Velocity Vectors

X = 

Y = 

Velocity Vectors

X = V cosθ

Y = V sinθ

Kinematic Equations

V = 

ΔX =

V­²= 

Kinematic Equations

V = V₀ + at

ΔX = V₀t + at²_/2

V­²= V₀² + 2aΔX

Torque

τ= 

Torque

τ= rF sinθ

Centripetal Motion

F = 

a =

Centripetal Motion

F = mV²/r

a = V²/r

Noconserv. Forces

W =     = 

Noconserv. Forces

W =   ΔE  = ΔK + ΔU

Work

W = 

Work

W = Fd cosθ

Work/Energy Theorem

W = 

Work/Energy Theorem

W = ΔKE

Momentum

p = 

Momentum

p = mV

Impulse

I =    = 

Impulse

I =  FΔt  = Δp

Electrostatic Force

F = 

Electrostatic Force

F = Kq₁q₂/r²

Electric Field Mag

E =   = 

Electric Field Mag

E = F/q₀  = Kq/r²

Electric Potent. Energy

U =  = 

Electric Potent. Energy

U = KqQ/r = Vq₀

Electric Potential

V =  =  = 

Electric Potential

V = W/q₀ = Kq/r = Ed

Electric Potential

Near Dipole

V = 

P =

Electric Potential

Near Dipole

V = [KP/r²] cosθ

P = qd

E-Field Perpendicular Bisector

E = 

E-Field Perpendicular Bisector

E = KP/r³

Torque on Dipole via E-Field

τ = 

Torque on Dipole via E-Field

τ = pE sinθ

Force Moving Charge

F = 

Force Moving Charge

F = qvβ sinθ

Centripetal Mag Force

F =

V = 

Centripetal Mag Force

F = mV²/r

V = qrβ/m

Resistance

R = 

Resistance

R = ρ L/A

Ohm’s Law

V = 

ε = 

Ohm’s Law

V = iR

ε = iR + ir

Power in Circuit

P = 

Power in Circuit

P = iV

Power Diss. by Resist.

P = =

Power Diss. by Resist.

P = i²R = V²/R

Resistors in Parallel

R_p = 

Resistors in Parallel

R_p = 1/R₁ + 1/R₂

Capacitance

C =   = 

E = 

Capacitance

C =  Q/V = Kε₀ (A/d)

E = V/d

PE Capacitor

U = 

PE Capacitor

U = ½ CV²

Capacitor Series

C_s= 

Capacitor Series

C_s= 1/C₁ + 1/C₂

RMS

I_rms = 

V_rms = 

RMS

I_rms = I_max / √2

V_rms = V_max / √2

Rest Force on Spring

F = 

Rest Force on Spring

F = - kΔx

Spring Acceleration

a = 

ω =  =  =

Spring Acceleration

a = - ω²x

ω = 2πF = √k/m =2π/T

Potential Energy in a Spring

U = 

U = ½ kx²

KE in a Spring

K = 

KE in a Spring

K = ½ mv²

Rest. Force Pendulum

F = 

Rest. Force Pendulum

F = - mgSinθ

Ang. Freq. Pendulum

ω =  =   

Ang. Freq. Pendulum

ω =  2πF = √g/L   

Wave Speed

V =   =  = 

Wave Speed

V =  Fλ =  w/k = λ/T

Sound Intensity

I = 

Sound Intensity

I = Power/Area

Sound Level

β = 

β_f = 

Sound Level

β = 10 log[I/I₀]

β_f = β_i + 10 log[I_f/I_i]

Beat Frequency

F_beat = 

Beat Frequency

F_beat = [F₁ – F₂]

Doppler Effect

F’ = 

Doppler Effect

F’ = F [ V±V_d/V±V_s]

String Harmonics/Open Pipes

λ =         F = 

String Harmonics/Open Pipes

λ = 2L/n   F = nV/2L

Closed Pipes

λ =            F =  

Closed Pipes

λ = 4L/n     F = nV/4L

Thermal Expansion

ΔL = 

ΔV =   β = 

Thermal Expansion

ΔL = αLΔT

ΔV = βVΔT  β = 3α

Total Internal Energy

ΔU = 

U = 

Total Internal Energy

ΔU = Q -W

U = [3/2]nRT

Heat Transfer

Q = 

Heat Transfer

Q = mcΔT

Phase Change

Q = 

Phase Change

Q = mL

Work (P&V)

W =

Work (P&V)

W = PΔV

Entropy

ΔS =      =       

Entropy

ΔS = Q/T = L (m/T)       

Density

ρ = 

Density

ρ = m/v

Pressure

P = 

Pressure

P = F/A

Absolute Pressure

P =

Absolute Pressure

P = P⁰ + ρgh

Pascal’s Principle

P =  = 

V =  = 

W =  = 

Pascal’s Principle

P =  F₁/A₁ = F₂/A₂

V = A₁d₁ = A₂d₂ 

W =  F₁d₁ = F₂d₂

Buoyant Force

F_buoy  = 

Buoyant Force

F_buoy  = ρVg

Critical Velocity in a Tube

V_c = 

Critical Velocity Tube

V_c = N_Rn/ρD

Fluid Continuity

V₁A₁ = 

Fluid Continuity

V₁A₁ = V₂A₂    

Bernoulli’s Equation

= 

Bernoulli’s Equation

P₁ + ρv₁²/2 + ρgy₁ = P₂ + ρv₂²/2 + ρgy₂

Young’s Modulus

Y =

Young’s Modulus

Y =[FA]/[ΔL/L]

Shear Modulus

S =

Shear Modulus

S =[FA]/[x/h]

Bulk Modulus

B =

Bulk Modulus

B =[FA]/[ΔV/V]

