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Useful Information
Science and Technology
0
This appendix is broken into several tables.
[link]
, Important Constants
[link]
, Submicroscopic Masses
[link]
, Solar System Data
[link]
, Metric Prefixes for Powers of Ten and Their Symbols
[link]
, The Greek Alphabet
[link]
, SI units
[link]
, Selected British Units
[link]
, Other Units
[link]
, Useful Formulae
Important Constants
Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty,
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.
Symbol
Meaning
Best Value
Approximate Value
c
size 12{c} {}
Speed of light in vacuum
2
.
99792458
×
10
8
m
/
s
size 12{2 "." "99792458" times "10" rSup { size 8{8} } ` {m} slash {s} } {}
3
.
00
×
10
8
m
/
s
size 12{3 "." "00" times "10" rSup { size 8{8} } ` {m} slash {s} } {}
G
size 12{G} {}
Gravitational constant
6
.
67384
(
80
)
×
10
−
11
N
⋅
m
2
/
kg
2
size 12{6 "." "67384" \( "80" \) times "10" rSup { size 8{ - "11"} } ` {N cdot m rSup { size 8{2} } } slash {"kg" rSup { size 8{2} } } } {}
6
.
67
×
10
−
11
N
⋅
m
2
/
kg
2
size 12{6 "." "67" times "10" rSup { size 8{ - "11"} } ` {N cdot m rSup { size 8{2} } } slash {"kg" rSup { size 8{2} } } } {}
N
A
size 12{N rSub { size 8{A} } } {}
Avogadro’s number
6
.
02214129
(
27
)
×
10
23
size 12{6 "." "02214129" \( "27" \) times "10" rSup { size 8{"23"} } } {}
6
.
02
×
10
23
size 12{6 "." "02" times "10" rSup { size 8{"23"} } } {}
k
size 12{k} {}
Boltzmann’s constant
1
.
3806488
(
13
)
×
10
−
23
J
/
K
size 12{1 "." "3806488" \( "13" \) times "10" rSup { size 8{ - "23"} } ` {J} slash {K} } {}
1
.
38
×
10
−
23
J
/
K
size 12{1 "." "38" times "10" rSup { size 8{ - "23"} } ` {J} slash {K} } {}
R
size 12{R} {}
Gas constant
8
.
3144621
(
75
)
J
/
mol
⋅
K
size 12{8 "." "3144621" \( "75" \) ` {J} slash {"mol" cdot K} } {}
8
.
31
J
/
mol
⋅
K
=
1
.
99
cal
/
mol
⋅
K
=
0
.
0821
atm
⋅
L
/
mol
⋅
K
size 12{8 "." "31"` {J} slash {"mol" cdot K=1 "." "99"` {"cal"} slash {"mol" cdot K=0 "." "0821"` {"atm" cdot L} slash {"mol" cdot K} } } } {}
σ
size 12{σ} {}
Stefan-Boltzmann constant
5
.
670373
(
21
)
×
10
−
8
W
/
m
2
⋅
K
size 12{5 "." "670373" \( "21" \) times "10" rSup { size 8{ - 8} } ` {W} slash {m rSup { size 8{2} } cdot K} } {}
5
.
67
×
10
−
8
W
/
m
2
⋅
K
size 12{5 "." "67" times "10" rSup { size 8{ - 8} } ` {W} slash {m rSup { size 8{2} } cdot K} } {}
k
size 12{k} {}
Coulomb force constant
8
.
987551788
.
.
.
×
10
9
N
⋅
m
2
/
C
2
size 12{8 "." "987551788" "." "." "." `` times "10" rSup { size 8{9} } ` {N cdot m rSup { size 8{2} } } slash {C rSup { size 8{2} } } } {}
8.99
×
10
9
N
⋅
m
2
/
C
2
size 12{9 times "10" rSup { size 8{9} } ` {N cdot m rSup { size 8{2} } } slash {C rSup { size 8{2} } } } {}
q
e
size 12{q rSub { size 8{e} } } {}
Charge on electron
−
1
.
602176565
(
35
)
×
10
−
19
C
size 12{ - 1 "." "602176565" \( "35" \) times "10" rSup { size 8{ - "19"} } `C} {}
−
1
.
60
×
10
−
19
C
size 12{ - 1 "." "60" times "10" rSup { size 8{ - "19"} } `C} {}
ε
0
size 12{ε rSub { size 8{0} } } {}
Permittivity of free space
8
.
