Physics Laws & Theorems

Named laws, principles and theorems that govern the physical universe

Physics laws and theorems explain the fundamental rules that shape motion, forces, energy, fluids, and gravity in the universe. This category is useful for students, exam revision, and anyone applying physics in real-world problem solving, from engineering to research, because these formulas help predict how objects and systems behave with clarity and confidence.

Newton's First Law (Inertia)

\sum F = 0 \Rightarrow v = \text{const}

An object stays at rest or in uniform motion unless acted on by a net force.

Newton's Second Law

F = ma = \frac{dp}{dt}

Net force equals mass times acceleration (rate of change of momentum).

Newton's Third Law

F_{AB} = -F_{BA}

For every action there is an equal and opposite reaction.

Conservation of Momentum

\sum p_i = \sum p_f

Total momentum of an isolated system stays constant.

Conservation of Energy

E_{total} = \text{const}

Energy cannot be created or destroyed, only transformed.

Archimedes' Principle

F_b = \rho g V

Buoyant force equals the weight of fluid displaced.

Pascal's Law

P = \frac{F_1}{A_1} = \frac{F_2}{A_2}

Pressure applied to a confined fluid transmits equally in all directions.

Bernoulli's Principle

P + \tfrac{1}{2}\rho v^2 + \rho g h = \text{const}

Faster-moving fluid has lower pressure (energy conservation in flow).

Hooke's Law

F = -kx

The restoring force of a spring is proportional to its extension.

Law of Universal Gravitation

F = G\frac{m_1 m_2}{r^2}

Every mass attracts every other mass.

Kepler's First Law

r = \frac{a(1-e^2)}{1 + e\cos\theta}

Planets orbit the Sun in ellipses with the Sun at one focus.

Kepler's Second Law

\frac{dA}{dt} = \text{const}

A line from a planet to the Sun sweeps equal areas in equal times.

Kepler's Third Law

T^2 \propto a^3

The square of the orbital period is proportional to the cube of the semi-major axis.

Zeroth Law of Thermodynamics

A = B, \ B = C \Rightarrow A = C

Two systems in thermal equilibrium with a third are in equilibrium with each other.

First Law of Thermodynamics

\Delta U = Q - W

Energy conservation: change in internal energy equals heat added minus work done.

Second Law of Thermodynamics

\Delta S_{universe} \ge 0

The entropy of an isolated system never decreases.

Boyle's Law

P_1 V_1 = P_2 V_2

At constant temperature, pressure and volume of a gas are inversely proportional.

Charles's Law

\frac{V_1}{T_1} = \frac{V_2}{T_2}

At constant pressure, volume of a gas is proportional to absolute temperature.

Gay-Lussac's Law

\frac{P_1}{T_1} = \frac{P_2}{T_2}

At constant volume, pressure of a gas is proportional to absolute temperature.

Stefan–Boltzmann Law

j = \sigma T^4

Total energy radiated by a black body scales with the fourth power of temperature.

Ohm's Law

V = IR

Voltage across a resistor equals current times resistance.

Coulomb's Law

F = k\frac{q_1 q_2}{r^2}

Electrostatic force between two point charges.

Gauss's Law

\oint \vec{E} \cdot d\vec{A} = \frac{Q}{\varepsilon_0}

Electric flux through a closed surface is proportional to the enclosed charge.

Faraday's Law of Induction

\varepsilon = -\frac{d\Phi_B}{dt}

A changing magnetic flux induces an electromotive force.

Lenz's Law

\varepsilon \propto -\frac{d\Phi_B}{dt}

Induced current opposes the change in flux that produced it.

Ampère's Law

\oint \vec{B} \cdot d\vec{l} = \mu_0 I

A magnetic field circulates around an electric current.

Kirchhoff's Current Law

\sum I_{in} = \sum I_{out}

Current into a junction equals current out of it (charge conservation).

Kirchhoff's Voltage Law

\sum V = 0

The sum of voltages around any closed loop is zero.

Lens Maker's / Thin Lens

\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

Relates focal length to object and image distances for a thin lens.

Snell's Law

n_1 \sin\theta_1 = n_2 \sin\theta_2

Light bends when passing between media of different refractive index.

Mass–Energy Equivalence

E = mc^2

Mass and energy are equivalent and interconvertible.

Planck–Einstein Relation

E = hf

The energy of a photon is proportional to its frequency.

Heisenberg Uncertainty Principle

\Delta x \, \Delta p \ge \frac{\hbar}{2}

Position and momentum cannot both be known with unlimited precision.

Newton First Law

\sum F = 0 \Rightarrow \text{constant } v

An object stays at rest or in uniform motion unless acted upon.

Newton Third Law

F_{AB} = -F_{BA}

Every action has an equal and opposite reaction.

Conservation of Energy

E_{total} = \text{constant}

Energy cannot be created or destroyed, only transformed.

Conservation of Momentum

\sum p_i = \sum p_f

Total momentum is conserved without external forces.

Conservation of Charge

\sum q = \text{constant}

Total electric charge in an isolated system is conserved.

First Law of Thermodynamics

\Delta U = Q - W

Change in internal energy equals heat added minus work done.

Second Law of Thermodynamics

\Delta S_{universe} \geq 0

Total entropy of an isolated system never decreases.

Hooke Law

F = -kx

Elastic restoring force is proportional to displacement.

Faraday Law of Induction

\varepsilon = -\frac{d\Phi_B}{dt}

A changing magnetic flux induces an EMF.

Lenz Law

\text{induced current opposes change}

Induced currents oppose the change producing them.

Archimedes Principle

F_b = \rho V g

Buoyant force equals the weight of displaced fluid.

Pascal Principle

\Delta P = \text{transmitted equally}

Pressure applied to a confined fluid transmits undiminished.