Download Physics Reference Tables

Physics Reference Tables
*
Contents:
Table A. Metric Prefixes ................................................................................................................................................................... 1
Table B. Physical Constants .............................................................................................................................................................. 2
Table C. Approximate Coëfficients of Friction ................................................................................................................................. 2
Table D. Quantities, Variables and Units.......................................................................................................................................... 3
Table E. Mechanics Formulas and Equations ................................................................................................................................... 4
Table F. Moments of Inertia ............................................................................................................................................................. 4
Table G. Heat and Thermal Physics Formulas and Equations .......................................................................................................... 5
Table H. Thermal Properties of Selected Materials ......................................................................................................................... 5
Table I. Electricity Formulas & Equations ......................................................................................................................................... 6
Table J. Electricity & Magnetism Formulas & Equations .................................................................................................................. 7
Table K. Resistor Color Code ............................................................................................................................................................ 7
Table L. Symbols Used in Electrical Circuit Diagrams ....................................................................................................................... 7
Table M. Resistivities at 20°C ........................................................................................................................................................... 7
Table N. Waves & Optics .................................................................................................................................................................. 8
Figure O. The Electcromagnetic Spectrum ....................................................................................................................................... 8
Table P. Properties of Water and Air ............................................................................................................................................... 9
Table Q. Absolute Indices of Refraction ........................................................................................................................................... 9
Table R. Fluid Mechanics Formulas and Equations ........................................................................................................................ 10
Table S. Planetary Data .................................................................................................................................................................. 10
Table T. Sun & Moon Data ............................................................................................................................................................ 10
Table U. Atomic & Particle Physics (Modern Physics) .................................................................................................................... 11
Figure V. Quantum Energy Levels .................................................................................................................................................. 11
Figure W. Particle Sizes .................................................................................................................................................................. 12
Table X. The Standard Model ......................................................................................................................................................... 12
Table Y. Geometry & Trigonometry Formulas ............................................................................................................................... 13
Table Z. Values of Trigonometric Functions ................................................................................................................................... 14
Table AA. Some Exact and Approximate Conversions ................................................................................................................... 15
Table BB. Greek Alphabet .............................................................................................................................................................. 15
Table A. Metric Prefixes
Factor
1 000 000 000 000 000 000 000 000
1 000 000 000 000 000 000 000
1 000 000 000 000 000 000
1 000 000 000 000 000
1 000 000 000 000
1 000 000 000
1 000 000
1 000
100
10
1
0.1
0.01
0.001
0.000 001
0.000 000 001
0.000 000 000 001
0.000 000 000 000 001
0.000 000 000 000 000 001
0.000 000 000 000 000 000 001
0.000 000 000 000 000 000 000 001
*
24
10
21
10
18
10
15
10
12
10
9
10
6
10
3
10
2
10
1
10
0
10
−1
10
−2
10
−3
10
−6
10
−9
10
−12
10
−15
10
−18
10
−21
10
−24
10
Prefix
yotta
zeta
exa
peta
tera
giga
mega
kilo
hecto
deca
—
deci
centi
milli
micro
nano
pico
femto
atto
zepto
yocto
Symbol
Y
Z
E
P
T
G
M
k
h
da
—
d
c
m
μ
n
p
f
a
z
y
Data from various sources, including: The University of the State of New York, The State Education Department. Albany, NY,
Reference Tables for Physical Setting/Physics, 2006 Edition.http://www.p12.nysed.gov/apda/reftable/physics-rt/physics06tbl.pdf,
SparkNotes: SAT Physics website. http://www.sparknotes.com/testprep/books/sat2/physics/,
and College Board: Equations and Constants for AP Physics 1 and AP Physics 2.
Physics Reference Tables
Page 2
Table B. Physical Constants
Description
Symbol
universal gravitational constant
6.673 84(80)  1011
G
acceleration due to gravity on Earth’s
surface
g
Common
Approximation
Precise Value
6.67 1011
Nm2
kg2
9.7639 m2 to 9.8337 m2
s
s
average value at sea level is 9.806 65 m2
9.8
m
s2
Nm2
kg 2
m
s2
or 10
s
3.00  108
speed of light in a vacuum
c
299 792 458 ms *
elementary charge (proton or electron)
e
 1.602176 565(35)  1019 C
 1.6  1019 C
6.241 509 65(16)  1018
elementary charges
6.24 1018
1 coulomb (C)
(electric) permittivity of a vacuum
o
(magnetic) permeability of a vacuum
o
electrostatic constant
k
Planck’s constant
4  107  1.256 637 06 10-6
8.85 10 12
1 universal (atomic) mass unit (u)
9.0  109
Tm
A
Nm2
C2
1.6  1019 J
6.626 069 57(29)  1034 J  s
6.6  1034 J  s
931.494 061(21) MeV/ c2
931MeV/c2
1.660 538 921(73)  1027 kg
1.66 1027 kg
6.02214129(27) 1023 mol 1
6.02 1023 mol1
NA
Boltzmann constant
kB
1.380 6488(13)  1023
universal gas constant
R
J
8.314 4621(75) mol
K
standard atmospheric pressure at sea
level
Nm2 *
C2
A2 s4
kgm3
1.602176 565(35)  1019 J
Avogadro’s constant
RH
1.26 106
Tm
A
1
 8.987 551 787 368 176 4  109
4 o
h
Rydberg constant
elementary charges
2 4
8.854 187 82 10-12 A s 3
kgm
1 electron volt (eV)
m
s
me e 4
8 o2 h 3 c
1.38 1023
J
K
J
K
J
8.31 mol
K
1
 10 973731.6 m
1.1 107 m-1
*
101 325 Pa ≡ 1.01325 bar
100 000 Pa ≡ 1.0 bar
rest mass of an electron
me
9.109 38215(45)  1031 kg
9.11 1031 kg
mass of a proton
mp
1.672621777(74)  1027 kg
1.67  1027 kg
mass of a neutron
mn
1.674 927351(74)  1027 kg
1.67  1027 kg
*
denotes an exact value (by definition)
Table C. Approximate Coëfficients of Friction
Substance
Static (μs)
Kinetic (μk)
rubber on concrete (dry)
0.90
0.68
rubber on concrete (wet)
0.58
rubber on asphalt (dry)
0.85
0.67
rubber on asphalt (wet)
0.53
rubber on ice
0.15
steel on ice
0.03
0.01
waxed ski on snow
0.14
0.05
aluminum on aluminum
1.2
1.4
cast iron on cast iron
1.1
0.15
steel on steel
0.74
0.57
copper on steel
0.53
0.36
diamond on diamond
0.1
diamond on metal
0.1–0.15
Substance
wood on wood (dry)
wood on wood (wet)
wood on metal
wood on brick
wood on concrete
Teflon on Teflon
Teflon on steel
graphite on steel
leather on wood
leather on metal (dry)
leather on metal (wet)
glass on glass
metal on glass
Static (μs)
0.42
0.2
0.3
0.6
0.62
0.04
0.04
0.1
0.3–0.4
0.6
0.4
0.9–1.0
0.5–0.7
Kinetic (μk)
0.30
0.04
0.04
0.4
Physics Reference Tables
Table D. Quantities, Variables and Units
Quantity
position
distance/displacement, (length, height)
angle
area
volume
time
velocity
speed of light
angular velocity
Page 3
Variable

