Volume
1 liter ( L) = 10−3 m3
1 U.S. gallon (gal) = 3.785×10−3 m3
Mass
1 solar mass = 1.99×1030 kg
1 metric ton = 103 kg
1 atomic mass unit ( u) = 1.6605×10−27 kg
Time
1 year ( y) = 3.16×107 s
1 day ( d) = 86 , 400 s
Speed
1 mile per hour (mph) = 1.609 km / h
1 nautical mile per hour (naut) = 1.852 km / h
Angle
1 degree ( °) = 1.745×10−2 rad
1 minute of arc (') = 1 / 60 degree
1 second of arc ('') = 1 / 60 minute of arc
1 grad = 1.571×10−2 rad
Energy
1 kiloton TNT (kT) = 4.2×1012 J
1 kilowatt hour (kW ⋅ h) = 3.60×106 J
1 food calorie (kcal) = 4186 J
1 calorie (cal) = 4.186 J
1 electron volt (eV) = 1.60×10−19 J
Pressure
1 atmosphere (atm) = 1.013×105 Pa
1 millimeter of mercury (mm Hg) = 133.3 Pa
1 torricelli (torr) = 1 mm Hg = 133.3 Pa
Nuclear decay rate 1 curie (Ci) = 3.70×1010 Bq
APPENDIX C | USEFUL INFORMATION 1249
Table C9 Useful Formulae
Circumference of a circle with radius r or diameter d C = 2 πr = πd
Area of a circle with radius r or diameter d
A = πr 2 = πd 2 / 4
Area of a sphere with radius r
A = 4 πr 2
Volume of a sphere with radius r
V = (4 / 3)⎛⎝ πr 3⎞⎠
3. Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty,
www.physics.nist.gov/cuu (http://www.physics.nist.gov/cuu) (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.
4. Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty,
www.physics.nist.gov/cuu (http://www.physics.nist.gov/cuu) (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.
1250 APPENDIX C | USEFUL INFORMATION
APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION 1251
D
GLOSSARY OF KEY SYMBOLS AND NOTATION
In this glossary, key symbols and notation are briefly defined.
1252 APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION
Table D1
Symbol
Definition
any symbol
average (indicated by a bar over a symbol—e.g., v¯ is average velocity)
° C
Celsius degree
° F
Fahrenheit degree
//
parallel
⊥
perpendicular
∝
proportional to
±
plus or minus
0
zero as a subscript denotes an initial value
α
alpha rays
α
angular acceleration
α
temperature coefficient(s) of resistivity
β
beta rays
β
sound level
β
volume coefficient of expansion
β−
electron emitted in nuclear beta decay
β+
positron decay
γ
gamma rays
γ
surface tension
γ = 1 / 1 − v 2 / c 2 a constant used in relativity
Δ
change in whatever quantity follows
δ
uncertainty in whatever quantity follows
ΔE
change in energy between the initial and final orbits of an electron in an atom
ΔE
uncertainty in energy
Δm
difference in mass between initial and final products
ΔN
number of decays that occur
Δp
change in momentum
Δp
uncertainty in momentum
Δ PEg
change in gravitational potential energy
Δθ
rotation angle
Δs
distance traveled along a circular path
Δt
uncertainty in time
Δt 0
proper time as measured by an observer at rest relative to the process
ΔV
potential difference
Δx
uncertainty in position
ε 0
permittivity of free space
η
viscosity
APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION 1253
Symbol
Definition
θ
angle between the force vector and the displacement vector
θ
angle between two lines
θ
contact angle
θ
direction of the resultant
θb
Brewster's angle
θc
critical angle
κ
dielectric constant
λ
decay constant of a nuclide
λ
wavelength
λn
wavelength in a medium
µ 0
permeability of free space
µ k
coefficient of kinetic friction
µ s
coefficient of static friction
ve
electron neutrino
π+
positive pion
π−
negative pion
π 0
neutral pion
ρ
density
ρ c
critical density, the density needed to just halt universal expansion
ρ fl
fluid density
ρ¯ obj
average density of an object
ρ / ρ w
specific gravity
τ
characteristic time constant for a resistance and inductance ( RL) or resistance and capacitance ( RC) circuit
τ
characteristic time for a resistor and capacitor ( RC) circuit
τ
torque
Υ
upsilon meson
Φ
magnetic flux
ϕ
phase angle
Ω
ohm (unit)
ω
angular velocity
A
ampere (current unit)
A
area
A
cross-sectional area
A
total number of nucleons
a
acceleration
a B
Bohr radius
a c
centripetal acceleration
1254 APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION
Symbol
Definition
a t
tangential acceleration
AC
alternating current
AM
amplitude modulation
atm
atmosphere
B
baryon number
B
blue quark color
B¯
antiblue (yellow) antiquark color
b
quark flavor bottom or beauty
B
bulk modulus
B
magnetic field strength
Bint
electron’s intrinsic magnetic field
Borb
orbital magnetic field
BE
binding energy of a nucleus—it is the energy required to completely disassemble it into separate protons and neutrons
BE / A
binding energy per nucleon
Bq
becquerel—one decay per second
C
capacitance (amount of charge stored per volt)
C
coulomb (a fundamental SI unit of charge)
C p
total capacitance in parallel
C s
total capacitance in series
CG
center of gravity
CM
center of mass
c
quark flavor charm
c
specific heat
c
speed of light
Cal
kilocalorie
cal
calorie
COP hp
heat pump’s coefficient of performance
COP ref
coefficient of performance for refrigerators and air conditioners
cos θ
cosine
cot θ
cotangent
csc θ
cosecant
D
diffusion constant
d
displacement
d
quark flavor down
dB
decibel
d i
distance of an image from the center of a lens
d o
distance of an object from the center of a lens
DC
direct current
APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION 1255
