Pleasant Valley High School Physics Reference

SI Base Units Quantity Name Symbol

Amount of Substance mole mol Electric Current ampere A Length meter m Luminous Intensity candela cd Mass kilogram kg Temperature kelvin K Time second s

SI Derived Units Quantity Unit Base Expression

Acceleration m/s2 - Area m2 - Capacitance Farad (F) A2·s4/kg·m2 Density kg/m3 -

Electric Charge Coulomb (C) A·s Electric Field N/C kg·m/A·s3

Electric Resistance Ohm (Ω) kg·m2/A2·s3

Energy, Work Joule (J) kg·m2/s2

EMF Volt (V) kg·m2/A·s3 Force Newton (N) kg·m/s2 Frequency Hertz (HZ) s-1 Illuminance Lux (Lx) Cd/m2 Magnetic Field Tesla (T) Kg/A·s2 Potential Difference Volt (V) kg·m2/A·s3 Power Watt (W) kg·m2/s3 Pressure Pascal (Pa) Kg/m·s2 Velocity m/s - Volume m3 -

SI Prefixes Prefix Symbol Meaning Factor Exa E Quintillion 1018

Peta P Quadrillion 1015

Tera T Trillion 1012 Giga G Billion 109 Mega M Million 106 Kilo k Thousand 103

Hecto h Hundred 102 Deka da Ten 101

Base Deci d Tenth 10-1 Centi c Hundredth 10-2 Milli m Thousandth 10-3 Micro µ Millionth 10-6 Nano n Billionth 10-9 Pico p Trillionth 10-12

Femto f Quadrillionth 10-15

Atto a Quintillionth 10-18

Common Indices of Refraction Air 1.00 Glass, Flint 1.61

Alcohol 1.36 Glycerol 1.47 Corn Oil 1.47 Lucite 1.50 Diamond 2.42 Quartz 1.46

Glass, Crown 1.52 Water 1.33

Constants Name Symbol Value

Acceleration of Gravity g 9.801 m/s2 Atomic Mass Unit u 1.66 x 10-27 kg Avogadro’s # NA 6.022 x 1023 /mol Boltzman Constant k 1.38 x 10-23 J/K Coulomb’s Law Constant K 9.0 x 109N m2/C2 Electron Mass me 9.11 x 10-31 kg Elementary Charge e -1.602 x 10-19 C Gravitational Constant G 6.67 x10-11

N•m2/kg2

Molar Gas Constant R 8.314 L•J/mol•K Neutron Mass mn 1.6749 x 10-27 kg Permeability of Vacuum µo 4π x 10-7N/A2 Permittivity of Vacuum εo 8.85 x 10-12F/m Planck’s Constant h 6.63 x 10-34 Js Proton Mass mp 1.6726 x 10-27 kg Sound – Ref. Intensity Io 1.0 x 10-12 W/m2 Speed of Light (Vacuum) c 2.998 x 108 m/s Speed of Sound (20oC) 343 m/s Standard Pressure SAP 101.325 kPa Stefan-Boltzmann σ 5.67 x 10-8 W/m2K4 Conversion Factors

1L = 1 dm3 = 1000 mL = 1000cm3 1 atm = 760 mm Hg = 101.325 kPa = 1.01 x 105 N/m2

1 cal = 4.184 J 1 lb = 4.45 N 1 ev = 1.6 x 10-19 J 1 oz ~ 28.4 g 1 inch = 2.54 cm 1 kg ~ 2.21 lb 1 mile = 1.61 km 1 atm = 1 lb/in2

1 rad = 57.3o = 0.159 rev 1 KWh = 3.60 MJ Planetary Data

Name Avg. Radius (m)

Mass (kg) Avg. Distance from Sun (m)

Sun 696 x 106 1.99 x 1030 - Mercury 2.44 x 106 3.30 x 1023 5.79 x 1010 Venus 6.05 x 106 4.87 x 1024 1.08 x 1011 Earth 6.38 x 106 5.97 x 1024 1.50 x 1011 Mars 3.40 x 106 6.42 x 1023 2.28 x 1011 Jupiter 71.5 x 106 1.90 x 1027 7.78 x 1011 Saturn 60.3 x 106 5.69 x 1026 1.43 x 1012 Uranus 25.6 x 106 8.66 x 1025 2.87 x 1012 Neptune 24.8 x 106 1.03 x 1026 4.50 x 1012 Pluto 1.15 x 106 1.5 x 1022 5.91 x 1012 Physical Data for Water

Quantity Value Water - Specific Heat (solid) 2.06 J/goC Water - Specific Heat (liquid) 4.184 J/goC Water - Specific Heat (gas) 2.02 J/goC Water - Enthalpy of Fusion 334 J/g Water - Enthalpy of Vaporization 2260 J/g Freezing Point 0.0oC or 273 K Boiling Point 100.0oC or 373 K