xx

d ,d , ( , h)
θ
A
V
t

v
c

ω
acceleration due to gravity

a

g
mass
m
acceleration
MKS Unit Name
meter*
MKS Unit Symbol
m
S.I. Base Unit
m
meter*
m
m
radian, degree
square meter
cubic meter, liter
second*
—, °
2
m
3
m , ,L
s
—
2
m
3
m
s
meter/second
m
s
m
s
radians/second
1
s
1
s
m
s2
m
s2
meter/second
2
kilogram*
kg
kg
newton
N
kgm
s2
force

F
pressure
P
pascal
Pa
kg
ms 2
energy
potential energy
kinetic energy
heat
E
U
K
Q
joule
J
kgm 2
s2
work
W
newton-meter
N∙m
kgm 2
s2
torque

τ
newton-meter
N∙m
kgm 2
s2
watt
W
kgm 2
s3
newton-second
N∙s
kgm
s
2
kg∙m
power
angular momentum
P

p

J
I

L
frequency
wavelength
period
index of refraction
electric current
electric charge
potential difference (voltage)
electromotive force (emf)
f
λ
T
n

I
q
V
ε
electrical resistance
momentum
impulse
moment of inertia
kilogram-meter
newton-metersecond
hertz
meter
second
—
ampere*
coulomb
2
kg∙m
2
N∙m∙s
kgm2
s
Hz
m
s
—
A
C
s
m
s
—
A
A∙s
volt
V
kgm 2
As 3
R
ohm
Ω
kg m2
A 2 s 3
capacitance
C
farad
F
A2 s4
m2 kg
electric field

