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04 // Interactive Formula Compendium10 / 62 TOOLS SHOWN

PHYSICS — 04 // Interactive Formula Compendium

Master foundational physics, finance, calculus, and engineering equations with live evaluators, derivations, and worked examples.

physicsF_net = m · a = dp / dt

Newton's Second Law of Motion & SUVAT Kinematics Equations Sheet

Connects net external force F_net on mass m to acceleration a and the four constant-acceleration SUVAT kinematic equations.

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physicsF = G · (m₁ · m₂) / r²

Newton's Law of Universal Gravitation, Orbital & Escape Velocity Sheet

Inverse-square law governing gravitational attraction, surface gravity g, circular orbital velocity, escape velocity, and Kepler's Third Law.

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physicsE_total = K + U = ½ m v² + m g h + ½ k x² = constant

Conservation of Mechanical Energy — Kinetic, Potential & Spring Sheet

States that in a conservative system free of non-conservative friction/drag, the sum of kinetic energy K and potential energy U remains invariant.

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physicsW = F · d · cos(θ) = ΔK = ½ m v_f² − ½ m v_i²

Work-Energy Theorem & Mechanical Power Formula Sheet

Relates the dot-product mechanical work W = F·d cos(θ) performed on a body to its exact change in kinetic energy ΔK and instantaneous power P = F·v.

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physicsJ = ∫ F(t) dt = F_avg · Δt = Δp = m(v_f − v_i)

Impulse-Momentum Theorem & Elastic/Inelastic Collisions Sheet

Links force-time impulse J = F_avg Δt to momentum change Δp and governs elastic, partially elastic, and perfectly inelastic collisions.

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physicsV = I · R, P = V · I = I² R = V² / R

Ohm's Law, Joule Power & Kirchhoff's Circuit Laws (KCL / KVL) Sheet

Fundamental electrical circuit equations relating voltage V, current I, resistance R, Joule power P, and Kirchhoff's node/loop laws.

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physicsF = k_e · |q₁ · q₂| / r², where k_e = 1 / (4π ε₀)

Coulomb's Law of Electrostatic Force & Electric Field Potential Sheet

Inverse-square electrostatic force, electric field E, and electric potential V between point charges in vacuum or dielectric media.

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physicsℰ = −N · (dΦ_B / dt), where Φ_B = B · A · cos(θ)

Faraday's Law of Electromagnetic Induction & Lenz's Law Sheet

Governs voltage generation in electric generators, transformers, inductors, and wireless chargers from time-varying magnetic flux Φ_B.

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physicsc = 1 / √(μ₀ · ε₀) = f · λ, E_photon = h · f = h · c / λ

Maxwell's Equations, Electromagnetic Wave Speed & Photon Energy Sheet

Unifies electricity, magnetism, and optics via Maxwell's four field equations, wave propagation speed c = fλ, and Planck photon energy E = hf.

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physicsE = γ m c², where γ = 1 / √(1 − v² / c²)

Einstein Mass-Energy Equivalence, Lorentz Factor & Time Dilation Sheet

Einstein's special relativity equations for the Lorentz factor γ, rest energy E₀ = mc², relativistic kinetic energy, time dilation, and length contraction.

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