Symbol
Definition
E
electric field strength
ε
emf (voltage) or Hall electromotive force
emf
electromotive force
E
energy of a single photon
E
nuclear reaction energy
E
relativistic total energy
E
total energy
E 0
ground state energy for hydrogen
E 0
rest energy
EC
electron capture
E cap
energy stored in a capacitor
Eff
efficiency—the useful work output divided by the energy input
EffC
Carnot efficiency
E in
energy consumed (food digested in humans)
E ind
energy stored in an inductor
E out
energy output
e
emissivity of an object
e+
antielectron or positron
eV
electron volt
F
farad (unit of capacitance, a coulomb per volt)
F
focal point of a lens
F
force
F
magnitude of a force
F
restoring force
F B
buoyant force
F c
centripetal force
F i
force input
Fnet
net force
F o
force output
FM
frequency modulation
f
focal length
f
frequency
f 0
resonant frequency of a resistance, inductance, and capacitance ( RLC) series circuit
f 0
threshold frequency for a particular material (photoelectric effect)
f 1
fundamental
f 2
first overtone
f 3
second overtone
1256 APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION
Symbol
Definition
f B
beat frequency
f k
magnitude of kinetic friction
f s
magnitude of static friction
G
gravitational constant
G
green quark color
G¯
antigreen (magenta) antiquark color
g
acceleration due to gravity
g
gluons (carrier particles for strong nuclear force)
h
change in vertical position
h
height above some reference point
h
maximum height of a projectile
h
Planck's constant
hf
photon energy
h i
height of the image
h o
height of the object
I
electric current
I
intensity
I
intensity of a transmitted wave
I
moment of inertia (also called rotational inertia)
I 0
intensity of a polarized wave before passing through a filter
I ave
average intensity for a continuous sinusoidal electromagnetic wave
I rms
average current
J
joule
J / Ψ
Joules/psi meson
K
kelvin
k
Boltzmann constant
k
force constant of a spring
Kα
x rays created when an electron falls into an n = 1 shell vacancy from the n = 3 shell
Kβ
x rays created when an electron falls into an n = 2 shell vacancy from the n = 3 shell
kcal
kilocalorie
KE
translational kinetic energy
KE + PE
mechanical energy
KE e
kinetic energy of an ejected electron
KErel
relativistic kinetic energy
KErot
rotational kinetic energy
KE
thermal energy
APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION 1257
Symbol
Definition
kg
kilogram (a fundamental SI unit of mass)
L
angular momentum
L
liter
L
magnitude of angular momentum
L
self-inductance
ℓ
angular momentum quantum number
Lα
x rays created when an electron falls into an n = 2 shell from the n = 3 shell
Le
electron total family number
Lµ
muon family total number
Lτ
tau family total number
L f
heat of fusion
L f and L v
latent heat coefficients
Lorb
orbital angular momentum
L s
heat of sublimation
L v
heat of vaporization
Lz
z - component of the angular momentum
M
angular magnification
M
mutual inductance
m
indicates metastable state
m
magnification
m
mass
m
mass of an object as measured by a person at rest relative to the object
m
meter (a fundamental SI unit of length)
m
order of interference
m
overall magnification (product of the individual magnifications)
m⎛ A
⎝ X⎞⎠
atomic mass of a nuclide
MA
mechanical advantage
m e
magnification of the eyepiece
me
mass of the electron
mℓ
angular momentum projection quantum number
mn
mass of a neutron
m o
magnification of the objective lens
mol
mole
mp
mass of a proton
m s
spin projection quantum number
N
magnitude of the normal force
N
newton
N
normal force
1258 APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION
Symbol
Definition
N
number of neutrons
n
index of refraction
n
number of free charges per unit volume
N A
Avogadro's number
N r
Reynolds number
N ⋅ m
newton-meter (work-energy unit)
N ⋅ m
newtons times meters (SI unit of torque)
OE
other energy
P
power
P
power of a lens
P
pressure
p
momentum
p
momentum magnitude
p
relativistic momentum
ptot
total momentum
p ' tot
total momentum some time later
P abs
absolute pressure
P atm
atmospheric pressure
P atm
standard atmospheric pressure
PE
potential energy
PEel
elastic potential energy
PEelec
electric potential energy
PEs
potential energy of a spring
P g
gauge pressure
P in
power consumption or input
P out
useful power output going into useful work or a desired, form of energy
Q
latent heat
Q
net heat transferred into a system
Q
flow rate—volume per unit time flowing past a point
+ Q
positive charge
− Q
negative charge
q
electron charge
qp
charge of a proton
q
test charge
QF
quality factor
R
activity, the rate of decay
R
radius of curvature of a spherical mirror
APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION 1259
Symbol
Definition
R
red quark color
R¯
antired (cyan) quark color
R
resistance
R
resultant or total displacement
R
Rydberg constant
R
universal gas constant
r
distance from pivot point to the point where a force is applied
r
internal resistance
r⊥
perpendicular lever arm
r
radius of a nucleus
r
radius of curvature
r
resistivity
r or rad
radiation dose unit
rem
roentgen equivalent man
rad
radian
RBE
relative biological effectiveness
RC
resistor and capacitor circuit