Mirror Equation

     =            =

Mirror Equation

     1/o + 1/I = 1/f = 2/r

Magnification

M = 

Magnification

M = - i/o

Snell’s Law

= 

                            Θ_critical = 

Snell’s Law

n₁ sinθ₁= n₂ sinθ₂

Θ_critical = Sin^-1 n₂/n₁

Lens Power

P = 

Lens Power

P = 1/f

Lenses in Contact

M =

Lenses in Contact

M = m₁*m₂*m₃

Not in Contact

1/f =

P = 

Not in Contact

1/f = 1/f₁ + 1/f₂ +1/f₃ 

P = P₁ + P₂ + P₃

Lensmaker EQ (Thick)

1/f= 

Lensmaker EQ (Thick)

1/f= (n-1) (1/r₁ – 1/r₂)

Energy of Photon

E = hf

Energy of Photon

E = hf

Max KE Ejected e^-

K_max = 

W =

Max KE Ejected e^-

K_max = hf - W

W = hf_t

Angular Momentum e^-

L =        = 

Angular Momentum e^-

L = nh/2π = mvr

Energy of e ^-

E =         =      

Energy of e ^-

E = -R_h/n² =-13.6eV/n²

Exponential Decay

n = 

λ = 

Exponential Decay

n = n₀ e^{- λt}

λ = 0.7/t_1/2

KE Gas Particle

KE = 

KE Gas Particle

KE = 3/2 KT

RMS Speed

μ_rms= 

RMS Speed

μ_rms= √3RT/m

Rate Effus/Diffusion

r₁/r₂= 

Rate Effus/Diffusion

r₁/r₂= √μ₂/μ₁

Gas Density

d = 

Gas Density

d = m/V₂

Gas Molar Mass

M = 

Gas Molar Mass

M = (d_STP)(V_STP)

Boyle’s Law

P₁V₁ = 

Boyle’s Law

P₁V₁ = P₂V₂

Charles’ Law

V₁/T₁ = 

Charles’ Law

V₁/T₁ = V2/T2

Collision Theory Rate

Rate = 

Collision Theory Rate

Rate = fZ

Enthalpy

ΔH_rxn =

Enthalpy

ΔH_rxn = H_prod - H_react

Bond Dissoc. Energy

ΔH°_rxn = 

Bond Dissoc. Energy

ΔH°_rxn = ΔH_brkn + ΔH_frmd

ΔS°_rxn = 

Gibbs Free Energy

ΔG = 

ΔG°_rxn = 

Gibbs Free Energy

ΔG = ΔH - TΔS

ΔG°_rxn = ΔG°_prod - ΔG°_reac

ΔG°_rxn  (Keq)=

ΔG°_{rxn (Keq & Q)}= 

ΔG _{(ΔG° & Q)} =

ΔG°_rxn  (Keq)= -RT lnK_eq

ΔG°_{rxn (Keq & Q)}= RT ln (Q/K_eq)

ΔG _{(ΔG° & Q)} =ΔG°+RT lnQ

Gibbs Phase Fn @ Eq

G (liq.) =

Gibbs Phase Fn @ Eq

G (liq.) = G (s)

Raoult’s Law

P_A = 

ΔP = 

Raoult’s Law

P_A = X_AP^o

ΔP = X_BP^o

FP & BP Elevation

ΔT_b = 

ΔT_f = 

FP & BP Elevation

ΔT_b = iK_bm

ΔT_f = iK_fm

Osmotic Pressure

Π = 

Osmotic Pressure

Π = imRT

Dilution

M_iV_i = 

Dilution

M_iV_i = M_fV_f

Solubility Prod. Const.

ABè

K_sp = 

Solubility Prod. Const.

ABèxA+yB

K_sp = [A]^x[B]^y

H₂O Diss. Cnst @ 298K

K_w =            =

H₂O Diss. Cnst @ 298K

K_w =[H₃O⁺][OH^-] =10^-14

pH

pH =                       =

pH = - log [H⁺] =log 1/[H⁺]

pOH

pOH =                     = 

pOH

pOH = - log [OH^-]  = log 1/[OH^-]

Acid Dissoc. Constant

K_a =

Acid Dissoc. Constant

K_a = [H+][A-]/[HA]

Base Dissoc. Constant

Kb = 

Base Dissoc. Constant

K_b = [OH-][B+]/[BOH]

Titration

N_aV_a = 

Titration

N_aV_a = N_bV_b

Henderson-Hasslebach

pH = 

pOH = 

Henderson-Hasslebach

pH = pKa + log c. base/w. acid

pOH= pKb + log c. acid/w. base

Faraday’s Equation

= 

F = 

Faraday’s Equation

it = nf

F = 10⁵  C/mol e^-

EMF

Emf ° =

ΔG = 

EMF

Emf ° =E°_cathode-E°_andode

ΔG = - nf E°_cell

Nernst Equation

E_cell =

Nernst Equation

E_cell = E°_cell -(RT/nf) ln Q

Specific Rotation

[α] = 

Specific Rotation

[α] = α observed/ conc'n*length

Rate of S_N1

Rate =

Rate of S_N1

Rate = [RL]

Rate of S_N2

Rate = 

Rate of S_N2

Rate = [RL][Nuc:]

Electrophoresis Migratory velocity

V = 

Electrophoresis Migratory velocity

V = EZ/f

Hardy-Weinberg EQ

= 1

= 1

Hardy-Weinberg EQ

P²+²pq+q² = 1

P + q = 1

Diffraction Min/Max

=

Diffraction Min/Max

a Sinθ = nλ

Gauge Pressure

P_g=

Gauge Pressure

P_g= P - P_atm

Magnetic Field

β_{(long straight wire)}= 

β_{(center loop)}=

Magnetic Field

β_{(long straight wire)}= μi/2πr

β_{(center loop)}= μi/2r