Oops All Formulas

Fg = mg

Gravitational force near Earth's surface

ΔV = Ed

Change in voltage as you move through an electric field

U = kq₁q₂/r

Electrical potential energy between two point charges

E=hf

Energy of a photon

Fgravitational = Gm₁m₂/r²

Gravitational force between two masses

Felectric = qE

Electric force on a charge in an electric field

Felectric = kq₁q₂/r²

Electric force between two charges

E = kQ/r²

Electric field strength at a distance from a point charge

ΔU = qEd

Electrical potential energy as a charge moves through a field

V = kQ/r

Voltage at a distance from a point charge

I = P/A

Intensity of a wave

(I₁r₁²) = (I₂r₂²)

Intensity of a wave decreases with distance (inverse square law)

Decibels = 10 log(I/I₀)

Sound intensity level in decibels

fbeat = |f₁ - f₂|

Beat frequency from two interfering sound waves

ω = 2πf

Angular frequency

f(perceived) = f(emitted) [v(wave) ± v(detector)] / [v(wave) ± v(source)]

Doppler effect

ω = √(g/L) (Pendulum)

Angular frequency of a pendulum

ω = √(k/m) (Spring)

Angular frequency of a mass-spring system

P(total) = P(atmospheric) + P(gauge)

Total pressure

Fraction of object submerged = density(object) / density(fluid)

Fraction of a floating object submerged in fluid

P + 1/2rho*v² + rho*g*h = constant

Bernoulli's equation

T = F/d

Surface tension

C = (kε₀A)/d

Capacitance of a parallel plate capacitor

Pconduction = (kAΔT)/L

Rate of heat conduction

Y = (F/A) / (ΔL/L)

Young's modulus (elasticity of materials)

ΔL = αLΔT

Linear thermal expansion

ΔV = βVΔT

β = 3α

Volumetric thermal expansion

Fnet(centripetal) = mv²/r

Centripetal force

a(centripetal) = v²/r

Centripetal acceleration

ΔU = Q + W

Change in internal energy (First law of thermodynamics)

P(radiation) = kAT⁴

Radiated power (Stefan-Boltzmann law)

U = 3/2nRT

Internal energy of an ideal gas

Fnet = ma

Net force

F=kx

Force exerted by a spring

Fmax static = Mu_s*N

Maximum static friction

Fkinetic = mu_k N

Force of Kinetic friction

Fbuoyant = Rho_fluid V_submerged g

Buoyant force

a = DeltaV/t

Acceleration

d = vt

Distance traveled

P = DeltaE/t

Power in terms of energy

P = Fv

Power in terms of force and velocity

P = IV

Electrical power

P = I²R

Power dissipated in a resistor (current)

P = V²/R

Power dissipated in a resistor (voltage)

Fmagnetic = qvBsin(θ)

Magnetic force on a charged particle

Torque = rFsin(θ)

Torque (rotational force)

Fnet = mg sin(θ)

Net force on an incline

Fnormal = mg cos(θ)

Normal force on an incline

Vf = V₀ + at

Final velocity (with constant acceleration)

d = d_⁰ + V₀t + 1/2 at²

Displacement (with constant acceleration)

Vf² = V₀² + 2ad

Final velocity squared

g (other planet) = GM/r²

Gravitational acceleration on another planet

KE = 1/2 mv²

Kinetic energy

W = Fd cos(θ)

Work done by a force

Wnet = Fnet d cos(θ)

Net work

U = mgh

Gravitational potential energy

Uspring = 1/2 kx²

Potential energy stored in a spring

Uelectrical = qV

Electrical potential energy of a charge at a particular voltage

V = kQ/r

Electric potential (point charge)

W = -Fkinetic d

Work done by friction

v = fλ

Wave speed

I = q/t

Electric current

V = IR

Ohm's Law

R = ρL/A

Resistance (based on material and geometry)

Req = R₁ + R₂ + R₃...

Equivalent resistance (series circuit)

1/Req = 1/R₁ + 1/R₂ + 1/R₃...

Equivalent resistance (parallel circuit)

Q = CV

Charge on a capacitor

Ceq = C₁ + C₂ + C₃...

Equivalent capacitance (parallel circuit)

1/Ceq = 1/C₁ + 1/C₂ + 1/C₃...

Equivalent capacitance (series circuit)

U = 1/2 Q²/C

U = ½ CV²

U = ½ QV

Energy stored in a capacitor (3 Formulas)

P = 1/f

Power of a lens

n=c/v

Index of Refraction

n1*sin(theta1) = n2*sin(theta2)

n * sin(theta) = constant

Snell’s Law

f = ½ r

Focal Length of a Spherical Mirror

1/f = 1/do + 1/di

relationship between the focal length of a system, the object distance, and the image distance

m = -di/do

magnification

PV=nRT

P=Pressure

V=Volume

n=moles of gas

R=Gas Constant

T=Temp in K

Ideal Gas Law

moles solute / liter solvent

Molarity

moles solute / kg solvent

Molality

How many particles a substance dissociates into per one compound

Examples

• C₆H₁₂O₆ i=1

• NaCl i=2

• Ca₃(PO₄)₂ i=5

• NH₄Cl i=2

Particle Dissociation Factor / Van’t Hoff Factor

P_{Vap Solution} = P_{Vap pure liquid} * X_Solvent

X_solvent = mole fraction of solvent

Vapor pressure formula

X_solvent = Moles of solvent / (Moles of solute + moles of solvent)

Mole fraction of solvent

ΔT_B = K_Bmi

ΔT_B will always be positive and represents the amount which the boiling point raises

Boiling Point Elevation

ΔT_F=K_Fmi

ΔT_F will always be positive and always means the amount by which the freezing point LOWERS

Freezing Point Depression

𝛑 = iMRT

• T is temp in KELVIN

• M is MOLARITY instead of m which is molality

• R = 0.08

• Pi is a variable NOT the constant 3.14

Osmotic Pressure

1/F_eq = 1/F₁ + 1/F₂

Equivalent Focal Length of a Multi-Lens System

Flow = ΔPπr⁴ / 8Lη

• ΔP is the pressure difference across the pipe

• r is the radius of the pipe

• L is the length of the pipe

• η is the viscosity of the fluid in the pipe

Poiseuille’s Law

F = ILBsin(theta)

• I = current

• L = length

• B = magnetic field

• Theta = angle between the wire and the field lines

Still use right hand rule with

• thumb = wire

• Fingers = magnetic field

• Palm = magnetic force

Magnetic Force produced by a Current Carrying Wire in a Magnetic Field

m_eq = m₁ * m₂ * m₃ …

Equivalent magnification of a multi-lens system

ΔG = nFE_cell

• n = moles of e^- involved in a redox reaction

• F = Faraday’s Constant (10⁵ C per mol e^-)

  • 1 Faraday of charge = 10⁵ C = charge in 1 mol e^-

• E_cell = voltage of the redox reaction

ΔG in Redox Reactions

ΔG = -RTln(K_eq)

Delta G with equilibrium

KE_electron = E_photon - ɸ

• ɸ = work function — the energy needed to free the electron from the bound state

Kinetic energy of an ejected electron

Double Doppler Formula for an object moving away from you at velocity “x”

f = nv/2L All integer values of n allowed

Frequency of the nth harmonic of a string

f = nv/4L Only odd integer values of n allowed

Frequency of the nth harmonic of a pipe open at one end and closed at the other

f = nv/2L All integer values of n allowed

Frequency of the nth harmonic of a pipe open at both ends

MA = F_o / F_i

F_o = force out

F_i = force in

Mechanical Advantage

Molar Heat Capacity