854187817
.
.
.
×
10
−
12
C
2
/
N
⋅
m
2
size 12{8 "." "854187817" "." "." "." `` times "10" rSup { size 8{ - "12"} } ` {C rSup { size 8{2} } } slash {N cdot m rSup { size 8{2} } } } {}
8
.
85
×
10
−
12
C
2
/
N
⋅
m
2
size 12{8 "." "85" times "10" rSup { size 8{ - "12"} } ` {C rSup { size 8{2} } } slash {N cdot m rSup { size 8{2} } } } {}
μ
0
size 12{μ rSub { size 8{0} } } {}
Permeability of free space
4π
×
10
−
7
T
⋅
m
/
A
size 12{4π times "10" rSup { size 8{ - 7} } ` {T cdot m} slash {A} } {}
1
.
26
×
10
−
6
T
⋅
m
/
A
size 12{1 "." "26" times "10" rSup { size 8{ - 6} } ` {T cdot m} slash {A} } {}
h
size 12{h} {}
Planck’s constant
6
.
62606957
(
29
)
×
10
−
34
J
⋅
s
size 12{6 "." "62606957" \( "29" \) times "10" rSup { size 8{ - "34"} } `J cdot s} {}
6
.
63
×
10
−
34
J
⋅
s
size 12{6 "." "63" times "10" rSup { size 8{ - "34"} } `J cdot s} {}
Submicroscopic Masses
Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty,
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.
Symbol
Meaning
Best Value
Approximate Value
m
e
size 12{m rSub { size 8{e} } } {}
Electron mass
9
.
10938291
(
40
)
×
10
−
31
kg
size 12{9 "." "10938291" \( "40" \) times "10" rSup { size 8{ - "31"} } `"kg"} {}
9
.
11
×
10
−
31
kg
size 12{9 "." "11" times "10" rSup { size 8{ - "31"} } `"kg"} {}
m
p
size 12{m rSub { size 8{p} } } {}
Proton mass
1
.
672621777
(
74
)
×
10
−
27
kg
size 12{1 "." "672621777" \( "74" \) times "10" rSup { size 8{ - "27"} } `"kg"} {}
1
.
6726
×
10
−
27
kg
size 12{1 "." "6726" times "10" rSup { size 8{ - "27"} } `"kg"} {}
m
n
size 12{m rSub { size 8{n} } } {}
Neutron mass
1
.
674927351
(
74
)
×
10
−
27
kg
size 12{1 "." "674927351" \( "74" \) times "10" rSup { size 8{ - "27"} } `"kg"} {}
1
.
6749
×
10
−
27
kg
size 12{1 "." "6749" times "10" rSup { size 8{ - "27"} } `"kg"} {}
u
size 12{u} {}
Atomic mass unit
1
.
660538921
(
73
)
×
10
−
27
kg
size 12{1 "." "660538921" \( "73" \) times "10" rSup { size 8{ - "27"} } `"kg"} {}
1
.
6605
×
10
−
27
kg
size 12{1 "." "6605" times "10" rSup { size 8{ - "27"} } `"kg"} {}
Solar System Data
Sun
mass
1
.
99
×
10
30
kg
size 12{1 "." "99" times "10" rSup { size 8{"30"} } `"kg"} {}
average radius
6
.
96
×
10
8
m
size 12{6 "." "96" times "10" rSup { size 8{8} } `m} {}
Earth-sun distance (average)
1
.
496
×
10
11
m
size 12{1 "." "496" times "10" rSup { size 8{"11"} } " m"} {}
Earth
mass
5
.
9736
×
10
24
kg
size 12{5 "." "9736" times "10" rSup { size 8{"24"} } `"kg"} {}
average radius
6
.
376
×
10
6
m
size 12{6 "." "376" times "10" rSup { size 8{6} } `m} {}
{}
orbital period
3
.
16
×
10
7
s
size 12{3 "." "16" times "10" rSup { size 8{7} } " s "} {}
Moon
mass
7
.
35
×
10
22
kg
size 12{7 "." "35" times "10" rSup { size 8{"22"} } `"kg"} {}
average radius
1
.
74
×
10
6
m
size 12{1 "." "74" times "10" rSup { size 8{6} } `m} {}
orbital period (average)
2
.
36
×
10
6
s
size 12{2 "." "36" times "10" rSup { size 8{6} } " s"} {}
Earth-moon distance (average)
3
.