Alphabetic Variables

Useful Atomic Data Symbol Quantity Value

me Mass of Electron 9.109 x 10-31 kg

5.49 x 10-4 u

mn Mass of Neutron 1.675 x 10-27 kg

1.008665 u

mp Mass of Proton 1.673 x 10-27 kg

1.007276 u

Greek Variables

Coefficients of Friction

Material µs µk

Steel / Steel 0.74 0.57 Aluminum / Steel 0.61 0.47

Rubber / Dry Concrete 1.0 0.8 Rubber / Wet Concrete - 0.5

Wood / Wood 0.4 0.2 Glass / Glass 0.9 0.4

Ice / Ice 0.1 0.03 Wood / Wet Snow 0.14 0.1 Wood / Dry Snow - 0.04

Human Synovial Joints 0.01 0.003

Densities Specific Heat Capacities

Substance Ρ (kg/m3) Substance Cp (J/kgoC) Air 1.29 Aluminum 8.99x102

Fresh Water (4oC) 1.00x103 Copper 3.87x102 Sea Water (15oC) 1.025x103 Glass 8.37x102 Aluminum 2.70x103 Gold 1.29x102 Iron 7.86x103 Ice 2.09x103 Copper 8.92x103 Iron 4.48x102 Silver 10.5x103 Lead 1.28x102 Lead 11.3x103 Mercury 1.38x102 Mercury 13.6x103 Silver 2.34x102 Gold 19.3x103 Steam 2.01x103 Glycerine 1.26x103 Water 4.184x103

A-a acceleration, Area, Ax = Cross-sectional Area, Amperes, Amplitude of a Wave, Angle

B-b Magnetic Field, Decibel Level of Sound, Angle

C-c specific heat, speed of light, Capacitance, Angle, Coulombs, oCelsius, candela

D-d displacement, differential change in a variable, Distance, Distance Moved, distance

E-e base of the natural logarithms, charge on the electron, Energy

F-f Force, frequency of a wave or periodic motion, Farads

G-g Universal Gravitational Constant, acceleration due to gravity, Gauss, grams, Giga-,

H-h depth of a fluid, height, vertical distance, Henrys, Hz=Hertz

I-i Current, Moment of Inertia, image distance, Intensity of Sound

J-j Joules

K-k

K or KE = Kinetic Energy, force constant of a spring, thermal conductivity, coulomb's law constant, kg=kilograms, Kelvins, kilo-, rate constant for Radioactive decay =1/τ=ln2 / half-life

L-l Length, Length of a wire, Latent Heat of Fusion or Vaporization, Angular Momentum, Thickness, Inductance

M-m mass, Total Mass, meters, milli-, Mega-, mo=rest mass, mol=moles

N-n index of refraction, moles of a gas, Newtons, Number of Loops, nano-,

O-o -

P-p Power, Pressure of a Gas or Fluid, Potential Energy, momentum, Power, Pa=Pascal

Q-q Heat gained or lost, Maximum Charge on a Capacitor, object distance, Flow Rate

R-r radius, Ideal Gas Law Constant, Resistance, magnitude or length of a vector, rad=radians

S-s speed, seconds, Entropy, length along an arc

T-t time, Temperature, Period of a Wave, Tension, Teslas, t1/2=half-life

U-u Potential Energy, Internal Energy V-v velocity, Volume, Voltage, Volts W-w weight, Work, Watts, Wb=Weber

X-x distance, horizontal distance, x-coordinate east-and-west coordinate

Y-y vertical distance, y-coordinate, north-and-south coordinate

Z-z z-coordinate, up-and-down coordinate

Α-α Alpha angular acceleration, coefficient of linear expansion

Β-β Beta coefficient of volume expansion, Lorentz transformation factor

Γ-γ Gamma surface tension = F / L, 1 / γ = Lorentz transformation factor

∆-δ Delta ∆=change in a variable Ε-ε Epsilon εο = permittivity of free space Ζ-ζ Zeta - Η-η Eta - Θ-θ Theta angle between two vectors

Ι-ι Iota - Κ-κ Kappa dielectric constant

Λ-λ Lambda wavelength of a wave, rate constant for Radioactive decay =1/τ=ln2/half-life

Μ-µ Mu friction, µo = permeability of free space, micro-

Ν-ν Nu alternate symbol for frequency Ξ-ξ Xi - Ο-ο Omicron - Π-π Pi Osmotic pressure, 3.14159 Ρ-ρ Rho density, resistivity Σ-σ Sigma Summation, standard deviation

Τ-τ Tau torque, time constant for exponential processes; eg τ=RC or τ=L/R or τ=1/k=1/λ

Υ-υ Upsilon - Φ-φ Phi Magnetic Flux, angle Χ-χ Chi - Ψ-ψ Psi - Ω-ω Omega angular speed or angular velocity, Ohms