E
netwon/coulomb
volt/meter
N, V
C m
kgm
As 3
magnetic field

B
tesla
T
kg
As 2
temperature
T
kelvin*
amount of substance
n
mole*
luminous intensity
Iv
candela*
Variables representing vector quantities are typeset in bold italics.
K
mol
cd
* = S.I. base unit
−1
K
mol
cd
Physics Reference Tables
Page 4
Table E. Mechanics Formulas and Equations

  
d  x  x  x o

 d x v o  v
Kinematics
v 

(Distance,
t
t
2

  
Velocity &
v  v  v o  at
Acceler 

 
x  x o  d  v o t  12 at 2
ation)



v 2  v o2  2ad




s  r
vT  rω aT  rα
Circular
Motion
ac 
v2
 ω2 r
r


   0  ω0t  21 α t 2
 



Fg  mg
F  Fnet  ma
Forces &
Dynamics
F f   k FN
F f   s FN

Gm1 m2
Fg 
r2
x cm 
 mi x i
 mi
m
Rotational
Dynamics
I   r 2 dm  mr 2
0
mv 2
Fc  ma c 
r
  
τ  r  F   rF sin  r F


τ  τ net
T
Simple
Harmonic
Motion
Ts  2
2



 Iα
1
f
L
m
Tp  2
g
k


Fs  kx
U s  12 kx 2
Momentum


p  mv


 mi v i   m f v f

 
J  p  Fnet t
  

L  r  p  Iω L  rp sin  I
 
L  τ t
 
W  F  d  Fd cos  Flld
W   
Gm1 m2
Ug  mgh 
r
Energy,
Work &
Power
p2
K  1 mv 2 
2
2m
2
1
K  I
2
Etotal  U  E k  Q
W  K  U
W  
P
 F  v  Fv cos   
t
Table F. Moments of
Inertia
  change, difference
  sum
d  distance (m)

d  displacement (m)

x  position (m)
s  arc length (m)
t  time (s)

v  velocity ms

v  average velocity ms


Point Mass:
I  mr 2
Hollow Cylinder:
I  mr 2

a  accelerati on  m2 
s 

f  frequency Hz 
1
s

a c  centripeta l accelerati on  m2 
s 

F  force (N)
F f  force due to friction (N)

Fg  force due to gravity (N)
FN  normal force (N)
Fc  centripeta l force (N)
m  mass (kg)

g  acceler ation due to gravity  m2 
s 
2 

G  gravitatio nal constant  Nm2 
 kg 
r  radius (m)

r  radius (vector)
  coefficient of friction (dimensionless)
θ  angle (, rad)
rads 
N
k  spring constant m
  angular velocity

x  displacement of spring (m)
L  length of pendulum (m)

τ  torque (N m)
K  kinetic energy (J)
U  potential energy (J)
h  height (m)
Q  heat (J)
P  power (W)
W  work (N m)
T  (time) period (Hz)

p  momentum (N s)

J  impulse (N s)

L  angular momentum (N m  s)
Solid Cylinder:
I  1 mr 2
2
Hoop About Diameter:
I  1 mr 2
2
Hollow Sphere:
I  2 mr 2
3
Solid Sphere:
I  2 mr 2
5
Rod About the Middle:
I  1 mL2
12
Rod About the End:
I  1 mL2
3
Physics Reference Tables
Page 5
Table G. Heat and Thermal Physics Formulas and Equations
F  1.8(C)  32
Temperature
  change
K  C  273.15
F  Fahrenheit temperatur e (F)
C  Celsius temperatur e (C)
K  Kelvin temperatur e (K)
Q  heat (J, kJ)
m  mass (kg)
Q  m C T
Qmelt  m H fus
Qboil  m Hvap
C p  Cv  R
C  specific heat capacity  kgkJC  (C p  const. pressure; Cv  const. volume)


T  temperatur e (K)
t  time (s)
L  length (m)
L  Li T
Heat
V  Vi T
V1 V2 Q
T

 kA
T1 T2 t
L
k  coëfficient of thermal conductivity
V  volume (m3 )
Q
1
  AT
t
Ri
  linear coëfficient of thermal expansion (C-1 )
U  Q  W
K  3 k BT
2
3
U  NkB T  3 nRT
2
2
W  (PV )
Thermodynamics
msJC , mWC 
  volumetric coëfficient of thermal expansion (C-1 )
Ri "R" value of insulation
R  gas constant
molJK 
U  internal energy (J)
W  work (N  m)
Table H. Thermal Properties of Selected Materials
Substance
Melting
Point
(°C)
Boiling
Point
(°C)
Heat of
Fusion
ΔH fus
Heat of
Vaporization
ΔH vap
kJ
kg
 
kJ
kg
 
Specific Heat
Capacity
C p kgkJC
Thermal
Conductivity
k msJC
Linear
Volumetric
at 25°C
at 25°C
α (C -1 )
β (C -1 )
—
—
 


