Reference

Formula Reference

29 formulas across 6 units of physics

Mechanics

Speed and Velocity

v=ΔdΔtv = \dfrac{\Delta d}{\Delta t}

v = speed (m/s), Δd = displacement (m), Δt = time (s)

Full lesson
Mechanics

Acceleration

a=ΔvΔta = \dfrac{\Delta v}{\Delta t}

a = acceleration (m/s²), Δv = change in velocity (m/s), Δt = time interval (s)

Full lesson
Mechanics

Newton's Second Law

F=maF = ma

F = net force (N), m = mass (kg), a = acceleration (m/s²)

Full lesson
Mechanics

Work & Kinetic Energy

KE=12mv2W=Fdcos⁡θKE = \tfrac{1}{2}mv^2 \qquad W = Fd\cos\theta

KE = kinetic energy (J), m = mass (kg), v = speed (m/s), W = work (J), F = force (N), d = displacement (m), θ = angle

Full lesson
Mechanics

Momentum & Impulse

p=mvJ=F Δtp = mv \qquad J = F\,\Delta t

p = momentum (kg·m/s), m = mass (kg), v = velocity (m/s), J = impulse (N·s), F = force (N), Δt = time (s)

Full lesson
Mechanics

Projectile Motion

x=v0cos⁡θ⋅ty=v0sin⁡θ⋅t−12gt2x = v_0\cos\theta\cdot t \qquad y = v_0\sin\theta\cdot t - \tfrac{1}{2}gt^2

x = horizontal displacement (m), y = vertical displacement (m), v₀ = initial speed (m/s), θ = launch angle, g = 9.8 m/s², t = time (s)

Full lesson
Mechanics

Circular Motion

ac=v2rFc=mv2ra_c = \dfrac{v^2}{r} \qquad F_c = \dfrac{mv^2}{r}

aₒ = centripetal acceleration (m/s²), v = speed (m/s), r = radius (m), F = centripetal force (N), m = mass (kg)

Full lesson
Mechanics

Universal Gravitation

F=Gm1m2r2F = \dfrac{Gm_1 m_2}{r^2}

F = gravitational force (N), G = 6.67×10⁻¹¹ N·m²/kg², m₁, m₂ = masses (kg), r = distance between centres (m)

Full lesson
Mechanics

Simple Harmonic Motion

T=2πmkT=2πLgT = 2\pi\sqrt{\dfrac{m}{k}} \qquad T = 2\pi\sqrt{\dfrac{L}{g}}

T = period (s), m = mass (kg), k = spring constant (N/m), L = pendulum length (m), g = 9.8 m/s²

Full lesson
Waves

Wave Properties

T=1fT = \dfrac{1}{f}

T = period (s), f = frequency (Hz)

Soon
Waves

Wave Speed

v=fλv = f\lambda

v = wave speed (m/s), f = frequency (Hz), λ = wavelength (m)

Soon
Waves

Wave Interference

Δd=nλΔd=(n+12)λ\Delta d = n\lambda \quad \Delta d = \left(n+\tfrac{1}{2}\right)\lambda

Δd = path difference (m), n = 0,1,2…, λ = wavelength (m). First: constructive; second: destructive.

Soon
Waves

Sound Waves

v=331+0.6Tβ=10log⁡ ⁣II0v = 331 + 0.6T \qquad \beta = 10\log\!\dfrac{I}{I_0}

v = speed of sound (m/s), T = temperature (°C), β = sound level (dB), I = intensity (W/m²), I₀ = 10⁻¹² W/m²

Soon
Waves

Standing Waves & Resonance

fn=nv2Ln=1,2,3…f_n = \dfrac{nv}{2L} \quad n = 1,2,3\ldots

fₙ = nth harmonic (Hz), v = wave speed (m/s), L = string/pipe length (m), n = harmonic number

Soon
Waves

The Doppler Effect

f′=f v±vov∓vsf' = f\,\dfrac{v \pm v_o}{v \mp v_s}

f' = observed frequency, f = source frequency, v = wave speed, v_o = observer speed, v_s = source speed (+ when approaching)

