Physics Equations, Units, and Constants

Physics Equations, Units, and Constants

Vectors

Pythagorean Theory

c2 = a2 + b2

Angles

arcTan = opposite/adjacent

arcSin = opposite/hypotenuse

arcCos = adjacent/hypotenuse

Distance

d = vit + ½at2

Velocity

v = d/t

vf = vi + at

vf = (2aΔd)½

Acceleration

a = Δv/t

Newton's Second Law of Motion (Law of Acceleration)

F = ma

F = mg

1 Newton (N) = 1 kg-m/s2

g = 9.8 m/s2

Newton's Law of Universal Gravitation

F = G(m1m2)/d2

G = 6.67 x 10-11 N-m2/kg2

Coefficient of Friction

μ = Ff / Fn

Resolution of Forces

Fp = FH = Fw cosΘ

FN = FV = Fw sinΘ

Circular Motion

Acceleration

a = v2/r

Centripetal Force

Fc = mv2/r

Critical Velocity

vmin = (rg)½

Periodic Motion

Period of Pendulum

T = 2π(l/g)½

Work

W = Fd

1 joule (J) = 1 N-m

Power

p = W/Δt

1 watt (W) = 1 J/s

Efficiency

Eff = (Woutput / Winput) x 100

Potential Energy

Ep = Fd = mgΔh

Kinetic Energy

EK = ½mv2

Elastic Potential Energy

Ep = ½k(Δd)2

Momentum

p = mv

Impulse

FΔt = mΔv

Conservation of Momentum

mava = mbvb

Accuracy - Absolute Error

Ea = O - A

Accuracy - Relative Error

ER = (Ea/A) x 100

Precision - Absolute Deviation

Da = O - M

Precision - Relative Deviation

Dr = (Da (avg)/M) x 100

Temperature Conversions

oC = (5/9)(oF - 32)

oF = ((9/5)oC) + 32

K = oC + 273

Specific Heat Equation

Q = mcΔT

Specific Heat

c = J/g-oC

Law of Heat Exchange

Qlost = Qgained

Heat of Fusion Equation

Q = mLf

Heat of Fusion

Lf = J/g

Heat of Vaporization Equation

Q = mLv

Heat of Vaporization

Lv = J/g

Entropy

ΔS = ΔQ/T

ΔS = joules per kelvin

Ideal Gas Law

PV = nRT

Universal Gas Constant

R = 0.0821 L-atm/mol-K

Linear Expansion

Δl = αlΔT

Volume Expansion

ΔV = βVΔT

Coefficient of Linear Expansion and Volume Expansion

β = 3α

Period

T = 1/f

Frequency

f = v/λ

Doppler Effect

f ' = f (v±vo)/(v±vs)

Speed of Sound

In Air = 343 m/s + 0.6 m/s/oC x T

Law of Strings - Length

f/f ' = l '/l

Law of Strings - Diameter

f / f ' = d'/d

Law of Strings - Tension

f / f ' = (F)½/(F')½

Law of Strings - Densities

f / f ' = (D')½/(D)½

Fundamental Resonant Wavelength- Closed Tube

λ = 4(l + 0.4d)

Fundamental Resonant Wavelength - Open Tube

λ = 2(l + 0.8d)

Electromagnetic Wave Energy

E = hf

Plank's Constant = h = 6.63 x 10-34 J-s

Electromagnetic Wave Frequency

f = c/λ

c = speed of light = 3 x 108 m/s

Electromagnetic Wave Wavelength

λ = h/mv

Focal Length of a Mirror

1/f = 1/do + 1/di

Relationship between Object and Image Size

hi/ho = di/do

Index of Refraction (Snell's Law)

Index of Refraction (n) = sin i/sin r

Index of Refraction (n) = speed of light in a vacuum/speed of light in referenced material

Critical Angle (ic)

ic = 1/n

Diffraction Grating Equation

λ = d sin Θn/n

Coulomb's Law of Electrostatics

F = kQ1Q2/d2

Q = coulombs (C)

k = 8.987 x 109 N-m2/C2 for vacuum and 8.93 x 109 N-m2/C2 for air

Electric Field Intensity

E = F/q

Capacitance

C = Q/V

1 farad (F) = 1 coulomb/ 1 volt

1 coulomb = 6.25 x 1018 electrons

1 electron (e-) = 1.60 x 10-19 C

1 electron = 1.67 x 10-27 kg

Potential Difference

V = W/q

1 volt = 1 joule/ 1 coulomb

Potential Difference Gradient

V/m = N/C

Parallel Circuits

CT = C1 + C2 + C3

QT = Q1 + Q2 + Q3

VT = V1 = V2 = V3

Series Circuits

1/CT = 1/C1 + 1/C2 + 1/C3

QT = Q1 = Q2 = Q3

VT = V1 + V2 + V3

Ohm's Law of Resistance

V = IR

Current in a Circuit

I = Q/t

1 amp (A) = 1 coulomb (C)/ time (s)

Power in Electric Circuits

P = VI = I2R = V2/R

Work in Electric Circuits

W = Pt = I2Rt = QV = Vit

Series Circuits

RT = R1 + R2 + R3

IT = I1 = I2 = I3

VT = V1 + V2 + V3

Parallel Circuits

1/RT = 1/R1 + 1/R2 + 1/R3

IT = I1 + I2 + I3

VT = V1 = V2 = V3

Magnetic Flux Density

B = Φ/A

B = 2 x 10-7 (N/A2) I/r or B = 2kI/r

B = magnetic flux density (N/A-m)

Φ = magnetic flux in webers (Wb)

F = kM1M2/d2

Magnetic Force

F = 2 x 10-7(N/A2) lI1I2/d

I = current (Amperes [A])

d = distance (meters [m])

A = area (meters2 [m2])

Magnetism Units

1 weber (Wb) = 1 N-m/A

r = radius (meters [m])

F = force (Newtons [N])

1 Tesla (T) = 1 weber/m2 = 1 Wb/m2 = 1 N/m-A

Prefixes and Numerical Values

The use of prefixes with basic metric units gives units that are multiples or submultiples based on

powers of 10 (Orders of Magnitude).

peta (P) = 1,000,000,000,000,000 = 1015

tera (T) = 1,000,000,000,000 = 1012

giga (G) = 1,000,000,000 = 109

mega (M) = 1,000,000 = 106

kilo (k) = 1,000 = 103

deka (da) = 10 = 101

deci (d) = 0.1 = 10-1

centi (c) = 0.01 = 10-2

milli (m) = 0.001 = 10-3

micro (μ) = 0.000001 = 10-6

nano (n) = 0.000000001 = 10-9

pico (p) = 0.000000000001 = 10-12

femto (f) = 0.000000000000001 = 10-15

atto (a) = 0.000000000000000001 = 10-18