Coefficients of Expansion
at 20°C
air (gas)
aluminum (solid)
—
659
—
2467
—
395
—
10460
1.012
0.897
0.024
250
ammonia (gas)
−75
−33.3
339
1369
4.7
0.024
argon (gas)
carbon dioxide (gas)
−189
−186
29.5
161
0.520
0.839
0.016
0.0146
—
—
—
—
copper (solid)
1086
1187
134
5063
0.385
401
1.7  105
5.1  105
brass (solid)
diamond (solid)
—
3550
—
4827
—
10 000
—
30 000
0.380
0.509
120
2200
1.9  105
1  106
5.6  105
3  106
ethanol (liquid)
−117
78
104
858
2.44
0.171
2.5  104
7.5  104
−78
574
0.142
0.168
—
—
—
—
0.450
80
1.18 105
3.33 105
0.160
0.140
35
8
2.9  105
6.1  105
—
8.7  105
1.82 104
—
1.8  105
—
5.4  105
—
6.9  105
—
2.07 104
—
—
2660
—
64.4
—
1577
0.84
0.129
0.96–1.05
310
granite (solid)
1240
—
—
—
0.790
1.7–4.0
helium (gas)
hydrogen (gas)
—
−259
−269
−253
—
58.6
21
452
5.193
14.30
iron (solid)
1535
2750
289
6360
lead (solid)
mercury (liquid)
327
−39
1750
357
24.7
11.3
870
293
paraffin wax (solid)
46–68
~300
~210
—
2.5
0.25
silver (solid)
steam (gas) @
100°C
water (liq.) @ 25°C
962
2212
111
2360
0.233
429
2.080
0.016
0
100
4.181
0.58
2.11
2.18
ice (solid) @ −10°C
334
—
6
6.9  105
—
2.55 105
4.2  105
—
1063
2260
2.3  10
—
8.5  10
1.4  105
glass (solid)
gold (solid)
—
5
Physics Reference Tables
Page 6
Table I. Electricity Formulas & Equations
Electrostatic Charges
& Electric Fields

kq q
1 q1 q 2
Fe  1 2 
2
2
4

r
o r


 F
1 q
V
Q
E

E e 
4 o r 2
r
q oA
 
W  q E  d  qEd cos
W  
1 q
V
 E d 
q
4 o r
UE  qV
I
UE 
Q V

t R
kq1q2
r
V2
R
W  QH  P t  V I t  I 2 R t 
Circuits
R
V 2t
R

A
Q
V
C
C  k o
A
d
Ucapacitor  1 QV  1 CV 2
2
2
I  I1  I 2  I 3  
V  V1  V2  V3    Vi
Series Circuits
Req  R1  R2  R3     Ri
1
C total

1
1
1
1


 
C1 C 2 C 3
Ci
Ptotal  P1  P2  P3     Pi
I  I1  I 2  I 3     I i
V  V1  V2  V3  
Parallel Circuits
k  electrostatic constant
q  point charge (C)
Q  charge (C)

V
E  electric field NC , m

V  IR
P  V I  I 2R 
  change

Fe  force due to electric field (N)
1
1
1
1
1



 
Req R1 R2 R3
Ri
Ctotal  C1  C2  C 3     C i
Ptotal  P1  P2  P3     Pi
 
Nm2
C2

V  voltage  electric potential difference (V)
W  work (N  m)
d  distance (m)
r  radius (m)

I  current (A)
t  time (s)
R  resistance ()
P  power (W)
QH  heat (J)
ρ  resistivity (  m)
  length (m)
A  cross - sectional area (m2 )
 o  electric permittivi ty of free space
U  potential energy (J)
C  capacitance (F)

v  velocity (of moving charge or wire) ms

B  magnetic field (T)
 o  magnetic permeabili ty of free space
r  radius (distance) from wire
 
Physics Reference Tables
Page 7
Table J. Electricity & Magnetism Formulas & Equations

 
FM  q (v  B)
 

FM   (I  B)
 
V   (v  B)
  change

FM  force due to magnetic field (N)
FM  q v B sin
FM   I B sin
k  electrostatic constant
V  v Bsin
  emf  electromot ive force (V)
 
 B  B  A  BAcos

Electromagnetic
Induction
Nm2
C2
q  point charge (C)
V  voltage  electric potential difference (V)
 I
B o
2 r
Magnetism
 
r  radius (m)

I  current (A)
B
 Bv
t
  length (m)
t  time (s)
I
# turnsin
V
 in  out
# turnsout Vout
I in
A  cross - sectional area (m2 )

v  velocity (of moving charge or wire)