Soon
Thermodynamics

Temperature & Heat

Q=mc ΔTQ = mc\,\Delta T

Q = heat energy (J), m = mass (kg), c = specific heat capacity (J/kg·K), ΔT = temperature change (K)

Soon
Thermodynamics

Thermal Expansion

ΔL=αL0 ΔT\Delta L = \alpha L_0\,\Delta T

ΔL = change in length (m), α = linear expansion coefficient (1/K), L₀ = original length (m), ΔT = temperature change (K)

Soon
Thermodynamics

The Ideal Gas Law

PV=nRTPV = nRT

P = pressure (Pa), V = volume (m³), n = amount (mol), R = 8.314 J/(mol·K), T = temperature (K)

Soon
Thermodynamics

Heat Transfer

Qt=kA ΔTL\dfrac{Q}{t} = \dfrac{kA\,\Delta T}{L}

Q/t = rate of heat flow (W), k = thermal conductivity (W/m·K), A = area (m²), ΔT = temperature difference (K), L = thickness (m)

Soon
Electromagnetism

Electric Charge & Coulomb's Law

F=kq1q2r2F = \dfrac{kq_1 q_2}{r^2}

F = electrostatic force (N), k = 8.99×10⁹ N·m²/C², q₁, q₂ = charges (C), r = separation (m)

Soon
Electromagnetism

Electric Current & Ohm's Law

V=IRP=IVV = IR \qquad P = IV

V = voltage (V), I = current (A), R = resistance (Ω), P = power (W)

Soon
Electromagnetism

Series & Parallel Circuits

Rs=R1+R21Rp=1R1+1R2R_s = R_1+R_2 \qquad \dfrac{1}{R_p} = \dfrac{1}{R_1}+\dfrac{1}{R_2}

Rₛ = series total (Ω), R_p = parallel total (Ω). Series: same current, voltages add. Parallel: same voltage, currents add.

Soon
Electromagnetism

Magnetic Fields & Forces

F=qvBsin⁡θF=BILsin⁡θF = qvB\sin\theta \qquad F = BIL\sin\theta

F = magnetic force (N), q = charge (C), v = velocity (m/s), B = magnetic field (T), I = current (A), L = wire length (m), θ = angle

Soon
Electromagnetism

Electromagnetic Induction

ε=−N ΔΦΔt\varepsilon = -N\,\dfrac{\Delta\Phi}{\Delta t}

ε = induced EMF (V), N = number of turns, ΔΦ = change in magnetic flux (Wb), Δt = time interval (s). Minus sign = Lenz's law.

Soon
Optics

Reflection & Refraction

n1sin⁡θ1=n2sin⁡θ2θi=θrn_1\sin\theta_1 = n_2\sin\theta_2 \qquad \theta_i = \theta_r

n₁, n₂ = refractive indices, θ₁, θ₂ = angles of incidence/refraction, θᵢ = angle of incidence, θᵣ = angle of reflection (from normal)

Soon
Optics

Lenses & Image Formation

1f=1do+1diM=−dido\dfrac{1}{f} = \dfrac{1}{d_o} + \dfrac{1}{d_i} \qquad M = -\dfrac{d_i}{d_o}

f = focal length (m), dₒ = object distance (m), dᵢ = image distance (m), M = magnification. Positive f = converging; negative = diverging.

Soon
Modern Physics

The Atomic Model

E=hfΔE=hfE = hf \qquad \Delta E = hf

E = photon energy (J or eV), h = 6.63×10⁻³⁴ J·s (Planck's constant), f = frequency (Hz). ΔE = energy gap between atomic levels.

Soon
Modern Physics

Radioactive Decay & Half-Life

N=N0 ⁣(12)t/t1/2N = N_0\!\left(\tfrac{1}{2}\right)^{t/t_{1/2}}

N = remaining nuclei, N₀ = initial number, t = elapsed time, t₁/₂ = half-life. Activity A = λN, λ = ln 2 / t₁/₂.

Soon
Modern Physics

The Photoelectric Effect

KEmax⁡=hf−ϕKE_{\max} = hf - \phi

KE_max = max kinetic energy of ejected electron (J or eV), h = 6.63×10⁻³⁴ J·s, f = frequency (Hz), φ = work function (J or eV).

Soon