84
×
10
8
m
size 12{3 "." "84" times "10" rSup { size 8{8} } " m"} {}
Metric Prefixes for Powers of Ten and Their Symbols
Prefix
Symbol
Value
Prefix
Symbol
Value
tera
T
10
12
size 12{"10" rSup { size 8{"12"} } } {}
deci
d
10
−
1
size 12{"10" rSup { size 8{ - 1} } } {}
giga
G
10
9
size 12{"10" rSup { size 8{9} } } {}
centi
c
10
−
2
size 12{"10" rSup { size 8{ - 2} } } {}
mega
M
10
6
size 12{"10" rSup { size 8{6} } } {}
milli
m
10
−
3
size 12{"10" rSup { size 8{ - 3} } } {}
kilo
k
10
3
size 12{"10" rSup { size 8{3} } } {}
micro
μ
size 12{μ} {}
10
−
6
size 12{"10" rSup { size 8{ - 6} } } {}
hecto
h
10
2
size 12{"10" rSup { size 8{2} } } {}
nano
n
10
−
9
size 12{"10" rSup { size 8{ - 9} } } {}
deka
da
10
1
size 12{"10" rSup { size 8{1} } } {}
pico
p
10
−
12
size 12{"10" rSup { size 8{ - "12"} } } {}
—
—
10
0
(
=
1
)
size 12{"10" rSup { size 8{0} } \( `=1` \) } {}
femto
f
10
−
15
size 12{"10" rSup { size 8{ - "15"} } } {}
The Greek Alphabet
Alpha
Α
size 12{Α} {}
α
size 12{α} {}
Eta
Η
size 12{Η} {}
η
size 12{η} {}
Nu
Ν
size 12{Ν} {}
ν
size 12{ν} {}
Tau
Τ
size 12{Τ} {}
τ
size 12{τ} {}
Beta
Β
size 12{Β} {}
β
size 12{β} {}
Theta
Θ
size 12{Θ} {}
θ
size 12{θ} {}
Xi
Ξ
size 12{Ξ} {}
ξ
size 12{ξ} {}
Upsilon
Υ
size 12{Υ} {}
υ
size 12{υ} {}
Gamma
Γ
size 12{Γ} {}
γ
size 12{γ} {}
Iota
Ι
size 12{Ι} {}
ι
size 12{ι} {}
Omicron
Ο
size 12{Ο} {}
ο
size 12{ο} {}
Phi
Φ
size 12{Φ} {}
ϕ
size 12{ϕ} {}
Delta
Δ
size 12{Δ} {}
δ
size 12{δ} {}
Kappa
Κ
size 12{Κ} {}
κ
size 12{κ} {}
Pi
Π
size 12{Π} {}
π
size 12{π} {}
Chi
Χ
size 12{Χ} {}
χ
size 12{χ} {}
Epsilon
Ε
size 12{Ε} {}
ε
size 12{ε} {}
Lambda
Λ
size 12{Λ} {}
λ
size 12{λ} {}
Rho
Ρ
size 12{Ρ} {}
ρ
size 12{ρ} {}
Psi
Ψ
size 12{Ψ} {}
ψ
size 12{ψ} {}
Zeta
Ζ
size 12{Ζ} {}
ζ
size 12{ζ} {}
Mu
Μ
size 12{Μ} {}
μ
size 12{μ} {}
Sigma
Σ
size 12{Σ} {}
σ
size 12{σ} {}
Omega
Ω
size 12{ %OMEGA } {}
ω
size 12{ω} {}
SI Units
Entity
Abbreviation
Name
Fundamental units
Length
m
meter
Mass
kg
kilogram
Time
s
second
Current
A
ampere
Supplementary unit
Angle
rad
radian
Derived units
Force
N
=
kg
⋅
m
/
s
2
size 12{N="kg" cdot {m} slash {s rSup { size 8{2} } } } {}
newton
Energy
J
=
kg
⋅
m
2
/
s
2
size 12{J="kg" cdot {m rSup { size 8{2} } } slash {s rSup { size 8{2} } } } {}
joule
Power
W
=
J
/
s
size 12{W= {J} slash {s} } {}
watt
Pressure
Pa
=
N
/
m
2
size 12{"Pa"= {N} slash {m rSup { size 8{2} } } } {}
pascal
Frequency
Hz
=
1
/
s
size 12{"Hz"= {1} slash {s} } {}
hertz
Electronic potential
V
=
J
/
C
size 12{V= {J} slash {C} } {}
volt
Capacitance
F
=
C
/
V
size 12{F= {C} slash {V} } {}
farad
Charge
C
=
s
⋅
A
size 12{C=s cdot A} {}
coulomb
Resistance
Ω
=
V
/
A
size 12{ %OMEGA = {V} slash {A} } {}
ohm
Magnetic field
T
=
N
/
A
⋅
m
size 12{T= {N} slash { left (A cdot m right )} } {}
tesla
Nuclear decay rate
Bq
=
1
/
s
size 12{"Bq"= {1} slash {s} } {}
becquerel
Selected British Units
Length
1
inch
(
in
.
