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Physics and Astronomy
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 called absolute
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 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 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 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
6.02 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
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 which say 'You could have a mole of
stars, grains of sand, or people.' In science we do
use entities which are just numbers, such as , e, 3,
100, etc. 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.
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 1023 mole-1.
Because. Here's a word best avoided in
physics. Whenever it appears one can be almost
certain that it's a filler word 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 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 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. The capacitance of 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 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
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 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.
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 not by itself the definition of capacitance, but
merely a formula which allows us to relate the
capacitance to the charge and potential when the
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 the relative amount 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, or capacitance is
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 law F = ma is not correct unless
one adds to the real forces a fictitious force
called the centrifugal force. The centrifugal force
required in the non-inertial system is equal and
opposite to the centripetal force calculated in the
inertial system. Since the centrifugal and
centripetal forces are concepts used in two
different formulations 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. The centripetal force is
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 mv2/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 be conserved if
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 word data is the plural of datum.
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 ML2T-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 the
experimental 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 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 '... 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 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 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 (pronounced chee gung) something called
qi is believed to circulate through the body on
specific, mappable pathways called meridians. This
idea pervades the contrived
explanations/rationalizations of acupuncture, and
the qi is generally translated into English as
energy. 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
of qi can'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 a thing we
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 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 ...'
Equal. [Not all 'equals' are equal.] The word equal
and the symbol '=' have many different uses. 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 and direction.
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 are defining the
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, =, 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.
When we write 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 is more
than 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: When reading equations 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 is
not saying that F is physically 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 usage error is a synonym for the
experimental uncertainty in 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 word analysis is synonymous with
calculus, or 'a method for mathematical
calculation.' Calculus courses used to be named
Analysis.]
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. This should be called the
experimental 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 a converging
(positive) lens. The second case is that of a
diverging (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 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. 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, 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. See: work.
Heisenberg's Uncertainty Principle. 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. 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 of any measurement 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 some other measurement 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 for thin lenses, and for paraxial 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.
Inertia A 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 which F = ma holds, where F is the
sum of all real forces acting on a body of mass m
whose acceleration is a. In classical mechanics, the
real forces on 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 forces are those which arise
solely from formulating a problem in a non-inertial
system, in which ma = 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 is defined by ½mv2. 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 mc2,
which can be expressed as ½mv2 + an infinite series
of terms. 2 = 1/(1-(v/c)2), where c is 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 its angular magnification. These have
different definitions, and are based on
fundamentally different concepts.
Linear Magnification is the ratio of the size of the
object to the size of the image.
Angular Magnification is the ratio of the angular
size of the object as seen through the instrument to
the angular size of the object as seen with the
'naked eye'. The 'naked eye' view is without use 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 fo/fe, 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.
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 term mole is short for the name
gram-molar-weight; it is not a shortened form of the
word molecule. (However, the word molecule does also
derive from the word molar.) 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 of any kind 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 only when dealing with physical laws about
matter on the molecular scale. The only physical and
chemical laws which use the mole are those dealing
with gases, or systems behaving like gases.
Molecular mass. The molecular mass of
something is the mass of one mole of it (in cgs
units), or one kilomole of 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 is
not the mass of one molecule. Some books still call
this the molecular weight.
One dictionary definition of molar is 'Pertaining to
a body of matter as a whole: contrasted with
molecular and atomic.' The mole is a measure
appropriate for a macroscopic amount of material, as
contrasted with a microscopic 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.
F is the net (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 on different bodies. The forces need
not be net forces.
Ohm's law. V = IR, where V is the potential
across a circuit element, I is the current through
it, and R is its resistance. This is not a generally
applicable definition of resistance. It is only
applicable to ohmic resistors, those whose
resistance R is constant over the range of interest
and V obeys a strictly linear relation to I.
Materials are said to be ohmic when V depends
linearly on R. Metals are ohmic so long as one holds
their temperature constant. But changing the
temperature of a metal changes R slightly. 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, R is a function of current
and the definition R = dV/dI is far more useful.
This is sometimes called the dynamic 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 complicated I-V curve 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 an experimental procedure by which a
numeric value of the quantity may be determined. See
dimensions.
Example: Length is operationally defined by
specifying a procedure for subdividing a standard of
length into smaller units to make a measuring stick,
then laying that stick on the object to be measured,
etc..
Very few quantities in physics need to be
operationally defined. They are the fundamental
quantities, 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 written 1/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:
p is the object-to-lens distance. q is the lens to
image distance. The coordinate axis along the optic
axis is in the direction of passage of light through
the lens, this defining the positive direction.
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)/R where s and s' are the
object and image distances, and n and n' 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 negative f. From this fact
we conclude that R is 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 of R we used above, for refraction. One
can say that the mirror folds the length axis at the
mirror, so that emergent rays to a real image at the
left represent a positive value of s'. 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 of s' and R is the same for
mirrors as for refractive surfaces.
In advanced optics courses, a cartesian sign
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 written 1/p + 1/f = 1/q. (The sign of the 1/p
term is opposite that in the other sign convention).
This is a particularly meaningful version, for 1/p
is the measure of vergence (convergence or
divergence) of the rays as they enter the lens, 1/f
is the amount the lens changes the vergence, and 1/q
is the vergence of the emergent rays.
Pascal's Principle of Hydrostatics. Pascal actually
has three separate principles of hydrostatics. When
a textbook refers to Pascal's Principle it 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 as F/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 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.' Though newer
dictionaries are more permissive, I find the
indiscriminate and unnecessary use of the ugly word
percentage to 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 better when expressed as percents.
Some experimental uncertainties must not be
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 temperature is
meaningful.
Per unit. In my opinion this expression is a
barbarism best avoided. When a student is told that
electric field is force per unit charge and in the
MKS system one unit of charge is a coulomb (a huge
amount) must we obtain that much charge to measure
the field? Certainly not. In fact, one must take the
limit of F/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.
Per is one of those frustrating words in English.
The American Heritage Dictionary definition is: 'To,
for, or by each; for every.' Example: '40 cents per
gallon.' We must put the blame for per unit squarely
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 a proof.
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 not
asking for experimental demonstration!
So, in a laboratory report, we should not say 'We
proved Newton's law.' Rather say, 'Today we
demonstrated (or verified) 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: Radioactive is least misleading when
used as an adjective, not as a noun. It is sometimes
used in the noun form as an shortened stand-in for
radioactive 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 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 which 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 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 an action and reaction pair,
one never sees a single force referred to as an
action 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 the
theory of relativity observations of moving
observers are quantitatively compared. These
observers obtain different values when measuring the
same quantities, and these quantities are said to be
relative. 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 called invariant. 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 called invariance 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, not relative,
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 be
scale-limited if 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 word
specific in the name of a quantity usually means
‘divided by an extensive measure that is, divided by
a quantity representing an amount of material.
Specific volume means volume divided by mass, which
is the reciprocal of the density. Specific heat
capacity is the heat capacity divided by the mass.
See: extensive, and capacity.
Tele-. A prefix meaning at a distance, as in
telescope, 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 of provisional
or tentative truths. 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 a theoretical
value, 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
comes not from theory, but from experiment, and
therefore should not be called theoretical. The word
theoretically suffers the same abuse. Only when a
numeric value is a prediction from theory, can one
properly refer to it as a 'theoretical value'.
Theory. A well-tested mathematical 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 called error 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: indeterminate and determinate.
Indeterminate uncertainties are those whose size and
sign are unknown, and are sometimes (misleadingly)
called random. 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 weight
of a body immersed in a liquid, etc.
This glossary was
originally created by Donald E. Simanek, Lock Haven
University but has endured many revisions. |
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