Reference

Formula Reference

29 formulas across 6 units of physics

Mechanics

Speed and Velocity

v=ΔdΔt

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

Mechanics

Acceleration

a=ΔvΔt

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

Mechanics

Newton's Second Law

F=ma

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

Mechanics

Work & Kinetic Energy

KE=12mv2W=Fdcos⁡θ

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

Mechanics

Momentum & Impulse

p=mvJ=F Δt

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

Mechanics

Projectile Motion

x=v0cos⁡θ⋅ty=v0sin⁡θ⋅t−12gt2

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

Mechanics

Circular Motion

ac=v2rFc=mv2r

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

Mechanics

Universal Gravitation

F=Gm1m2r2

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

Mechanics

Simple Harmonic Motion

T=2πmkT=2πLg

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

Waves

Wave Properties

T=1f

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

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Waves

Wave Speed

v=fλ

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

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Waves

Wave Interference

Δd=nλΔd=(n+12)λ

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

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Waves

Sound Waves

v=331+0.6Tβ=10log⁡ ⁣II0

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

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Waves

Standing Waves & Resonance

fn=nv2Ln=1,2,3…

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

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Waves

The Doppler Effect

f′=f v±vov∓vs

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

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Thermodynamics

Temperature & Heat

Q=mc ΔT

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

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Thermodynamics

Thermal Expansion

ΔL=αL0 ΔT

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

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Thermodynamics

The Ideal Gas Law

PV=nRT

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

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Thermodynamics

Heat Transfer

Qt=kA ΔTL

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

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Electromagnetism

Electric Charge & Coulomb's Law

F=kq1q2r2

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

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Electromagnetism

Electric Current & Ohm's Law

V=IRP=IV

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

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Electromagnetism

Series & Parallel Circuits

Rs=R1+R21Rp=1R1+1R2

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

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Electromagnetism

Magnetic Fields & Forces

F=qvBsin⁡θF=BILsin⁡θ

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

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Electromagnetism

Electromagnetic Induction

ε=−N ΔΦΔt

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

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Optics

Reflection & Refraction

n1sin⁡θ1=n2sin⁡θ2θi=θr

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

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Optics

Lenses & Image Formation

1f=1do+1diM=−dido

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

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Modern Physics

The Atomic Model

E=hfΔE=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.

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Modern Physics

Radioactive Decay & Half-Life

N=N0 ⁣(12)t/t1/2

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

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Modern Physics

The Photoelectric Effect

KEmax⁡=hf−ϕ

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).

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