Also, we often ask students in upper level courses to do proofs of certain theorems of mathematical physics, and we are

notasking for experimental demonstration!So, in a laboratory report, we should not say "We proved Newton's law." Rather say, "Today we

demonstrated(orverified) the validity of Newton's law in the particular case of…"

Radioactive material.A material whose nuclei spontaneously give off nuclear radiation. Naturally radioactive materials (found in the earth's crust) give off alpha, beta, or gamma particles. Alpha particles are Helium nuclei, beta particles are electrons, and gamma particles are high energy photons.

Radioactive.A word distinguishing radioactive materials from those which aren't. Usage: "U-235 is radioactive; He-4 is not."Note:Radioactiveis least misleading when used as an adjective, not as a noun. It is sometimes used in the noun form as an shortened stand-in forradioactive material, as in the example above.Radioactivity.The process of emitting particles from the nucleus. Usage: "Certain materials found in nature demonstrate radioactivity."Misuse alert:Radioactivity is aprocess, not athing, and not asubstance. It is just as incorrect to say "U-235 emits radioactivity" as it is to say "current flows." A malfunctioning nuclear reactor does notrelease radioactivity, though it mayrelease radioactive materialsinto the surrounding environment. A patient being treated by radiation therapy does notabsorb radioactivity, but does absorb some of theradiation(alpha, beta, gamma) given off by the radioactive materials being used.This misuse of the word

radioactivitycauses many people to incorrectly think of radioactivity as something one cangetby being near radioactive materials. There is only one process which behaves anything like that, and it is calledartificially 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 which are radioactive.Rate.A quantity of one thing compared to a quantity of another. [Dictionary definition]In physics the comparison is generally made by taking a quotient. Thus speed is defined to be the dx/dt, the ‘time rate of change of position’.

Common misuse: We often hear non-scientists say such things as "The car was going at a high rate of speed." This is redundant at best, since it merely means "The car was moving at high speed." It is the sort of mistake made by people who don't think while they talk.

Ratio.The quotient of two similar quantities. In physics, the two quantities must have the same units to be ‘similar’. Therefore we may properly speak of the ratio of two lengths. But to say "the ratio of charge to mass of the electron" is improper. The latter is properly called "the specific charge of the electron." See: specific.

Reaction.Reaction forces are those equal and opposite forces of Newton's Third Law. Though they are sometimes called anaction and reactionpair, one never sees a single force referred to as anaction force. See: Newton’s Third Law.

Real force.See: inertial frame.

Real image.The point(s) to which light rays converge as they emerge from a lens or mirror. See: virtual image.

Real object.The point(s) from which light rays diverge as they enter a lens or mirror. See: virtual object.

Relative.Colloquially "compared to". In thetheory of relativityobservations of moving observers are quantitatively compared. These observers obtain different values when measuring the same quantities, and these quantities are said to berelative.The theory, however, shows us how the differing measured values are precisely related to the relative velocity of the two observers. Some quantities are found to be the same for all observers, and are calledinvariant.One postulate of relativity theory is that the speed of light is an invariant quantity. When the theory is expressed in four dimensional form, with the appropriate choice of quantities, new invariant quantities emerge: the world-displacement(x + y + z +ict), the energy-momentum four-vector, and the electric and magnetic potentials may be combined into an invariant four-vector. Thus relativity theory might properly be calledinvariance theory.

Misuse alert:One hears some folks with superficial minds say "Einstein showed that everything is relative." In fact, special relativity shows that only certain measurable things are relative, but in a precisely and mathematically specific way, and other things are,notrelative, for all observers agree on them.

Relative uncertainty.The uncertainty in a quantity compared to the quantity itself, expressed as a ratio of the absolute uncertainty to the size of the quantity. It may also be expressed as a percent uncertainty. The relative uncertainty is dimensionless and unitless. See: absolute uncertainty.

Scale-limited.A measuring instrument is said to bescale-limitedif the experimental uncertainty in that instrument is smaller than the smallest division readable on its scale. Therefore the experimental uncertainty is taken to be half the smallest readable increment on the scale.

Specific.In physics and chemistry the wordspecificin the name of a quantity usually means ‘divided by an extensive measure that is, divided by a quantity representing an amount of material.Specific volumemeans volume divided by mass, which is the reciprocal of the density.Specific heat capacityis the heat capacity divided by the mass. See: extensive, and capacity.

Tele-.A prefix meaningat a distance, as intelescope,telemetry,television.

Term.One of several quantities which are added together.Confusion can arise with another use of the word, as when one is asked to “Express the result in terms of mass and time.” This means “as a function of mass and time,” obviously it doesn’t mean that mass and time are to be added as terms.

Truth.This is a word best avoided entirely in physics except when placed in quotes, or with careful qualification. Its colloquial use has so many shades of meaning from ‘it seems to be correct’ to the absolute truths claimed by religion, that it’s use causes nothing but misunderstanding. Someone once said "Science seeks proximate (approximate) truths." Others speak ofprovisionalortentativetruths. Certainly science claims no final or absolute truths.

Theoretical.Describing an idea which is part of a theory, or a consequence derived from theory.

Misuse alert:Do not call an authoritative or ‘book’ value of a physical quantity atheoreticalvalue, as in: "We compared our experimentally determined value of index of refraction with the theoretical value and found they differed by 0.07." The value obtained from index of refraction tables comesnotfrom theory, but from experiment, and therefore should not be calledtheoretical.The wordtheoreticallysuffers the same abuse. Only when a numeric valueisa prediction from theory, can one properly refer to it as a "theoretical value".