)
=
2
.
54
cm
(
exactly
)
size 12{1" inch " \( "in" "." \) =2 "." "54"" cm " \( "exactly" \) } {}
1
foot
(
ft
)
=
0
.
3048
m
size 12{1" foot " \( "ft" \) =0 "." "3048"" m"} {}
1
mile
(
mi
)
=
1
.
609
km
size 12{1" mile " \( "mi" \) =1 "." "609"" km"} {}
Force
1
pound
(
lb
)
=
4
.
448
N
size 12{1" pound " \( "lb" \) =4 "." "448"" N"} {}
Energy
1
British thermal unit
(
Btu
)
=
1
.
055
×
10
3
J
size 12{1" British thermal unit " \( "Btu" \) =1 "." "055" times "10" rSup { size 8{3} } " J"} {}
Power
1
horsepower
(
hp
)
=
746
W
size 12{1" horsepower " \( "hp" \) ="746"" W"} {}
Pressure
1
lb
/
in
2
=
6
.
895
×
10
3
Pa
size 12{1 {"lb"} slash {"in" rSup { size 8{2} } } =6 "." "895" times "10" rSup { size 8{3} } " Pa"} {}
Other Units
Length
1
light year
(
ly
)
=
9
.
46
×
10
15
m
size 12{1`" light"`" year"` \( "ly" \) ` =9 "." "46" times "10" rSup { size 8{"15"} } " m"} {}
1
astronomical unit
(
au
)
=
1
.
50
×
10
11
m
size 12{1`" astronomical"`" unit"` \( "au" \) ` =1 "." "50" times "10" rSup { size 8{"11"} } " m"} {}
1
nautical mile
=
1
.
852
km
size 12{1`" nautical"`" mile"` =1 "." "852"`" km"} {}
1
angstrom
(
Å
)
=
10
−
10
m
size 12{1`" angstrom"` \( Å \) ` ="10" rSup { size 8{ - "10"} } " m"} {}
Area
1
acre
(
ac
)
=
4
.
05
×
10
3
m
2
size 12{1`" acre"` \( "ac" \) ` =4 "." "05" times "10" rSup { size 8{3} } " m" rSup { size 8{2} } } {}
1
square foot
(
ft
2
)
=
9
.
29
×
10
−
2
m
2
size 12{1`"square"`"foot"` \( "ft" rSup { size 8{2} } \) ` =9 "." "29" times "10" rSup { size 8{ - 2} } " m" rSup { size 8{2} } } {}
1
barn
(
b
)
=
10
−
28
m
2
size 12{1`" barn"` \( b \) ` ="10" rSup { size 8{ - "28"} } " m" rSup { size 8{2} } } {}
Volume
1
liter
(
L
)
=
10
−
3
m
3
size 12{1`" liter"` \( L \) ` ="10" rSup { size 8{ - 3} } " m" rSup { size 8{3} } } {}
1
U.S. gallon
(
gal
)
=
3
.
785
×
10
−
3
m
3
size 12{1`" U" "." S "." `" gallon"` \( "gal" \) ` =3 "." "785" times "10" rSup { size 8{ - 3} } " m" rSup { size 8{3} } } {}
Mass
1
solar mass
=
1
.
99
×
10
30
kg
size 12{1`" solar"`" mass"` =1 "." "99" times "10" rSup { size 8{"30"} } " kg"} {}
1
metric ton
=
10
3
kg
size 12{1`" metric"`" ton"` ="10" rSup { size 8{3} } " kg"} {}
1
atomic mass unit
(
u
)
=
1
.
6605
×
10
−
27
kg
size 12{1`" atomic"`" mass"`" unit"`` \( u \) ` =1 "." "6605" times "10" rSup { size 8{ - "27"} } " kg"} {}
Time
1
year
(
y
)
=
3
.
