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Table C6SI Units
Entity
Abbreviation
Name
Fundamental units Length
m
meter
Mass
kg
kilogram
Time
s
second
Current
A
ampere
Supplementary unit Angle
Derived units
Force
N=kg⋅m/s
2
newton
Energy
J=kg⋅m
2
/s
2
joule
Power
W=J/s
watt
Pressure
Pa=N/m
2
pascal
Frequency
Hz=1/s
hertz
Electronic potential
V=J/C
volt
Capacitance
F=C/V
Charge
C=s⋅A
coulomb
Resistance
Ω =V/A
ohm
Magnetic field
T=N/
(
A⋅m
)
tesla
Nuclear decay rate
Bq=1/s
becquerel
Table C7Selected British Units
Length
1inch(in.)=2.54cm(exactly)
1foot(ft)=0.3048m
1mile(mi)=1.609km
Force
1pound(lb)=4.448N
Energy
1British thermal unit(Btu)=1.055×10
3
J
Power
1horsepower(hp)=746W
Pressure
1lb/in
2
=6.895×10
3
Pa
APPENDIX C | USEFUL INFORMATION N 1249
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Table C8Other Units
Length
1light year(ly)=9.46×10
15
m
1astronomical unit(au)=1.50×10
11
m
1nautical mile=1.852km
1angstrom(Å) =10
−10
m
Area
1acre(ac)=4.05×10
3
m
2
1square foot(ft
2
)=9.29×10
−2
m
2
1barn(b)=10
−28
m
2
Volume
1liter(L)=10
−3
m
3
1U.S. gallon(gal)=3.785×10
−3
m
3
Mass
1solar mass s =1.99×10
30
kg
1metric ton=10
3
kg
1atomic mass unit(u)=1.6605×10
−27
kg
Time
1year(y)=3.16×10
7
s
1day(d)=86,400s
Speed
1mile per hour(mph)=1.609km/h
1nautical mile per hour(naut)=1.852km/h
Angle
1degree(°)=1.745×10
−2
1minute of arc(
'
)=1/60degree
1second of arc(
''
)=1/60minute of arc
−2
Energy
1kiloton TNT(kT)=4.2×10
12
J
1kilowatt hour(kW⋅h)=3.60×10
6
J
1food calorie(kcal)=4186J
1calorie(cal)=4.186J
1electron volt(eV)=1.60×10
−19
J
Pressure
1atmosphere(atm)=1.013×10
5
Pa
1millimeter of mercury(mmHg)=133.3Pa
1torricelli(torr)=1mmHg=133.3Pa
Nuclear decay rate
1curie(Ci)=3.70×10
10
Bq
1250 APPENDIX C | USEFUL INFORMATION
This content is available for free at http://cnx.org/content/col11406/1.7
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Table C9Useful Formulae
Circumference of a circle with radius
r
or diameter
d C=2πr=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=4πr
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.
APPENDIX C | USEFUL INFORMATION N 1251
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1252 APPENDIX C | USEFUL INFORMATION
This content is available for free at http://cnx.org/content/col11406/1.7
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D
GLOSSARY OF KEY SYMBOLS AND NOTATION
In this glossary, key symbols and notation are briefly defined.
APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION N 1253
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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
ΔPE
g
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
1254 APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION
This content is available for free at http://cnx.org/content/col11406/1.7
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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
θ
b
Brewster's angle
θ
c
critical angle
κ
dielectric constant
λ
decay constant of a nuclide
λ
wavelength
λ
n
wavelength in a medium
μ
0
permeability of free space
μ
k
coefficient of kinetic friction
μ
s
coefficient of static friction
v
e
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
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
a
c
centripetal acceleration
APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION N 1255
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
B
int
electron’s intrinsic magnetic field
B
orb
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
cosθ
cosine
cotθ
cotangent
cscθ
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
1256 APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION
This content is available for free at http://cnx.org/content/col11406/1.7
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
Eﬀ
C
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
F
net
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
APPENDIX D | GLOSSARY OF KEY SYMBOLS AND NOTATION N 1257