Theory.Awell-testedmathematical model of some part of science. In physics a theory usually takes the form of an equation or a group of equations, along with explanatory rules for their application. Theories are said to be successful if (1) they synthesize and unify a significant range of phenomena; (2) they have predictive power, either predicting new phenomena, or suggesting a direction for further research and testing. Compare: hypothesis, and law.

Uncertainty.Synonym:error.A measure of the the inherent variability of repeated measurements of a quantity. A prediction of the probable variability of a result, based on the inherent uncertainties in the data, found from a mathematical calculation of how the data uncertainties would, in combination, lead to uncertainty in the result. This calculation or process by which one predicts the size of the uncertainty in results from the uncertainties in data and procedure is callederror analysis.See: absolute uncertainty and relative uncertainty. Uncertainties are always present; the experimenter’s job is to keep them as small as required for a useful result. We recognize two kinds of uncertainties:

indeterminateanddeterminate.Indeterminate uncertainties are those whose size and sign are unknown, and are sometimes (misleadingly) calledrandom. Determinate uncertainties are those of definite sign, often referring to uncertainties due to instrument miscalibration, bias in reading scales, or some unknown influence on the measurement.

Units.Labels which distinguish one type of measurable quantity from other types. Length, mass and time are distinctly different physical quantities, and therefore have different unit names, meters, kilograms and seconds. We use several systems of units, including the metric (SI) units, the English (or U.S. customary units) , and a number of others of mainly historical interest.Note: Some dimensionless quantities are assigned unit names, some are not. Specific gravity has no unit name, but density does. Angles are dimensionless, but have unit names: degree, radian, grad. Some quantities which are physically different, and have different unit names, may have the same dimensions, for example, torque and work. Compare: dimensions.

Virtual image.The point(s) from which light rays converge as they emerge from a lens or mirror. The rays do not actually pass through each image point, but diverge from it. See: real image.

Virtual object.The point(s) to which light rays converge as they enter a lens. The rays pass through each object point. See: real object.

Weight.The size of the external force required to keep a body at rest in its frame of reference.Elementary textbooks almost universally define weight to be "the size of the gravitational force on a body." This would be fine if they would only consistently stick to that definition. But, no, they later speak of

weightless astronauts,loss of weightof a body immersed in a liquid, etc. The student who is really thinking about this is confused. Some books then tie themselves in verbal knots trying to explain (and defend)whythey use the word inconsistently. Our definition has the virtue of being consistent with all of these uses of the word.In the special case of a body supported near the earth's surface, where the acceleration due to gravity is g, the weight happens to have size mg. So this definition gives the same size for the weight as the more common definition.

This definition is consistent with the statement: "The astronauts in the orbiting spacecraft were in a weightless condition." This is because they and their spacecraft have the same acceleration, and in their frame of reference (the spacecraft) no force is needed to keep them at the same position relative to their spacecraft. They and their spacecraft are both falling at the same rate. The gravitational force on the astronauts is still mg (though g is about 12% smaller at an altitude of 400 km than it is at the surface of the earth. It is

notzero).This definition is consistent with statements about the "loss of weight" of a body immersed in a liquid (due to the buoyant force). The "weight" meant here is the external force (not counting the buoyant force) required to support the body in equilibrium in the liquid.

Why?Students often ask questions with the wordwhyin them. "Why is the sky blue?" "Why do objects fall to earth?" "Why are there no bodies with negative mass?" "Why is the universe lawful?" What sort of answers does one desire to such a question? What sort of answers can science give? If you want some mystical, ultimate or absolute answer, you won't get it from science. Philosophers of science point out that science doesn't answerwhyquestions, it only answershowquestions. Science doesn'texplain;sciencedescribes.Science postulates models todescribe howsome part of nature behaves, then tests and refines that model till it works as well as we can measure (as evidenced by repeated, skeptical testing). Science doesn’t provideultimateorabsoluteanswers, but onlyproximate(good enough) answers. Science can't find absolute truth, but it can expose errors and identify things whicharen'tso, thereby narrowing the region in which truth may reside. In the process, science has produced morereliable knowledgethan any other branch of human thought.

Work.The amount of energy transferred to or from a body or system as a result of forces acting upon the body, causing displacement of the body or parts of it. More specifically the work done by a particular force is the product of the displacement of the body and the component of the force in the direction of the displacement. A force acting perpendicular to the body's displacement does no work on the body. A force acting upon a body which undergoes no displacement does no work on that body. See: kinetic energy.

Zeroth law of thermodynamics.If body A is in thermal equilibrium with body B, and B is also in thermal equilibrium with C, then A is necessarily in thermal equilibrium with C.This is equivalent to saying that thermal equilibrium obeys a

transitivemathematical relation. Since we define equality of temperature as the condition of thermal equilibrium, then this law is necessary for the complete definition of temperature. It ensures that if a thermometer (body B) indicates that body A and C give the same thermometer reading, then they are at the same temperature.

## RELATED REFERENCES

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?" which documents and discusses errors and misleading statements in physics textbooks.

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 theHandbook of Chemistry and Physics,The Chemical Rubber Company.Warren, J. W.

The Teaching of Physics. Butterworth's, 1969.Symbols used:

‘Single quotes’; “double quotes”; plus or minus: ±; centered dot: ·.

Multiplication: × ; vertical bar: | ;_{subscript}and^{superscript}.

Footnote (dagger): †.

=defined equal to; em-dash (long hyphen): —; ellipsis: ….

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