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. Heat and Thermal Physics Formulas and Equations ........................................................................................................... 5
Table G. Thermal Properties of Selected Materials ......................................................................................................................... 5
Table H. Electricity Formulas & Equations ....................................................................................................................................... 6
Table I. Electricity & Magnetism Formulas & Equations .................................................................................................................. 7
Table J. Resistor Color Code ............................................................................................................................................................. 7
Table K. Symbols Used in Electrical Circuit Diagrams ....................................................................................................................... 7
Table L. Resistivities at 20°C ............................................................................................................................................................. 7
Table M. Waves & Optics ................................................................................................................................................................. 8
Figure N. The Electcromagnetic Spectrum ....................................................................................................................................... 8
Table O. Properties of Water and Air ............................................................................................................................................... 9
Table P. Absolute Indices of Refraction ........................................................................................................................................... 9
Table Q. Fluid Mechanics Formulas and Equations ........................................................................................................................ 10
Table R. Planetary Data .................................................................................................................................................................. 10
Table S. Sun & Moon Data ............................................................................................................................................................ 10
Table T. Atomic & Particle Physics (Modern Physics) .................................................................................................................... 11
Figure U. Quantum Energy Levels .................................................................................................................................................. 11
Figure V. Particle Sizes ................................................................................................................................................................... 12
Table W. The Standard Model ....................................................................................................................................................... 12
Table X. Geometry & Trigonometry Formulas ............................................................................................................................... 13
Table Y. Values of Trigonometric Functions ................................................................................................................................... 14
Table Z. Some Exact and Approximate Conversions ...................................................................................................................... 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
Common
Approximation
Precise Value
6.673 84(80)  1011
6.67 1011
Nm2
kg 2
Nm2
kg 2
universal gravitational constant
G
acceleration due to gravity at sea level
g
9.806 65 m2
acceleration due to gravity on Earth’s
surface
g
9.7639 m2 to 9.8337 m2
speed of light in a vacuum
c
299 792 458 ms
charge of a 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
elementary charges
o
(magnetic) permeability of a vacuum
o
electrostatic constant
k
8.854 187 82 10-12
*
1 universal mass unit (u)
9.8
m
s2
m
s
A2 s4
kgm3
1.26 106
Tm
A
Nm2 *
C2
8.99 109
Tm
A
Nm2
C2
1.602176 565(35)  1019 J
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
6.02214129(27) 1023 mol 1
6.02 1023 mol1
Avogadro’s constant
NA
Boltzmann constant
kB
1.380 6488(13)  1023
universal gas constant
R
J
8.314 4621(75) mol
K
1.38 1023
J
K
J
K
J
8.31 mol
K
*
standard atmospheric pressure at sea level
m
s2
8.85 1012
A2 s4
kgm3
1
 8.987 551 787 368 176 4  109
4 o
h
9.8
3.00  108
4  107  1.256 637 06 10-6
1 electron volt (eV)
Planck’s constant
s
s
1 coulomb (C)
(electric) permittivity of a vacuum
*
s
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
rubber on concrete (dry)
rubber on concrete (wet)
rubber on asphalt (dry)
rubber on asphalt (wet)
Static (μs)
Kinetic (μk)
Static (μs)
Kinetic (μk)
0.90
0.68
0.58
0.67
0.53
wood on wood (dry)
wood on wood (wet)
wood on metal
wood on brick
0.42
0.2
0.3
0.6
0.30
0.15
wood on concrete
0.62
0.85
rubber on ice
Substance
steel on ice
waxed ski on snow
0.03
0.14
0.01
0.05
Teflon on Teflon
Teflon on steel
0.04
0.04
aluminum on aluminum
1.2
1.4
graphite on steel
0.1
cast iron on cast iron
steel on steel
copper on steel
1.1
0.74
0.53
0.15
0.57
0.36
leather on wood
leather on metal (dry)
leather on metal (wet)
0.3–0.4
0.6
0.4
diamond on diamond
diamond on metal
0.1
0.1–0.15
glass on glass
metal on glass
0.9–1.0
0.5–0.7
0.04
0.04
0.4
Physics Reference Tables
Table D. Quantities, Variables and Units
Quantity
distance/displacement, (length, height)
angle
area
volume
time
velocity
speed of light
Page 3
Variable