Formulae General

bmxy +=

Linear

x

ym

∆∆=

Slope

2

Quadratic

kxy =

1

Inverse−

= kxy

hyp

opp=θsin

hyp

adj=θcos

adj

opp=θtan

θcos2

Cosines of Law222 abbac −+=

c

C

b

B

a

A sinsinsin

Sines of Law

==

a

acbbx

2

4

Formula Quadratic2 −±−=

V

m=ρ

Density

Geometric Relationships Trigonometric Identities

Circle Circumference rC π2= 1cossin 22 =+ xx

Circle Area 2rA π= yxyxyx sincoscossin)sin( ±=±

Cylinder Surface Area 222 rrhSA ππ += yxyxyx sinsincoscos)cos( m=±

Cylinder Volume hrV 2π=

yx

yxyx

tantan1

tantan)tan(

m

±=±

Sphere Surface Area 24 rSA π= xxx cossin22sin =

Sphere Volume ( )3

3

4rV π=

xxx 22 sincos2cos −=

Stats

Accepted

Accepted-alExperiment Error Fractional = 100

Accepted

Accepted - alExperiment Error % x=

∑=

=

N

iix

1N

1 ValueMean 100

2

x Difference %

12

12 xxx

x

+−= xx −== 11d Deviation Absolute

∑=

=

N

iid

1N

1d :Deviation Mean

2

1

)(N

1 :Deviation Standard ∑

=

−=

N

ii xxσ

Simple Motion & Acceleration

t

dv =

t

va

∆= atviv f += tvvd if )(2

1+= 2

2

1attvd i += advv if 222 +=

Forces

maF = mgW = Nf FF µ= 2112 FF −=

Motion in Two Dimensions

tvx x= 2

2

1gttvy y += gtvv yfinaly +=)(

g

lT π2=

g

vR o θ2sin2

= g

vT o θsin2=

r

vac

2

= 2

24

T

rac

π=

= 2

24

T

rmFc

π

T

rvπ2

= kxF −=

Universal Gravitation

32

=

b

a

b

a

r

r

T

T

221

d

mGmF =

r

mGv E=

EGm

rT

3

2π= 2

E

E

r

mGg =

2

=r

rga E

m

Fg =

Rotational Motion

r

s=θ

r

v=ω

r

aT=α raR2ω=

2

2

1ttii αωθθ ++= ti ωθθ += tfoi )(

2

1 ωωθθ ++=

tif αωω += αθωω 222 += if ∑= 2iirmI ωIL = ffii II ωω = vrmL ∆= ⊥= Fdτ

θτ sinFr= ατ I= KEW ∆= 2

2

1ωIKE = τω=P

Momentum

mvp = vmFt ∆= ptF ∆=∆ r

v=ω fπω 2= rac

2ω= T

f1=

t

vrm∆=τ

Work and Simple Machines

dFW ∆= θ∆= FrW θτ∆=W t

WP =

r

e

l

lMA =

e

r

F

FMA = rrout dFW = eein dFW =

r

e

d

dIMA = 100x

W

WEff

in

out= 100xIMA

MAEff =

Energy

mgdU =∆ 2

2

1mvKE = KEW ∆= 22

2

1ωmrKErot = 2

2

1ωIKErot

21

2

mr

Igh

v+

= UKEME +=

2

2

1kxU s =

Pressure

A

FP = ghP ρ= hgP ∆=∆ ρ

C

F

2=γ VgF ρ=

rgh ρ

θγ cos2= 2211 vAvA = VghW ∆= ρ

fi ghvPghvP ρρρρ ++=++ 222

211 2

1

2

1

Thermal Physics

TLL o ∆=∆ α TVV o∆=∆ β ( )( )oo TTLL −+= α1 pTCmQ ∆= fHmQ ∆= vHmQ ∆= K

LR =

( )

L

TTKA

t

Q 12 −=∆∆

4eATP σ= WQU −=∆ )()( kt

sost eTTTT −−+=

Waves

fv λ= f

T1=

r

inθθ

sin

sin= rrii nn θθ sinsin =

io ddf

111+=

c

nθsin

1= T) m/s. . ( vs 605331 +=

)(log10 10oI

I=β

v

cn =

1

2sinn

nc =θ hfE =

±±=

s

dsd vv

vvff

24 r

PEπ

=

π4

PI =

θ212 cosII = )1(

c

vffobs ±=

c

vobs λλλ ±=− )(

21

22

2

1

r

r

I

I= Ir4P 2π=

Electricity

2d

qKqF

′= IRV = IVP = RIP 2=

R

VP

2

= PtE = q

FE q

′= ′

2

'

d

kqE =

V

QC

∆=

d

AC oε=

d

AkC oε= QVW ∆=

21 2

21

CVW = CQW 2

21=

Series Parallel

321 IIIIT === 321 IIIIT ++=

321 RRRRT ++= 321

1111

RRRRT

++=

321 VVVVT ++= 321 VVVVT ===

...1111

321 CCCCT

++= ...321 CCCCT ++=

Magnetism

θsinqvBF = θsinIBlF = θτ sinNBIA= θτ sinBIA= AnqvI d= BqvF = BLvEMF =

qB

mvr =

qB

pr =

Moments of Inertia