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Physics Reference Tables

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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 Formulas & Equations.................... 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 of Elementary Particles ........ 12 Figure Y. Periodic Table of the Elements ............................. 13 Table Z. Symbols Used in Nuclear Physics ........................... 14 Table AA. Selected Radioisotopes ....................................... 14 Table BB. Constants Used in Nuclear Physics ...................... 14 Figure CC. Neutron/Proton Stability Band ........................... 14 Table DD. Geometry & Trigonometry Formulas .................. 15 Table EE. Values of Trigonometric Functions ...................... 16 Table FF. Some Exact and Approximate Conversions .......... 17 Table GG. Greek Alphabet ................................................... 17

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

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24

10 1021 1018 1015 1012 9 10 6 10 103 102 1 10 0 10 −1 10 −2 10 10−3 10−6 10−9 −12 10 −15 10 10−18 10−21 −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

Symb ol

Precise Value

Common Approximation

G

6.673 84(80) 1011 Nm2

6.67 10 11

2

universal gravitational constant

kg

9.7639 m2 to 9.8337 m2

2

N m kg 2

acceleration due to gravity on Earth’s surface

g

speed of light in a vacuum

c

299792458 m s

elementary charge (proton or electron)

e

 1.602176 565(35) 10 19 C

 1.6  10 19 C

6.24150965(16) 1018

6.24  10 18

s

s

9.8

average value at sea level is 9.806 65

1 coulomb (C)

m s2

*

(electric) permittivity of a vacuum

o

(magnetic) permeability of a vacuum

o

electrostatic constant

k

4 o

1 electron volt (eV) h

Planck’s constant

2

1 universal (atomic) mass unit (u)

9.0  109

2

4

A s kgm 3 T m A

 2 Nm C2

1.602176565(35) 10 19 J

1.6 1019 J

6.62606957(29) 10 34 J s

6.6  10 34 J  s

931.494 061(21) MeV/ c2

931MeV/ c 2

1.660538 921(73) 10 27 kg

1.66 1027 kg

6.02 1023 mol 1

6.02214129(27) 1023 mol 1

Boltzmann constant

kB

1.3806488(13) 10 23 KJ

universal gas constant

R

J 8.3144621(75) mol K

me e 4 8 2oh 3 c

standard atmospheric pressure at sea level

1.26 106

T m A

9 Nm 2 * C2

NA

RH

8.85 10 12

 8.987 551787 368176 4 10

Avogadro’s constant

Rydberg constant

m s

elementary charges 4

A s kg m 3

 4  10 7  1.2566370610-6

1

or 10 ms2

3.00 108

elementary charges 8.854187 82 10 -12

m 2 s

1.38 10 23 J 8.31 mol K

 10 973731.6 1m

101 325 Pa ≡ 1.01325 bar* 31

J K

1.1 10 7 m 1 100 000 Pa ≡ 1.0 bar

9.1110 31 kg

rest mass of an electron

me

9.10938215(45)  10

mass of a proton

mp

1.672621777(74) 10 27 kg

1.67 1027 kg

mass of a neutron

mn

1.674927351(74)  10 27 kg

1.67 1027 kg

*

kg

denotes an exact value (by definition)

Table C. Approximate Coëfficients of Friction Substance Static (μs) rubber on concrete (dry) 0.90 rubber on concrete (wet) rubber on asphalt (dry) 0.85 rubber on asphalt (wet) rubber on ice steel on ice 0.03 waxed ski on snow 0.14 aluminum on aluminum 1.2 cast iron on cast iron 1.1 steel on steel 0.74 copper on steel 0.53 diamond on diamond 0.1 diamond on metal 0.1–0.15

Kinetic (μk) 0.68 0.58 0.67 0.53 0.15 0.01 0.05 1.4 0.15 0.57 0.36

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)

