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THE INTERNATIONAL SYSTEM OF UNITS (SI)*
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APPENDIX A
THE INTERNATIONAL SYSTEM OF
UNITS (SI)*
Table A-1 The SI Base Units
Quantity
length
Name
Symbol
Definition
meter
“… the length of the path traveled by light in vacuum in
(1983)
mass
kilogram
“… this prototype [a certain platinum-iridium cylinder] shall henceforth be considered
to be the unit of mass.” (1889)
time
second
“… the duration of
periods of the radiation corresponding to the
transition between the two hyperfine levels of the ground state of the cesium.” (1967)
electric current
ampere
“… that constant current which, if maintained in two straight parallel conductors of
infinite length, of negligible circular cross section, and placed
apart in vacuum,
would produce between these conductors a force equal to
newton per meter
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of a second.”
of length.” (1946)
thermodynamic
temperature
kelvin
“… the fraction
water.” (1967)
of the thermodynamic temperature of the triple point of
amount of
substance
mole
“… the amount of substance of a system which contains as many elementary entities as
there are atoms in
of carbon-12.” (1971)
luminous
intensity
candela
“… the luminous intensity, in a given direction, of a source that emits monochromatic
radiation of frequency
hertz and that has a radiant intensity in that
direction of
watt per steradian.” (1979)
*
Table A-2 Some SI Derived Units
Quantity
Name of Unit
Symbol
area
square meter
volume
cubic meter
frequency
hertz
mass density (density)
kilogram per cubic meter
speed, velocity
meter per second
angular velocity
radian per second
acceleration
meter per second per second
angular acceleration
radian per second per second
force
newton
pressure
pascal
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THE INTERNATIONAL SYSTEM OF UNITS (SI)*
work, energy, quantity of heat
joule
power
watt
quantity of electric charge
coulomb
potential difference, electromotive force
volt
electric field strength
volt per meter (or newton per coulomb)
electric resistance
ohm
capacitance
farad
magnetic flux
weber
inductance
henry
magnetic flux density
tesla
magnetic field strength
ampere per meter
entropy
joule per kelvin
specific heat
joule per kilogram kelvin
thermal conductivity
watt per meter kelvin
radiant intensity
watt per steradian
Table A-3 The SI Supplementary Units
Quantity
Name of Unit
Symbol
plane angle
radian
rad
solid angle
steradian
sr
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SOME ASTRONOMICAL DATA
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APPENDIX C
SOME ASTRONOMICAL DATA
Some Distances from Earth
To the Moon *
To the left of our galaxy
To the Sun*
To the Andromeda Galaxy
To the nearest star (Proxima Centauri)
To the edge of the observable universe
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Mean
distance.
The Sun, Earth, and the Moon
Property
Unit
Sun
Earth
Moon
Mass
Mean radius
Mean density
1410
Free-fall acceleration at the surface
274
Escape velocity
618
Period of rotation a
at poles b
—
b The
3340
at equatorb
Radiation powerc
a Measured
5520
with respect to the distant stars.
Sun, a ball of gas, does not rotate as a rigid body.
c
Just outside Earth's atmosphere solar energy is received, assuming normal incidence, at the rate of
.
Some Properties of the Planets
Mean distance from
Sun,
Period of revolution,
y
Mercury
Venus
Earth
108
150
Mars
228
Jupiter
778
Saturn
1430
Uranus
2870
Neptune
Plutodd
4500
5900
165
248
Period of rotation, a d
Orbital speed,
Inclination of axis to
orbit
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SOME ASTRONOMICAL DATA
Inclination of orbit to
Earth's orbit
Eccentricity of orbit
Equatorial diameter,
4880
6790
Mass
2300
318
Density
Surface value of g, c ,
Escape velocity,c
Known satellites
a Measured
b Venus
0
1
2
4
with respect to the distant stars.
and Uranus rotate opposite their orbital motion.
c Gravitational
d Pluto
0
acceleration measured at the planet's equator.
is now classified as a dwarf planet.
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MATHEMATICAL FORMULAS
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APPENDIX E
MATHEMATICAL FORMULAS
Geometry
Circle of radius r:
;
.
;
Sphere of radius r:
.
Right circular cylinder of radius r and height h:
;
.
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Triangle of base a and altitude h:
.
Quadratic Formula
If
, then
.
Trigonometric Functions of Angle
Pythagorean Theorem
In this right triangle,
Triangles
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MATHEMATICAL FORMULAS
Angles are A, B, C
Opposite sides are a, b, c
Angles
Exterior angle
Mathematical Signs and Symbols
equals
equals approximately
is the order of magnitude of
is not equal to
is identical to, is defined as
is greater than (
is less than (
is much greater than)
is much less than)
is greater than or equal to (or, is no less than)
is less than or equal to (or, is no more than)
plus or minus
is proportional to
the sum of
x avg the average value of x
Trigonometric Identities
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MATHEMATICAL FORMULAS
Binomial Theorem
Exponential Expansion
Logarithmic Expansion
Trigonometric Expansions ( in radians)
Cramer's Rule
Two simultaneous equations in unknowns x and y,
have the solutions
and
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MATHEMATICAL FORMULAS
Products of Vectors
Let , , and
Any vector
Let
Let
,
be unit vectors in the x, y, and z directions. Then
with components ax , ay , and az along the x, y, and z axes can be written as
, and
be arbitrary vectors with magnitudes a, b, and c. Then
be the smaller of the two angles between
and
. Then
Derivatives and Integrals
In what follows, the letters u and v stand for any functions of x, and a and m are constants. To each of the indefinite integrals should
be added an arbitrary constant of integration. The Handbook of Chemistry and Physics (CRC Press Inc.) gives a more extensive
tabulation.