d , d , ( , h)
θ
A
V
t

v
c
acceleration due to gravity

ω

a

g
mass
m
force

F
pressure
angular velocity
acceleration
MKS Unit Name
MKS Unit Symbol
S.I. Base Unit
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
2
m
s2
m
s2
meter/second
kg
kg
newton
N
kgm
s2
P
pascal
Pa
kg
ms 2
energy
potential energy
heat
E
U
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
power
P
watt
W
momentum

p

J
kgm 2
s3
newton-second
N∙s
kgm
s
2
kg∙m
impulse
moment of inertia
I
angular momentum

L
frequency
wavelength
period
index of refraction
f
λ
T
n
kilogram*
kilogram-meter
newton-metersecond
hertz
meter
second
—
2
kg∙m
N∙m∙s
kgm2
s
Hz
m
s
—
s
m
s
—
ampere*
A
A
C
A∙s
2
−1
electric current

I
electric charge
potential difference (voltage)
electromotive force (emf)
q
V
ε
coulomb
volt
V
kgm 2
As 3
electrical resistance
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
amount of substance
luminous intensity
T
n
Iv
kelvin*
mole*
candela*
K
mol
cd
K
mol
cd
* S.I. base unit
Physics Reference Tables
Page 4
Table E. Mechanics Formulas and Equations
Kinematics
(Distance, Velocity &
Acceleration)

d  s  s  so

 
 d s v o  v
v 

t
t
2
   
v  v  vo  at
 

s  so  d  vot  21 at 2

 
v 2  v o2  2ad
Forces & Dynamics

 
  F Fnet
 Fg
a

g
m
m
m

Gm1m2
Fg 
r2
F f   s FN
F f   k FN
T
2
x cm 
1
 f
 mi x i

 mi


Fs  k x
m
Ts  2
k
Circular and Simple
Harmonic Motion
L
Tp  2
g
Us  12 kx2
v2
 ω2 r
r


  0  ω0t  12 α t 2
ac 
mv 2
Fc  mac 
r
  
τ  r  F   rF sin   rF
Momentum
Energy, Work &
Power
  change, difference
  sum
d  distance (m)

d  displaceme nt (m)
s  position (m)
t  time (s)

v  velocity ms 

v  average velocity ms 

a  accelerati on m2

s
f  frequency Hz  1s 
a c  centripeta l accelerati on

F  force (N)
F f  force due to friction (N)

Fg  force due to gravity (N)

m
s2
FN  normal force (N)
Fc  centripeta l force (N)
m  mass (kg)

g  acceler ation due to gravity

m
s2
2
G  gravitatio nal constant  Nm2 
 kg 
r  radius (m)

r  radius (vector)
  coefficien t of friction (dimensionless)
θ  angle (, rad)
 

  angular velocity rad
  τ τ net
s
α

N
I
I
k  spring constant m 



p  mv
x  displaceme nt of spring (m)


mi vi  m f v f
L  length of pendulum (m)

 

J  p  Fnet t
τ  torque (N  m)
  

L  r  p  Iω L  rp sin  I K  kinetic energy (J)
 
U  potential energy (J)
L  τ t
 
h  height (m)
W  F  d  Fd cos   Flld
Gm1 m2
Q  heat (J)
Ug  mgh 
r
P  power (W)
2
p
W  work (N  m)
K  12 mv 2 
2m
T  (time) period (Hz)

K  12 I 2
p  momentum (N  s)

Etotal  U  Ek  Q
J  impulse (N  s)

W  K  U
L  angular momentum (N  m  s)
W
P
t
Physics Reference Tables
Page 5
Table F. Heat and Thermal Physics Formulas and Equations
Temperature
  change
F  Fahrenheit temperatur e (F)
C  Celsius temperatur e (C)
K  Kelvin temperatur e (K)
Q  heat (J, kJ)
m  mass (kg)
F  1.8(C)  32
K  C  273.15
Q  m C T
Qmelt  m H fus
Qboil  m Hvap
Heat
C p  Cv  R
C  specific heat capacity
L  Li T
V  Vi T
T  temperatur e (K)
t  time (s)
L  length (m)
V1 V2

