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Mechanics
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Waves & Optics
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Thermodynamics
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Modern Physics
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Math Skills
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Angular momentum — L = r × p = IωAngular speed — ω = dθ/dt = 2πfAngular-momentum conservation — Lᵢ = L𝒇Archimedes’ principle — Fᵦ = ρVgAverage acceleration — a = Δv / ΔtAverage speed — v̄ = total distance / total timeAverage velocity — v̄ = Δx / ΔtBernoulli’s equation — p + ½ρv² + ρgh = constantCentripetal acceleration — aᶜ = v²/r = ω²rCentripetal force — Fᶜ = mv²/rCircular-orbit speed — v = Constant-acceleration displacement — s = ut + ½at²Constant-acceleration velocity — v = u + atConstant-speed motion — s = vtContinuity equation — A₁v₁ = A₂v₂Efficiency — η = useful output / total inputElastic potential energy — Uₛ = ½kx²Escape speed — vₑ = Friction — f = μNGravitational field strength — g = ²Gravitational potential energy — Uᵍ = mghHooke’s law — F = −kxImpulse–momentum theorem — J = Δp = FΔtInstantaneous acceleration — a = Instantaneous velocity — v = Kepler’s third law — T² = 4π²r³/(GM)Kinematics without time — v² = u² + 2asKinetic energy — K = ½mv²Laplace pressure for a soap bubble — Δp = 4γ/RLinear momentum — p = mvMass–spring angular frequency — ω = Mass–spring period — T = 2πMechanical power — P = FvMechanical-energy conservation — Kᵢ + Uᵢ = K𝒇 + U𝒇Momentum conservation — Σpᵢ = Σp𝒇Newton’s law of gravitation — F = Gm₁m₂/r²Newton’s second law — F = maOrbital energy — E = −GMm/(2a)Parallel-axis theorem — I = I꜀ₘ + Md²Power — P = = Projectile flight time — t = 2v₀ sin θ / gProjectile range — R = v₀² sin(2θ) / gPythagorean theorem — c² = a² + b²Quadratic drag — Fᴅ = ½ρCᴅAv²Rotational equation of motion — τ = IαRotational kinetic energy — Kᵣₒₜ = ½Iω²Static-friction limit — fₛ ≤ μₛNStokes’ law — Fᴅ = 6πηrvTangential acceleration — aₜ = αrTangential speed — v = ωrTorque — τ = rF sin θTsiolkovsky rocket equation — Δv = u lnVector components — Aₓ = A cos θ, Aᵧ = A sin θVector magnitude — A = Vis-viva equation — v² = GMWeight — Fᵍ = mgWork — W = Fd cos θWork by a variable force — W = ∫F · drWork–energy theorem — Wₙₑₜ = ΔK