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MATHEMATICAL FORMULAS
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MATHEMATICAL FORMULAS
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SOME FUNDAMENTAL CONSTANTS OF PHYSICS*
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APPENDIX B
SOME FUNDAMENTAL CONSTANTS OF
PHYSICS*
Constant
Symbol
Speed of light in a vacuum
c
Elementary charge
e
Gravitational constant
G
Universal gas constant
R
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Computational Value
Best (1998) Value
Valuea
Uncertainty b
exact
100
Avogadro constant
Boltzmann constant
k
Stefan-Boltzmann constant
Molar volume of ideal gas at STP d
Permittivity constant
e0
exact
Permeability constant
µ0
exact
Planck constant
h
Electron massc
Proton massc
Ratio of proton mass to electron mass
1840
Electron charge-to-mass ratio
Neutron massc
Hydrogen atom massc
Deuterium atom massc
Helium atom massc
Muon mass
mµ
Electron magnetic moment
Proton magnetic moment
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SOME FUNDAMENTAL CONSTANTS OF PHYSICS*
Bohr magneton
Nuclear magneton
Bohr radius
a
Rydberg constant
R
Electron Compton wavelength
a Values
b Parts
given in this column should be given the same unit and power of 10 as the computational value.
per million.
c
Masses given in are in unified atomic mass units, where
d STP
means standard temperature and pressure:
and
.
.
*
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Front End Paper
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Front End Paper
MATHEMATICAL FORMULAS*
Quadratic Formula
If
Derivatives and Integrals
, then
Binomial Theorem
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Let
Products of Vectors
be the smaller of the two angles between
and . Then
Cramer's Rule
Two simultaneous equations in unknowns x and y,
have the solutions
Trigonometric Identities
* See
and
Appendix E for a more complete list.
SI PREFIXES *
Factor
Prefix
Symbol
yotta
zetta
exa
peta
tera
giga
mega
kilo
hecto
deka
deci
centi
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Front End Paper
milli
micro
nano
pico
femto
atto
zepto
yocto
* In
all cases, the first syllable is accented, as in ná-no-mé-ter.
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Back End Paper
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Back End Paper
SOME PHYSICAL CONSTANTS *
Speed of light
c
Gravitational constant
G
Avogadro constant
Universal gas constant
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R
Mass-energy relation
Permittivity constant
?0
Permeability constant
µ0
Planck constant
h
Boltzmann constant
k
Elementary charge
e
Electron mass
Proton mass
Neutron mass
Deuteron mass
Bohr radius
a
Bohr magneton
* For
Rydberg constant
R
a more complete list, showing also the best experimental values, see Appendix B.
THE GREEK ALPHABET
Alpha
Beta
Gamma
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Back End Paper
Delta
Epsilon
Zeta
Eta
Theta
Iota
Kappa
Lambda
Mu
Nu
Xi
Omicron
Pi
Rho
Sigma
Tau
Upsilon
Phi
,
Chi
Psi
Omega
SOME CONVERSION FACTORS*
Mass and Density
Speed
Force and Pressure
Length and Volume
Energy and Power
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Back End Paper
Time
Angular Measure
* See
Magnetism
Appendix [XML NOT YET AVAILABLE] for a more complete list.
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CONVERSION FACTORS
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APPENDIX D
CONVERSION FACTORS
Conversion factors may be read directly from these tables. For example,
revolutions, so
. The SI units are fully capitalized. Adapted in part from G. Shortley and D.
Williams, Elements of Physics, 1971, Prentice-Hall, Englewood Cliffs, NJ.
Plane Angle
RADIAN
1
60
3600
1
60
1
3438
1
360
1
Solid Angle
Length
METER
1
100
1
1000
1
3281
1
12
1609
1
5280
1
Area
1
1550
1
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CONVERSION FACTORS
1
144
1
Volume
L
1
1000
1
1000
1
1
1728
1
Mass
Quantities in the colored areas are not mass units but are often used as such. For example, when we write
.
standard value of
g
KILOGRAM
, this means that a kilogram is a mass that weighs 2.205 pounds at a location where g has the
slug
u
oz
lb
ton
1
1000
1
1
1
1
16
1
2000
Density
Quantities in the colored areas are weight densities and, as such, are dimensionally different from mass densities. See the note for the mass table.
1
1
1000
1
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1
CONVERSION FACTORS
1
1728
1
Time
y
d
h
min
SECOND
1
1
24
1440
1
60
3600
1
60
1
Speed
ft/s
km/h
METER/SECOND
mi/h
cm/s
1
1
1
100
1
1
Force
Force units in the colored areas are now little used. To clarify:
is the force of gravity that would act on an object whose mass is 1 gram at a location where g has the standard value of
dyne
NEWTON
lb
pdl
gf
kgf
1
1
1
1
1
1000
1
Pressure
inch of water
1
cm Hg
PASCAL
76
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2116
.
CONVERSION FACTORS
1
1 inch of water a at
2491
1
1 centimeter of mercury at a
1
1333
10
1
1
144
1
a
Where the acceleration of gravity has the standard value of
.
Energy, Work, Heat
Quantities in the colored areas are not energy units but are included for convenience. They arise from the relativistic mass-energy equivalence formula
and represent the energy released if a kilogram or unified atomic
mass unit (u) is completely converted to energy (bottom two rows) or the mass that would be completely converted to one unit of energy (rightmost two columns).
Btu
erg
ft · lb
hp · h
JOULE
1
u
cal
1055
1
1
2545
1
1
1
3413
1
1
1
1
1
Power
WATT
1
1
2545
550
1
1
3413
1
1000
1
Magnetic Field
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CONVERSION FACTORS
gauss
TESLA
1
milligauss
1000
1
1
Magnetic Flux
maxwell
WEBER
1
1
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