T1 T2
Q
T
 kA
t
L
Q
1
  AT
t
Ri
kJ
(C p  const. pressure; Cv  const. volume)
kg C
k  coëfficien t of thermal conductivi ty
msJC , mWC 
V  volume (m3 )
  linear coëfficien t of thermal expansion (C-1 )
  volumetric coëfficien t of thermal expansion (C-1 )
Ri "R" value of insulation
U  Q  W
3
K  kBT
2
W  PV
Thermodynamics
 
R  gas constant
molJK 
U  internal energy (J)
W  work (N  m)
Table G. Thermal Properties of Selected Materials
Substance
air (gas)
aluminum (solid)
Melting Boiling
Point
Point
(°C)
(°C)
Heat of
Fusion
ΔH fus
Heat of
Vaporization
Specific Heat
Thermal
Capacity
Conductivity
Cp
 
kJ
kg C
k
msJC 
Coefficients of Expansion
at 20°C
 
ΔHvap
Linear
Volumetric
kJ
kg
at 25°C
at 25°C
α (C -1 )
β (C -1 )
—
395
—
10460
1.012
0.897
0.024
250
—
—
kJ
kg
 
—
659
—
2467
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
5
−78
574
5
2.3  10
—
6.9  105
—
—
—
brass (solid)
diamond (solid)
—
3550
—
4827
—
10 000
—
30 000
0.380
0.509
120
2200
1.9  10
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
glass (solid)
gold (solid)
—
1063
—
2660
—
64.4
—
1577
0.84
0.129
0.96–1.05
310
8.5  106
1.4  105
2.55 105
4.2  105
granite (solid)
1240
—
—
—
0.790
1.7–4.0
helium (gas)
hydrogen (gas)
—
−259
−269
−253
—
58.6
21
452
5.193
14.30
0.142
0.168
—
—
—
—
iron (solid)
1535
2750
289
6360
0.450
80
1.18 105
lead (solid)
mercury (liquid)
paraffin wax (solid)
silver (solid)
327
−39
1750
357
24.7
11.3
870
293
0.160
0.140
35
8
46–68
~300
~210
—
2.5
0.25
962
2212
111
2360
0.233
429
2.080
0.016
4.181
0.58
2.11
2.18
steam (gas) @ 100°C
water (liq.) @ 25°C
ice (solid) @ −10°C
—
0
100
334
2260
—
5
3.33 105
2.9  10
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
—
Physics Reference Tables
Page 6
Table H. Electricity Formulas & Equations

k q1 q 2
1 q1q2
Fe 

2
4 o r 2
r
Electrostatic Charges
& Electric Fields

 Fe
Q
E

q oA

E 
1
q
4 o r
 
W  q E  d  qEd cos 
W  
1 q
V
 E d 
q
4 o r
UE  qV
I
UE 

V
r
kq1q2
r
Q V

t
R
P  I ΔV  I 2 R 
V2
R
W  QH  P t  V I t  I 2 R t 
Circuits
2
R
V 2t
R

A
Q
V 
C
C  k o
Ucapacitor 
A
d
1 Q(V )  1 C (V )2
2
2
I  I1  I2  I 3  
V  Vi  V1  V2  V3  
Series Circuits
Req   Ri  R1  R2  R3  
1
1
1
1
1
 



C total
C i C1 C2 C 3
Ptotal   Pi  P1  P2  P3  
I   I i  I1  I 2  I 3  
V  V1  V2  V3  
Parallel Circuits
1
1
1
1
1
 



Req
Ri R1 R2 R3
C total   C i  C 1  C 2  C 3  
Ptotal   Pi  P1  P2  P3  
  change

Fe  force due to electric field (N)
k  electrosta tic constant
 
Nm2
C2
q  point charge (C)
Q  charge (C)

E  electric field NC , mV 
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  resistivit y (  m)
  length (m)
A  cross - sectional area (m2 )
U  potential energy (J)
C  capacitanc e (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 I. Electricity & Magnetism Formulas & Equations

 
FM  q (v  B)

 
FM   (I  B)
 
V  (v  B)
  change

Fe  force due to electric field (N)