Page 3 Variable x

d ,d ,(

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 s

— 2 m 3 m s

meter/second

m s

m s

ω

radians/second

1 s

1 s

acceleration due to gravity

a g

meter/second

m 2 s

m s2

mass

m

kilogram*

angle area volume time velocity speed of light

θ A V t

angular velocity acceleration

v c

2

kg

kg kgm s2

force

F

newton

N

pressure

P

pascal

Pa

joule

J

kgm 2 s2

energy potential energy kinetic energy heat

E U K , Ek

kg 2

ms

Q

work

W

newton-meter

N∙m

kgm 2 s2

torque

τ

newton-meter

N∙m

kgm 2 s2

power

P

watt

W

kgm 2 s3

momentum

p

impulse

newton-second

N∙s

kgm s

moment of inertia

J I

kg∙m2

kg∙m2

angular momentum

L

N∙m∙s

kg m2 s

frequency wavelength period index of refraction electric current electric charge potential difference (voltage) electromotive force (emf)

f λ T n

I q V ε

kilogram-meter 2 newton-metersecond hertz meter second — ampere* coulomb

Hz m s — A C

s m s — A A∙s

volt

V

kg m 2 As 3

electrical resistance

R

ohm

Ω

kg m 2 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  3 A s

magnetic field

B

tesla

T

temperature kelvin* T amount of substance mole* n luminous intensity candela* Iv Variables representing vector quantities are typeset in bold italics. * = S.I. base unit

K mol cd

−1

kg A s

2

K mol cd

Physics Reference Tables

Page 4

Table E. Mechanics Formulas and Equations     d  x  x  x o Kinematics (Distance, Velocity & Acceleration)

x d v o  v    v ave. t t 2     v  v  v o  at      x  x o  d  v ot  12 at 2    v2  v o2  2ad     s  r v T  rω a T  rα

Circular Motion

ac 

v2 2 ω r r

     0  ω0 t  21 αt2      F g  mg F  Fnet  ma

Forces & Dynamics

F f   k FN

Ff  s FN r

x cm 

2

 mi x i mi

m

I   r 2 dm  mr2

Rotational Dynamics

0

2

mv r   rFsin  r F

Fc  ma c  τ  r F





 τ  τ net

  Iα

2

Simple Harmonic Motion

Ts  2

t  time (s) v  velocity

Hollow Cylinder: I  mr 2

  m s

v ave.  average velocity a  acceleration

 

 

m s

m s2

1 s



 

a c  centripetal accelerati on

Solid Cylinder: I  12 mr 2

m s2

F  force (N) F  force due to friction (N) Fg  force due to gravity (N) FN  normal force (N) Fc  centripetal force (N) m mass (kg) g  acceler ation due to gravity

  m s2

L m Tp  2 k g   Fs   kx

r  ra dius (m) r  radius (vector)   coefficient of friction ( dimensionless) θ  angle ( , rad)

  L  τ t

  W  F  d  Fd cos  Flld

W   Gm1m 2 Ug  mgh  r 2 p K 12 mv 2  2m K  12 I 2 Etotal  U  K  Q

W  K  U P

cement (m) x position (m) s  arc length (m)

d

G  gravitational constant

  p  mv    mi v i   m fv f    J  p  F net t     L  r  p  Iω L  rp sin   I 

Energy, Work & Power

Point Mass: I  mr 2

  sum d  distance (m)

1 T  f 

U s  12 kx 2

Momentum

  change, difference

f  frequency Hz 

Gm 1m 2

Fg 

Table F. Moments of Inertia

W    F  v  Fv cos   t

ω  angular velocity k spring constant

  Nm2 kg2

    rad s

N m

Hoop About Diameter: I  12 mr

2

Hollow Sphere: I  23 mr 2

x displacement of spring (m) L length of pendulum (m) τ  torque (N m) K  E k  kinetic energy (J) U  potential energy (J) h height (m) Q  heat (J)

Solid Sphere: I  25 mr

2

P  power (W) W  work (N m) T  (time) period (Hz) p ntum (N s) se (N  s)

Rod About the Middle: 1 mr2 I  12

L angular momentum (N  m  s) Rod About the End: I  13 mr 2

Physics Reference Tables

Page 5

Table G. Heat and Thermal Physics Formulas and Equations

F  1.8 (C)  32

Temperature

  change F Fahrenheit temperature ( F) C  Celsius temperature ( C)