B  magnetic field (T)
Pin  Pout
 o  magnetic permeabili ty of free space
ms 
 B  magnetic flux
Table K. Resistor Color Code
Color
Digit
Table L. Symbols Used in Electrical Circuit Diagrams
Multiplier
Component
Symbol
Component
Symbol
0
black
0
× 10
brown
1
× 10
red
2
× 10
orange
3
× 10
yellow
4
× 10
green
5
× 10
blue
6
× 10
violet
7
× 10
gray
8
× 10
white
9
× 10
1
wire
battery
switch
ground
fuse
resistor
voltmeter
variable resistor (rheostat,
potentiometer, dimmer)
ammeter
lamp (light bulb)
ohmmeter
capacitor
2
3
4
5
6
7
8
9
gold
± 5%
silver
± 10%
diode
Table M. Resistivities at 20°C
Conductors
Resistivity Ω  m 
Substance
silver
copper
gold
aluminum
tungsten
iron
nichrome
graphite
1.59 10 8
8
1.72 10
2.44  10 8
2.82  10 8
8
5.60  10
9.7110 8
6
1.50 10
3  10 5 to 6  10 4
Substance
Semiconductors
Resistivity Ω  m 
germanium
silicon
sea water
drinking water
0.001 to 0.5
0.1 to 60
Substance
deionized water
glass
0.2
rubber, hard
20 to 2 000
paraffin (wax)
air
quartz, fused
Insulators
Resistivity Ω  m 
1.8  10 5
1 10 9 to 1 1013
1 1013 to 1 1013
1 1013 to 1 1017
1.3 1016 to 3.3 1016
7.51017
Physics Reference Tables
Page 8
Table N. Waves & Optics
v
f
1
f
T
λ
Waves
v wave on a string 
v  velocity of wave
FT

v
v
fdopplershifted  f  wave detector
 v wave  v source
i  r
c
v
n1 sin1  n2 sin2
n
Reflection,
Refraction &
Diffraction
1  n2

 c  sin  
 n1 
n2 v1 λ 1


n1 v 2 λ 2
L  m  d sin
sf 
Mirrors & Lenses
rc
2
1
1
1


si so s f
M
hi
s
 i
ho
so
Figure O. The Electcromagnetic Spectrum




ms 
f  frequency (Hz)
λ  wavelength (m)
T  period (of time) (s)
FT  tension (force) on string (N)
μ  elastic modulus of string
 
 i  angle of incidence (, rad)
 r  angle of reflection (, rad)
 c  critical angle (, rad)
kg
m
n  index of refraction (dimensionless)
c  speed of light in a vacuum
ms 
s f  distance to the focus of a mirror or lens (m)
rc  radius of curvature of a spherical mirror (m)
s i  distance from the mirror or lens to the image (m)
s o  distance from the mirror or lens to the object (m)
hi  height of the image (m)
ho  height of the object (m)
M  magnificat ion (dimensionless)
d  separation (m)
L  distance from the opening (m)
m  an integer
Physics Reference Tables
Page 9
Table P. Properties of Water and Air
Water
Speed
of
Vapor
Temp.
Density
Sound
Pressure
(°C)
kg
m
(Pa)
m3
 
0
5
10
20
25
30
40
50
60
70
80
90
100
999.78
999.94
999.69
998.19
997.02
995.61
992.17
990.17
983.16
980.53
971.79
965.33
954.75
s 
1 403
1 427
1 447
1 481
1 496
1 507
1 526
1 541
1 552
1 555
1 555
1 550
1 543
611.73
872.60
1 228.1
2 338.8
3 169.1
4 245.5
7 381.4
9 589.8
19 932
25 022
47 373
70 117
101 325
Air
Density
 
kg
m3
Speed of
Sound
1.288
1.265
1.243
1.200
1.180
1.161
1.124
1.089
1.056
1.025
0.996
0.969
0.943
ms 
331.30
334.32
337.31
343.22
346.13
349.02
354.73
360.35
365.88
371.33
376.71
382.00
387.23
Table Q. Absolute Indices of Refraction
Measured at f  5.09  1014 Hz (yellow light)
Substance
air
ice
water
ethyl alcohol
human eye, cornea
human eye, lens
safflower oil
corn oil
glycerol
honey
silicone oil
carbon disulfide
Index of
Refraction
1.000293
1.309
1.3330
1.36
1.38
1.41
1.466
1.47
1.473
1.484–1.504
1.52
1.628
Substance
silica (quartz), fused
plexiglass
Lucite
glass, borosilicate (Pyrex)
glass, crown
glass, flint
sodium chloride, solid
PET (#1 plastic)
zircon
cubic zirconia
diamond
silicon
Index of
Refraction
1.459
1.488
1.495
1.474
1.50–1.54
1.569–1.805
1.516
1.575
1.777–1.987
2.173–2.21
2.417
3.96
Physics Reference Tables
Page 10
Table R. Fluid Mechanics Formulas and Equations
m

