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AP Physics 2 — Equations & Constants

8 sections · 63 entries · print it and keep it beside your practice sets

Thermodynamics, electrostatics, circuits, magnetism, optics, and modern physics — algebra-based. This is the densest of the AP physics sheets, so the exam skill is navigation: know which section each quantity lives in before you open it.

Practise with the sheet, not from memory. The College Board hands out its own version of this page on exam day, so nothing here is worth memorising for its own sake. What earns points is speed: knowing which section a quantity lives in, and reading off the right line without breaking your train of thought. Keep this open (or printed) for every practice set you do.

Thermodynamics & kinetic theory

Quantity / relationshipWhat it means & how to use it

PV = nRT

P V = n R T = N k_B T

Ideal gas law; n in moles, T in kelvin

K_avg

K_avg = (3/2) k_B T

Average translational kinetic energy per molecule

Depends only on temperature — not on the identity of the gas.

v_rms

v_rms = √(3 R T / M) = √(3 k_B T / m)

Root-mean-square molecular speed; M is molar mass in kg/mol

Q = m c ΔT

Heat to change temperature of mass m

ΔU

ΔU = Q + W

First law of thermodynamics

W is work done ON the gas, which is why W = −P ΔV.

W = −P ΔV

Work done on a gas at constant pressure

e = |W_net| / |Q_H|

Efficiency of a heat engine

e_c

e_c = 1 − T_C/T_H

Maximum (Carnot) efficiency; temperatures in kelvin

ΔL, ΔV

ΔL = α L₀ ΔT

Thermal expansion

Electrostatics

Quantity / relationshipWhat it means & how to use it

F_E

|F_E| = (1/4πε₀) |q₁ q₂| / r²

Coulomb force between point charges

E = F_E / q

Electric field from a force on a test charge

E_point

E = (1/4πε₀) q / r²

Field of a point charge

U_E

U_E = (1/4πε₀) q₁ q₂ / r

Electric potential energy of a pair of point charges

Signed — negative for opposite charges. No absolute-value bars here.

V = (1/4πε₀) Σ qᵢ / rᵢ

Electric potential from point charges (scalar sum)

ΔU_E

ΔU_E = q ΔV

Energy change moving charge q through ΔV

E_uniform

|E| = |ΔV| / d

Uniform field between parallel plates separated by d

Capacitance

Quantity / relationshipWhat it means & how to use it

C = Q / ΔV

Capacitance

C_plates

C = κ ε₀ A / d

Parallel-plate capacitor with dielectric constant κ

U_C

U_C = ½ Q ΔV = ½ C (ΔV)²

Energy stored in a capacitor

C_series / C_parallel

1/C_s = Σ 1/Cᵢ, C_p = Σ Cᵢ

Combining capacitors

Opposite of the resistor rules — a very common slip.

Circuits

Quantity / relationshipWhat it means & how to use it

I = ΔQ / Δt

Current

R = ρ ℓ / A

Resistance of a wire of resistivity ρ

ΔV = IR

ΔV = I R

Ohm’s law

P = I ΔV = I² R = (ΔV)²/R

Power dissipated

R_series / R_parallel

R_s = Σ Rᵢ, 1/R_p = Σ 1/Rᵢ

Combining resistors

Loop / junction

Σ ΔV_loop = 0, Σ I_in = Σ I_out

Kirchhoff’s rules

Magnetism & induction

Quantity / relationshipWhat it means & how to use it

F_M

|F_M| = |q| v B sin θ

Magnetic force on a moving charge

Perpendicular to both v and B, so it changes direction but never speed.

F_wire

|F_M| = B I ℓ sin θ

Magnetic force on a current-carrying wire

B_wire

B = μ₀ I / (2π r)

Field a distance r from a long straight wire

Φ_B

Φ_B = B A cos θ

Magnetic flux through area A

θ is measured from the area’s normal, not from the plane of the loop.

ε = −ΔΦ_B / Δt

Faraday’s law of induction

Waves & optics

Quantity / relationshipWhat it means & how to use it

v = fλ

v = f λ

Wave speed

n = c / v

Index of refraction

Snell

n₁ sin θ₁ = n₂ sin θ₂

Refraction at a boundary

θ_c

sin θ_c = n₂ / n₁

Critical angle for total internal reflection

Only exists when going from higher n₁ to lower n₂.

Thin lens / mirror

1/s_o + 1/s_i = 1/f

Object distance s_o, image distance s_i, focal length f

M = h_i/h_o = −s_i/s_o

Magnification

Negative M means an inverted image.

Double slit

d sin θ = m λ, m = 0, 1, 2, …

Bright fringes for slit separation d

Modern & quantum physics

Quantity / relationshipWhat it means & how to use it

E_photon

E = h f = h c / λ

Energy of a photon

K_max

K_max = h f − φ

Photoelectric effect; φ is the work function

λ = h / p

de Broglie wavelength

E = mc²

E = m c²

Mass–energy equivalence

ΔE

ΔE = Δm c²

Energy released in a nuclear reaction from mass defect

Fluids (carried over from Physics 1)

Quantity / relationshipWhat it means & how to use it

ρ, P

ρ = m/V, P = F/A

Density and pressure

P(h)

P = P₀ + ρ g h

Pressure at depth h

F_b

F_b = ρ_fluid V_displaced g

Buoyant force

Continuity / Bernoulli

A₁v₁ = A₂v₂; P + ρgy + ½ρv² = constant

Flow of an ideal fluid

# Constants & conversions

e = 1.60 × 10⁻¹⁹ C

Elementary charge (magnitude of electron charge)

m_e

m_e = 9.11 × 10⁻³¹ kg

Mass of an electron

m_p

m_p = 1.67 × 10⁻²⁷ kg

Mass of a proton

ε₀

ε₀ = 8.85 × 10⁻¹² C²/(N·m²)

Vacuum permittivity

k = 1/(4πε₀)

k = 8.99 × 10⁹ N·m²/C²

Coulomb’s law constant

Use 9.0 × 10⁹ for hand arithmetic.

μ₀

μ₀ = 4π × 10⁻⁷ T·m/A = 1.26 × 10⁻⁶ T·m/A

Vacuum permeability

μ₀/(4π)

μ₀/(4π) = 1 × 10⁻⁷ T·m/A

Magnetostatic constant

c = 3.00 × 10⁸ m/s

Speed of light in vacuum

h = 6.63 × 10⁻³⁴ J·s = 4.14 × 10⁻¹⁵ eV·s

Planck’s constant

k_B

k_B = 1.38 × 10⁻²³ J/K

Boltzmann’s constant

R = 8.31 J/(mol·K)

Universal gas constant

N_A

N_A = 6.02 × 10²³ mol⁻¹

Avogadro’s number

1 eV

1 eV = 1.60 × 10⁻¹⁹ J

Electron-volt in joules

g = 9.8 m/s²

Free-fall acceleration

atm

1 atm = 1.0 × 10⁵ Pa

Standard atmospheric pressure

ρ_water

ρ = 1.0 × 10³ kg/m³

Density of water

Practise with the sheet open Cheatsheet