16
×
10
7
s
size 12{1`" year"` \( y \) ` =3 "." "16" times "10" rSup { size 8{7} } " s"} {}
1
day
(
d
)
=
86
,
400
s
size 12{1`" day"` \( d \) ` ="86","400"`" s"} {}
Speed
1
mile per hour
(
mph
)
=
1
.
609
km
/
h
size 12{1`" mile"`"per"`"hour"` \( "mph" \) `=1 "." "609"` {"km"} slash {h} } {}
1
nautical mile per hour
(
naut
)
=
1
.
852
km
/
h
size 12{1`" nautical"`"mile"`"per"`"hour"` \( "naut" \) `=1 "." "852"` {"km"} slash {h} } {}
Angle
1
degree
(
°
)
=
1
.
745
×
10
−
2
rad
size 12{1`" degree"` \( ° \) ` =1 "." "745" times "10" rSup { size 8{ - 2} } " rad"} {}
1
minute of arc
(
'
)
=
1
/
60
degree
size 12{1`" minute"`"of"`"arc"` { { \( }} sup { ' } \) `= {1} slash {"60"} `" degree"} {}
1
second of arc
(
''
)
=
1
/
60
minute of arc
size 12{1`" second"`"of"`"arc"` { { \( }} sup { '' } \) `= {1} slash {"60"`} " minute of arc"} {}
1
grad
=
1
.
571
×
10
−
2
rad
size 12{1`" grad"` =1 "." "571" times "10" rSup { size 8{ - 2} } " rad"} {}
Energy
1
kiloton TNT
(
kT
)
=
4
.
2
×
10
12
J
size 12{1`" kiloton"`" TNT"` \( "kT" \) ` =4 "." 2 times "10" rSup { size 8{"12"} } " J"} {}
1
kilowatt hour
(
kW
⋅
h
)
=
3
.
60
×
10
6
J
size 12{1`" kilowatt"`" hour"` \( "kW" cdot h \) ` =3 "." "60" times "10" rSup { size 8{6} } " J"} {}
1
food calorie
(
kcal
)
=
4186
J
size 12{1`" food"`"calorie"` \( "kcal" \) `="4186"`" J"} {}
1
calorie
(
cal
)
=
4
.
186
J
size 12{1`" calorie"` \( "cal" \) `=4 "." "186"`" J"} {}
1
electron volt
(
eV
)
=
1
.
60
×
10
−
19
J
size 12{1`" electron"`" volt"` \( "eV" \) ` =1 "." "60" times "10" rSup { size 8{ - "19"} } " J"} {}
Pressure
1
atmosphere
(
atm
)
=
1
.
013
×
10
5
Pa
size 12{1`" atmosphere"` \( "atm" \) ` =1 "." "013" times "10" rSup { size 8{5} } " Pa"} {}
1
millimeter of mercury
(
mm
Hg
)
=
133
.
3
Pa
size 12{1`" millimeter"`"of"`"mercury"` \( "mm"`"Hg" \) `="133" "." 3`" Pa"} {}
1
torricelli
(
torr
)
=
1
mm
Hg
=
133
.
3
Pa
size 12{1`" torricelli"` \( "torr" \) `=1`" mm"``"Hg "="133" "." 3`" Pa"} {}
Nuclear decay rate
1
curie
(
Ci
)
=
3
.
70
×
10
10
Bq
size 12{1`" curie"` \( "Ci" \) ` =3 "." "70" times "10" rSup { size 8{"10"} } " Bq"} {}
Useful Formulae
Circumference of a circle with radius
r
size 12{r} {}
or diameter
d
size 12{d} {}
C
=
2
πr
=
πd
size 12{C=2πr=πd} {}
Area of a circle with radius
r
size 12{r} {}
or diameter
d
size 12{d} {}
A
=
πr
2
=
πd
2
/
4
size 12{A=πr rSup { size 8{2} } = {πd rSup { size 8{2} } } slash {4} } {}
Area of a sphere with radius
r
size 12{r} {}
A
=
4
πr
2
size 12{A=4πr rSup { size 8{2} } } {}
Volume of a sphere with radius
r
size 12{r} {}
V
=
4
/
3
πr
3
size 12{V= left ( {4} slash {3} right ) left (πr rSup { size 8{3} } right )} {}
0
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College Physics
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