B sin 

B sin 
k  electrosta tic constant
V  v Bsin 

 B
 Bv
t
 
Pin  Pout
Table J. Resistor Color Code
Digit
Nm2
C2
A  cross - sectional area (m2 )

v  velocity (of moving charge or wire) ms

B  magnetic field (T)
o  magnetic permeabili ty of free space
B  magnetic flux
I
# turns in
V
 in  out
# turns out Vout
I in
Electromagnetic
Induction
 
q  point charge (C)
V  voltage  electric potential difference (V)
  emf  electromot ive force (V)
r  radius (m)

I  current (A)
  length (m)
t  time (s)
 I
B o
2 r
  

 B  B  A  B cos  A
Magnetism
Color

FM  q v

FM   I
Table K. 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
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
violet
7
× 10
gray
8
× 10
white
9
× 10
8
9
gold
± 5%
silver
± 10%
diode
Table L. Resistivities at 20°C
Conductors
Resistivity Ω  m 
Substance
silver
copper
gold
aluminum
tungsten
iron
nichrome
graphite
1.59 10 8
1.72 10 8
2.44  10 8
2.82  10 8
5.60  10 8
9.7110 8
1.50 10 6
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 M. Waves & Optics
Waves
λ
v
f
f
1
T
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
n 
 c  sin 1  2 
 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 N. 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)
si  distance from the mirror or lens to the image (m)
so  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 (dimensionl ess)
d  separation (m)
L  distance from the opening (m)
m  an integer
Physics Reference Tables
Page 9
Table O. Properties of Water and Air
Water
Air
Speed of
Sound
Vapor
Pressure
(Pa)
Density
999.78
999.94
999.69
998.19
997.02
1 403
1 427
1 447
1 481
1 496
611.73
872.60
1 228.1
2 338.8
3 169.1
1.288
1.265
1.243
1.200
1.180
331.30
334.32
337.31
343.22
346.13
30
40
50
60
995.61
992.17
990.17
983.16
1 507
1 526
1 541
1 552
4 245.5
7 381.4
9 589.8
19 932
1.161
1.124
1.089
1.056
349.02
354.73
360.35
365.88
70
80
90
100
980.53
971.79
965.33
954.75
1 555
1 555
1 550
1 543
25 022
47 373
70 117
101 325
1.025
0.996
0.969
0.943
371.33
376.71
382.00
387.23
Temp.
(°C)
Density
0
5
10
20
25
 
kg
m3
ms 
 
kg
m3
Speed of
Sound
ms 
Table P. Absolute Indices of Refraction
Measured at f  5.09  1014 Hz (yellow light)
Substance
Index of
Refraction
Substance
Index of
Refraction
air
ice
water
1.000293
1.309
1.3330
silica (quartz), fused
plexiglass
Lucite
1.459
1.488
1.495
1.474
ethyl alcohol
1.36
glass, borosilicate (Pyrex)
human eye, cornea
human eye, lens
1.38
1.41
glass, crown
glass, flint
1.50–1.54
1.569–1.805
sodium chloride, solid
PET (#1 plastic)
zircon
cubic zirconia
diamond
silicon
1.516
1.575
1.777–1.987
2.173–2.21
2.417
3.96
safflower oil
corn oil
glycerol
honey
silicone oil
carbon disulfide
1.466
1.47
1.473
1.484–1.504
1.52
1.628
Physics Reference Tables
Page 10
Table Q. Fluid Mechanics Formulas and Equations
m
V
F
P
A

  change
  density
V  volume (m 3 )
P  presure (Pa)
P  Po  gh
g  accelerati on due to gravity
A1v1  A2v2
h  height or depth (m)
P1  ρgh1  12 ρv 12 
P2  ρgh2  12 ρv 22
FB   Vd g
v  velocity (of fluid)
 
m
s2
ms 
F  force (N)
n  number of moles (mol)
molJK 
N  number of molecules
P1V1 P2V2

T1
T2
k B  Boltzmann' s constant
KJ 
T  temperatur e (K)
3
E k (molecular)  kBT
M  molar mass
2
3kBT
3RT

M

v rms 
A  area (m2 )
R  gas constant
PV  NkBT  nRT
Forces, Work &
Energy
kg
m3
m  mass (kg)
F1 F2