V
F
P
A
F1 F2

A1 A2
Density &
Pressure
P  P  gh
o
A1v1  A2v2
P1  ρgh1  1 ρv12 
2
P2  ρgh2  1 ρv22
2
 
kg
m3
m  mass (kg)
V  volume (m3 )
P  presure (Pa)
g  accelerati on due to gravity

m
s2
h  height or depth (m)
A  area (m2 )
ms 
v  velocity (of fluid)
F  force (N)
molJK 
R  gas constant
PV  NkBT  nRT
N  number of molecules
P1V1 P2V2

T1
T2
k B  Boltzmann's constant
KJ 
T  temperatur e (K)
Ek (molecular )  3 kBT
2
M  molar mass
3kBT
3RT

M

v rms 
  density
n  number of moles (mol)
FB   Vd g
Forces, Work &
Energy
  change
W  PV
 
g
mol
  molecular mass (kg)
E k  kinetic energy (J)
W  work (N m)
Table S. Planetary Data
Mercury
6
6.05 × 10
23
4.87 × 10
5.79 × 10
Radius (m)
2.44 × 10
Mass (kg)
3.30 × 10
 
kg
m3
Earth
1.08 × 10
Distance from Sun (m)
Density
Venus
10
Mars
11
1.50 × 10
6
6.37 × 10
24
5.97 × 10
Jupiter
11
2.28 × 10
6
3.39 × 10
24
6.42 × 10
Saturn
11
7.78 × 10
6
6.99 × 10
23
1.90 × 10
Uranus
11
1.43 × 10
7
5.82 × 10
27
5.68 × 10
Neptune
12
12
2.87 × 10
4.50 × 10
7
2.54 × 10
26
8.68 × 10
7
2.46 × 10
25
1.02 × 10
5430
5250
5520
3950
1330
690
1290
1640
Orbit (years)
0.24
0.62
1.00
1.88
11.86
84.01
164.79
248.54
Rotation Period (hours)
1408
5832
23.9
24.6
9.9
10.7
17.2
16.1
Tilt of axis
2°
177.3°
23.5°
25.2°
3.1°
26.7°
97.9°
29.6°
# of observed satellites
0
0
1
2
67
62
27
13
Table T. Sun & Moon Data
Radius of the sun (m)
6.96 × 10
Mass of the sun (kg)
1.99 × 10
Radius of the moon (m)
1.74 × 10
Mass of the moon (kg)
7.35 × 10
Distance of moon from Earth (m)
3.84 × 10
8
30
6
22
8
12
7
26
Physics Reference Tables
Page 11
Table U. Atomic & Particle Physics (Modern Physics)
E photon  hf 
E k ,max
hc
 pc  

 hf  
  reduced Planck's constant 
f  frequency (Hz)
h
p
E photon  E i  E f

Energy
c  speed of light
E 2  (pc)2  (mc 2 )2
 1
1
1
 RH 

 n2 n2

2
 1

Figure V. Quantum Energy Levels
ms 
  wavelength (m)
p  momentum (N s)
m  mass (kg)
E k  kinetic energy (J)
  work function
  Lorentz factor (dimensionless)
2
Lo
L
t 

t
mrel

mo

Special Relativity




h
(J s)
2π
1)
RH  Rydberg constant( m
1
1v
E  energy (J)
h  Planck's constant (J s)
c
2
L  length in moving reference frame (m)
Lo  length in stationary reference frame (m)
t   time in stationary reference frame (s)
t  time in moving reference frame (s)
m o  mass in stationary reference frame (kg)
m rel  apparent mass in moving reference frame (kg)
v  velocity
ms 
Physics Reference Tables
Page 12
Figure W. Particle Sizes
Table X. The Standard Model
Generation
mass →
charge →
quarks
spin →
II
2.4 MeV/c²
+⅔
½
u
III
1.27 GeV/c²
+⅔
½
c
½
t
0 MeV/c²
γ
0
1
up quark
charm quark
top quark
photon
4.8 MeV/c²
104 MeV/c²
4.2 GeV/c²
0 MeV/c²
−⅓
½
d
−⅓
½
s
−⅓
½
b
down quark
strange quark
bottom quark
< 2.2 eV/c²
< 0.17 MeV/c²
< 15.5 MeV/c²
0
½
νe
0
½
νμ
electron neutrino muon neutrino
leptons
171.2 GeV/c²
+⅔
0.511 MeV/c²
105.7 MeV/c²
−1
−1
½
e
electron
½
μ
muon
0
½
ντ
0
Z0
1
Z boson
tau
±1
1
W±
W boson
H0
Higgs boson
91.2 GeV/c²
0
80.4 GeV/c²
½
0
gluon
tau neutrino
τ
0
g
1
1.777 GeV/c²
−1
125.3 GeV/c²
gauge bosons
I
Physics Reference Tables
Page 13
Table Y. Geometry & Trigonometry Formulas
Triangles
Right Triangles
A  1 bh
2
c2  a2  b2  2ab cos C
a
b
c