K  C  273.15 Q  m C T

K  Kelvin temperature (K) Q  heat (J, kJ) m  mass (kg)

Qmelt  m H fus

Qboil  m Hvap

C  specific heat capacity

C p  Cv  R

T1



 const. pressure; Cv const. volume)

V2

k  coëfficient of thermal conductivity

T2

V  volume (m )



J m s C

, mWC 

3

Q T 1  kA  A T t L Ri

-1   linear coëfficient of thermal expansion ( C )

  volumetric coëfficient of thermal expansion ( C-1 ) R i  "R-valu e" of insulation

U  Q  W 3 K  kBT 2

Thermodynamics

p

t  time (s) L  length (m)

V  Vi T

V1

kJ kg C

T  temperature (K)

L  Li T

Heat

  (C

W  (PV )

R  gas constant



J  molK



U  internal energy (J) W  work (N  m)

Table H. Thermal Properties of Selected Materials

Substance

air (gas) aluminum (solid)

Melting Point (°C)

Boiling Point (°C)

Heat of Fusion

ΔH fus

Heat of Vaporization ΔH vap

kJ kg

  kJ kg

— 395

— 10460

 

Specific Heat Capacity Cp kgkJC

Thermal Conductivity

at 25°C

at 25°C

α (C -1 )

Volumetric β ( C -1 )

1.012 0.897

0.024 250

—

—

 

k

msJC 

Coefficients of Expansion at 20°C Linear

— 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

5063

0.385

401

1.7  10 5

5.1 10 5

120 2200

5

5.6  10 5 3 10 6 7.5 104

574

−78 1187

134

5

2.3  10 —

6.9  10 5 — — —

brass (solid) diamond (solid)

— 3550

— 4827

— 10 000

— 30 000

0.380 0.509

ethanol (liquid)

−117

78

104

858

2.44

0.171

1.9  10 1  106 2.5  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

3.33 105

lead (solid)

327

1750

24.7

870

0.160

35

5

−39 46–68

357 ~300

11.3 ~210

293 —

0.140 2.5

8 0.25

2.9  10 6.1 10 5 —

8.7  10 5 1. 82 104 —

962

2212

111

2360

0.233

429

2.080

0.016

1.8  10 5 —

5.4  10 5 —

4.181 2.11

0.58 2.18

6.9  10 5 —

2.07 104 —

mercury (liquid) paraffin wax (solid) silver (solid) steam (gas) @ water (liq.) @ 25°C ice (solid) @ −10°C

— 0

100

334

2260 —

Physics Reference Tables

Page 6

Table I. Electricity Formulas & Equations kq1 q 2

Fe 

E Electrostatic Charges & Electric Fields



q

r

2

Q



1 q1 q 2 4 o r 2

E

 oA

q V 2  r 4 o r

W  q E  d  qEd cos V

W q

 E d 

UE 

UE  qV

V IR

I

  change

q 4 o r

Fe  force due to electric field (N) k  electrostatic constant

kq1q 2 r

QH  heat (J) E  electric field  NC , Vm 

V2 P  V I  I R R 2

Circuits

R

V2 t R



P  power (W) ρ  resistivity (  m)

A d

Ucapacitor  12 QV  12CV 2 I  I1  I2  I 3  

(m)

 relative permittivity ( dimensionless) A  cross-sectional area (m ) U  potential energy (J) 2

Vi R eq  R 1  R 2  R 3   R i V  V1  V2  V3  

Series Circuits

1 Ctotal



1 1 1     C 1 C2 C 3

C  capacitance (F)

1

 Ci

Ptotal P1  P2  P3   Pi I  I1  I2  I3     Ii V  V1  V2  V3  

Parallel Circuits

1 1 1 1      Req R1 R2 R3

V  voltage  electric potential difference (V) W  work (N m) d  distance (m) r  radius (m) I  current (A) t  time (s) R  resistance ()

A Q V C

C   o

Nm  2 C2

q  point charge (C) Q  charge (C)

Q V  t R

2 W  QH  P t  V I...