A1 A2
Density &
Pressure
 
W  PV
 
g
mol
  molecular mass (kg)
E k  kinetic energy (J)
W  work (N  m)
Table R. Planetary Data
Mercury
Distance from Sun (m)
5.79 × 10
10
6.37 × 10
24
5.97 × 10
4.87 × 10
3.30 × 10
kg
m3
6
23
Mass (kg)
Mars
1.50 × 10
6.05 × 10
2.44 × 10
 
1.08 × 10
Earth
11
6
Radius (m)
Density
Venus
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 S. 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 T. Atomic & Particle Physics (Modern Physics)
E photon  hf 
K max
Energy
hc
 pc

 hf  

h
p
E  mc 2
1
1v
Special Relativity
Figure U. Quantum Energy Levels
2
Lo
L
t 

t
m
  rel
mo

c  speed of light
ms 
  wavelength (m)
E photon  E i  E f

E  energy (J)
h  Planck' s constant (J  s)
f  frequency (Hz)
c2
p  momentum (N  s)
m  mass (kg)
K  kinetic energy (J)
  work function
  Lorentz factor (dimensionless )
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 V. Particle Sizes
Table W. The Standard Model
Generation
charge →
spin →
I
II
III
2.4 MeV/c²
1.27 GeV/c²
171.2 GeV/c²
+⅔
½
u
up quark
quarks
4.8 MeV/c²
−⅓
½
d
+⅔
½
c
½
charm quark
104 MeV/c²
−⅓
½
s
t
γ
0
1
top quark
4.2 GeV/c²
−⅓
½
b
gluon
< 2.2 eV/c²
< 0.17 MeV/c²
< 15.5 MeV/c²
91.2 GeV/c²
0
½
νμ
electron neutrino muon neutrino
0.511 MeV/c²
105.7 MeV/c²
−1
−1
½
e
electron
½
μ
muon
0
½
ντ
Z0
0
1
tau neutrino
1.777 GeV/c²
−1
½
τ
tau
0
Z boson
80.4 GeV/c²
±1
1
W±
W boson
H0
Higgs boson
g
1
bottom quark
νe
0
0 MeV/c²
0
strange quark
0
125.3 GeV/c²
photon
down quark
½
leptons
+⅔
0 MeV/c²
gauge bosons
mass →
Physics Reference Tables
Page 13
Table X. Geometry & Trigonometry Formulas
A  12 bh
Triangles
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
cos  
Right Triangles
tan 
b
adjacent