sin A sin B sin C
c 2  a 2  b2
a
opposite
sin  
c hypotenuse
b
adjacent
cos   
c hypotenuse
sin a opposite
tan 
 
cos  b adjacent
b  c cos θ
a  c sin θ
Rectangles,
Parallelograms and
Trapezoids
Rectangular Solids
Circles
Cylinders
Spheres
A  bh
V  wh
C  2 r
A   r2
S  2 r  2 r 2  2 r (  r)
V   r 2
S  4 r 2
V  4  r3
3
a , b, c  length of a side of a triangle
  angle
A  area
C  circumfere nce
S  surface area
V  volume
b  base
h  height
  length
w  width
r  radius
Physics Reference Tables
Page 14
0°
1°
2°
3°
4°
5°
6°
7°
8°
9°
10°
11°
12°
13°
14°
15°
16°
17°
18°
19°
20°
21°
22°
23°
24°
25°
26°
27°
28°
29°
30°
31°
32°
33°
34°
35°
36°
37°
38°
39°
40°
41°
42°
43°
44°
45°
0.000
0.017
0.035
0.052
0.070
0.087
0.105
0.122
0.140
0.157
0.175
0.192
0.209
0.227
0.244
0.262
0.279
0.297
0.314
0.332
0.349
0.367
0.384
0.401
0.419
0.436
0.454
0.471
0.489
0.506
0.524
0.541
0.559
0.576
0.593
0.611
0.628
0.646
0.663
0.681
0.698
0.716
0.733
0.750
0.768
0.785
0.000
0.017
0.035
0.052
0.070
0.087
0.105
0.122
0.139
0.156
0.174
0.191
0.208
0.225
0.242
0.259
0.276
0.292
0.309
0.326
0.342
0.358
0.375
0.391
0.407
0.423
0.438
0.454
0.469
0.485
0.500
0.515
0.530
0.545
0.559
0.574
0.588
0.602
0.616
0.629
0.643
0.656
0.669
0.682
0.695
0.707
1.000
1.000
0.999
0.999
0.998
0.996
0.995
0.993
0.990
0.988
0.985
0.982
0.978
0.974
0.970
0.966
0.961
0.956
0.951
0.946
0.940
0.934
0.927
0.921
0.914
0.906
0.899
0.891
0.883
0.875
0.866
0.857
0.848
0.839
0.829
0.819
0.809
0.799
0.788
0.777
0.766
0.755
0.743
0.731
0.719
0.707
tangent
degree
radian
sine
cosine
tangent
0.000
0.017
0.035
0.052
0.070
0.087
0.105
0.123
0.141
0.158
0.176
0.194
0.213
0.231
0.249
0.268
0.287
0.306
0.325
0.344
0.364
0.384
0.404
0.424
0.445
0.466
0.488
0.510
0.532
0.554
0.577
0.601
0.625
0.649
0.675
0.700
0.727
0.754
0.781
0.810
0.839
0.869
0.900
0.933
0.966
1.000
46°
47°
48°
49°
50°
51°
52°
53°
54°
55°
56°
57°
58°
59°
60°
61°
62°
63°
64°
65°
66°
67°
68°
69°
70°
71°
72°
73°
74°
75°
76°
77°
78°
79°
80°
81°
82°
83°
84°
85°
86°
87°
88°
89°
90°
0.803
0.820
0.838
0.855
0.873
0.890
0.908
0.925
0.942
0.960
0.977
0.995
1.012
1.030
1.047
1.065
1.082
1.100
1.117
1.134
1.152
1.169
1.187
1.204
1.222
1.239
1.257
1.274
1.292
1.309
1.326
1.344
1.361
1.379
1.396
1.414
1.431
1.449
1.466
1.484
1.501
1.518
1.536
1.553
1.571
0.719
0.731
0.743
0.755
0.766
0.777
0.788
0.799
0.809
0.819
0.829
0.839
0.848
0.857
0.866
0.875
0.883
0.891
0.899
0.906
0.914
0.921
0.927
0.934
0.940
0.946
