<< Chapter < Page Chapter >> Page >

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 . 67408 ( 31 ) × 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 × 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 )} {}

Questions & Answers

if three forces F1.f2 .f3 act at a point on a Cartesian plane in the daigram .....so if the question says write down the x and y components ..... I really don't understand
Syamthanda Reply
hey , can you please explain oxidation reaction & redox ?
Boitumelo Reply
hey , can you please explain oxidation reaction and redox ?
Boitumelo
for grade 12 or grade 11?
Sibulele
the value of V1 and V2
Tumelo Reply
advantages of electrons in a circuit
Rethabile Reply
we're do you find electromagnetism past papers
Ntombifuthi
what a normal force
Tholulwazi Reply
it is the force or component of the force that the surface exert on an object incontact with it and which acts perpendicular to the surface
Sihle
what is physics?
Petrus Reply
what is the half reaction of Potassium and chlorine
Anna Reply
how to calculate coefficient of static friction
Lisa Reply
how to calculate static friction
Lisa
How to calculate a current
Tumelo
how to calculate the magnitude of horizontal component of the applied force
Mogano
How to calculate force
Monambi
a structure of a thermocouple used to measure inner temperature
Anna Reply
a fixed gas of a mass is held at standard pressure temperature of 15 degrees Celsius .Calculate the temperature of the gas in Celsius if the pressure is changed to 2×10 to the power 4
Amahle Reply
How is energy being used in bonding?
Raymond Reply
what is acceleration
Syamthanda Reply
a rate of change in velocity of an object whith respect to time
Khuthadzo
how can we find the moment of torque of a circular object
Kidist
Acceleration is a rate of change in velocity.
Justice
t =r×f
Khuthadzo
how to calculate tension by substitution
Precious Reply
hi
Shongi
hi
Leago
use fnet method. how many obects are being calculated ?
Khuthadzo
khuthadzo hii
Hulisani
how to calculate acceleration and tension force
Lungile Reply
you use Fnet equals ma , newtoms second law formula
Masego
please help me with vectors in two dimensions
Mulaudzi Reply
how to calculate normal force
Mulaudzi
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics for ap® courses' conversation and receive update notifications?

Ask