c hypotenuse
sin a opposite
 
cos  b adjacent
b  c cos θ
a  c sin θ
Rectangles,
Parallelograms and
Trapezoids
A  bh
Rectangular Solids
V  wh
C  2 r
Circles
Cylinders
A   r2
S  2 r  2 r 2  2 r(  r)
V   r 2
S  4 r 2
Spheres
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
Table Y. Values of Trigonometric Functions
radian
sine
cosine
tangent
degree
radian
sine
cosine
tangent
0°
0.000
0.000
1.000
0.000
1°
2°
3°
4°
5°
0.017
0.035
0.052
0.070
0.087
0.017
0.035
0.052
0.070
0.087
1.000
0.999
0.999
0.998
0.996
0.017
0.035
0.052
0.070
0.087
46°
47°
48°
49°
50°
0.803
0.820
0.838
0.855
0.873
0.719
0.731
0.743
0.755
0.766
0.695
0.682
0.669
0.656
0.643
1.036
1.072
1.111
1.150
1.192
6°
7°
8°
9°
10°
0.105
0.122
0.140
0.157
0.175
0.105
0.122
0.139
0.156
0.174
0.995
0.993
0.990
0.988
0.985
0.105
0.123
0.141
0.158
0.176
51°
52°
53°
54°
55°
0.890
0.908
0.925
0.942
0.960
0.777
0.788
0.799
0.809
0.819
0.629
0.616
0.602
0.588
0.574
1.235
1.280
1.327
1.376
1.428
11°
12°
13°
14°
15°
0.192
0.209
0.227
0.244
0.262
0.191
0.208
0.225
0.242
0.259
0.982
0.978
0.974
0.970
0.966
0.194
0.213
0.231
0.249
0.268
56°
57°
58°
59°
60°
0.977
0.995
1.012
1.030
1.047
0.829
0.839
0.848
0.857
0.866
0.559
0.545
0.530
0.515
0.500
1.483
1.540
1.600
1.664
1.732
16°
17°
18°
19°
20°
0.279
0.297
0.314
0.332
0.349
0.276
0.292
0.309
0.326
0.342
0.961
0.956
0.951
0.946
0.940
0.287
0.306
0.325
0.344
0.364
61°
62°
63°
64°
65°
1.065
1.082
1.100
1.117
1.134
0.875
0.883
0.891
0.899
0.906
0.485
0.469
0.454
0.438
0.423
1.804
1.881
1.963
2.050
2.145
21°
22°
23°
24°
25°
0.367
0.384
0.401
0.419
0.436
0.358
0.375
0.391
0.407
0.423
0.934
0.927
0.921
0.914
0.906
0.384
0.404
0.424
0.445
0.466
66°
67°
68°
69°
70°
1.152
1.169
1.187
1.204
1.222
0.914
0.921
0.927
0.934
0.940
0.407
0.391
0.375
0.358
0.342
2.246
2.356
2.475
2.605
2.747
26°
27°
28°
29°
30°
0.454
0.471
0.489
0.506
0.524
0.438
0.454
0.469
0.485
0.500
0.899
0.891
0.883
0.875
0.866
0.488
0.510
0.532
0.554
0.577
71°
72°
73°
74°
75°
1.239
1.257
1.274
1.292
1.309
0.946
0.951
0.956
0.961
0.966
0.326
0.309
0.292
0.276
0.259
2.904
3.078
3.271
3.487
3.732
31°
32°
33°
34°
35°
0.541
0.559
0.576
0.593
0.611
0.515
0.530
0.545
0.559
0.574
0.857
0.848
0.839
0.829
0.819
0.601
0.625
0.649
0.675
0.700
76°
77°
78°
79°
80°
1.326
1.344
1.361
1.379
1.396
0.970
0.974
0.978
0.982
0.985
0.242
0.225
0.208
0.191
0.174
4.011
4.331
4.705
5.145
5.671
36°
37°
38°
39°
40°
0.628
0.646
0.663
0.681
0.698
0.588
0.602
0.616
0.629
0.643
0.809
0.799
0.788
0.777
0.766
0.727
0.754
0.781
0.810
0.839
81°
82°
83°
84°
85°
1.414
1.431
1.449
1.466
1.484
0.988
0.990
0.993
0.995
0.996
0.156
0.139
0.122
0.105
0.087
6.314
7.115
8.144
9.514
11.430
41°
42°
43°
44°
45°
0.716
0.733
0.750
0.768
0.785
0.656
0.669
0.682
0.695
0.707
0.755
0.743
0.731
0.719
0.707
0.869
0.900
0.933
0.966
1.000
86°
87°
88°
89°
90°
1.501
1.518
1.536
1.553
1.571
0.998
0.999
0.999
1.000
1.000
0.070
0.052
0.035
0.017
0.000
14.301
19.081
28.636
57.290
8
degree
Physics Reference Tables
Page 15
Table Z. Some Exact and Approximate Conversions
Length
Mass/
Weight
Volume
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
= ≤ /8 teaspoon (tsp.)
≈ 10 drops
≈ 5 mL
≡ 1 tablespoon (Tbsp.)
≡ 1 fluid ounce (fl. oz.)
≡ 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)
m
60
Speed of
light
≈ 2.24
1 /s
mi.
15.6 cm
30 cm
1m
39.37 in.
≈
1.6 km
≈
≈
3.6 oz.
454 g
≈
≈
0.9 tonne
1.1 ton
≈
≈
≈
≈
≈
≈
≈
≈
≈
60 drops
15 mL
30 mL
250 mL
500 mL
600 mL
1L
3.8 L
4.7 L
≈
27 /s
≈
1 /ns
1
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.)
Speed
=
≈
≈
=
≈ 100
/h
m
300 000 000 /s
mi.
km
/h
/h
≈ 186 000
mi.
/s
m
ft.