0.951
0.956
0.961
0.966
0.970
0.974
0.978
0.982
0.985
0.988
0.990
0.993
0.995
0.996
0.998
0.999
0.999
1.000
1.000
0.695
0.682
0.669
0.656
0.643
0.629
0.616
0.602
0.588
0.574
0.559
0.545
0.530
0.515
0.500
0.485
0.469
0.454
0.438
0.423
0.407
0.391
0.375
0.358
0.342
0.326
0.309
0.292
0.276
0.259
0.242
0.225
0.208
0.191
0.174
0.156
0.139
0.122
0.105
0.087
0.070
0.052
0.035
0.017
0.000
1.036
1.072
1.111
1.150
1.192
1.235
1.280
1.327
1.376
1.428
1.483
1.540
1.600
1.664
1.732
1.804
1.881
1.963
2.050
2.145
2.246
2.356
2.475
2.605
2.747
2.904
3.078
3.271
3.487
3.732
4.011
4.331
4.705
5.145
5.671
6.314
7.115
8.144
9.514
11.430
14.301
19.081
28.636
57.290
8
Table Z. Values of Trigonometric Functions
degree
radian
sine
cosine
Physics Reference Tables
Page 15
Table AA. Some Exact and Approximate Conversions
Length
Mass/
Weight
Table BB. Greek Alphabet
1 cm
1 inch (in.)
length of a US dollar bill
12 in.
3 ft.
1m
1 km
5,280 ft.
≈
≡
=
≡
≡
=
≈
≡
width of a small paper clip
2.54 cm
6.14 in.
=
1 foot (ft.)
≈
1 yard (yd.)
≈
0.3048 ft.
=
0.6 mi.
1 mile (mi.)
≈
1 small paper clip
US 1¢ coin (1983–present)
US 5¢ coin
1 oz.
one medium-sized apple
1 pound (lb.)
1 pound (lb.)
1 ton
1 tonne
≈
=
=
≈
≈
≡
≈
≡
≡
0.5 gram (g)
2.5 g
5g
30 g
1N
16 oz.
4.45 N
2000 lb.
1000 kg
1 pinch
=
1 mL
1 tsp.
3 tsp.
2 Tbsp.
8 fl. oz.
16 fl. oz.
20 fl. oz.
2 pt.
4 qt. (U.S.)
4 qt. (UK) ≡ 5 qt. (U.S.)
15.6 cm
30 cm
1m
39.37 in.
1.6 km
≈
≈
3.6 oz.
454 g
≈
≈
0.9 tonne
1.1 ton
≈
≈
≡
≡
≤ /8 teaspoon (tsp.)
10 drops
5 mL
1 tablespoon (Tbsp.)
1 fluid ounce (fl. oz.)
≈
≈
≈
60 drops
15 mL
30 mL
≡
≡
≡
≡
≡
≡
1 cup (C)
1 U.S. pint (pt.)
1 Imperial pint (UK)
1 U.S. quart (qt.)
1 U.S. gallon (gal.)
1 Imperial gal. (UK)
≈
≈
≈
≈
≈
≈
250 mL
500 mL
600 mL
1L
3.8 L
4.7 L
≈
2.24
≈
100
≈
27 /s
1 cal
1 Calorie (food)
1 BTU
≈
≡
≈
4.18 J
1 kcal
1.05 kJ
≈
4.18 kJ
Power
1 hp
1 kW
≈
≈
746 W
1.34 hp
Temperature
0K
0°F
32°F
70°F
212°F
≡
≈
=
≈
=
−273.15°C
−18°C
0°C
= 273.15 K
21°C
100°C
=
absolute zero
=
≈
=
water freezes
room temperature
water boils
≈
186 000
mi.
≈
1 /ns
Volume
Speed
m
1 /s
60
Energy
Speed of
light
mi.
/h
m
300 000 000 /s
1
mi.
km
/h
/h
/s
m
ft.
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
α
β
γ
δ
ε, ϵ
ζ
η
θ
ι
alpha
beta
gamma
delta
epsilon
zeta
eta
theta
iota
Κ
Λ
Μ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
κ
λ
μ
ν
ξ
ο
π
ρ
σ
τ
υ
kappa
lambda
mu
nu
xi
omicron
pi
rho
sigma
tau
upsilon
Φ ϕ, ϕ
Χ
χ
Ψ ψ
Ω ω
phi
chi
psi
omega