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Physics Laws & Theorems

Named laws, principles and theorems that govern the physical universe

Newton's First Law (Inertia)

Basic
∑F=0⇒v=const\sum F = 0 \Rightarrow v = \text{const}

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

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Newton's Second Law

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

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

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Newton's Third Law

Basic
FAB=−FBAF_{AB} = -F_{BA}

For every action there is an equal and opposite reaction.

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Conservation of Momentum

Intermediate
∑pi=∑pf\sum p_i = \sum p_f

Total momentum of an isolated system stays constant.

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Conservation of Energy

Basic
Etotal=constE_{total} = \text{const}

Energy cannot be created or destroyed, only transformed.

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Archimedes' Principle

Intermediate
Fb=ρgVF_b = \rho g V

Buoyant force equals the weight of fluid displaced.

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Pascal's Law

Intermediate
P=F1A1=F2A2P = \frac{F_1}{A_1} = \frac{F_2}{A_2}

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

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Bernoulli's Principle

Advanced
P+12ρv2+ρgh=constP + \tfrac{1}{2}\rho v^2 + \rho g h = \text{const}

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

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Hooke's Law

Basic
F=−kxF = -kx

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

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Law of Universal Gravitation

Intermediate
F=Gm1m2r2F = G\frac{m_1 m_2}{r^2}

Every mass attracts every other mass.

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Kepler's First Law

Advanced
r=a(1−e2)1+ecos⁡θr = \frac{a(1-e^2)}{1 + e\cos\theta}

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

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Kepler's Second Law

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

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

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Kepler's Third Law

Intermediate
T2∝a3T^2 \propto a^3

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

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Zeroth Law of Thermodynamics

Intermediate
A=B, B=C⇒A=CA = B, \ B = C \Rightarrow A = C

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

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First Law of Thermodynamics

Intermediate
ΔU=Q−W\Delta U = Q - W

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

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Second Law of Thermodynamics

Advanced
ΔSuniverse≥0\Delta S_{universe} \ge 0

The entropy of an isolated system never decreases.

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Boyle's Law

Basic
P1V1=P2V2P_1 V_1 = P_2 V_2

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

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Charles's Law

Basic
V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}

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

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Gay-Lussac's Law

Basic
P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2}

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

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Stefan–Boltzmann Law

Advanced
j=σT4j = \sigma T^4

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

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Ohm's Law

Basic
V=IRV = IR

Voltage across a resistor equals current times resistance.

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Coulomb's Law

Intermediate
F=kq1q2r2F = k\frac{q_1 q_2}{r^2}

Electrostatic force between two point charges.

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Gauss's Law

Advanced
∮E⃗⋅dA⃗=Qε0\oint \vec{E} \cdot d\vec{A} = \frac{Q}{\varepsilon_0}

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

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Faraday's Law of Induction

Advanced
ε=−dΦBdt\varepsilon = -\frac{d\Phi_B}{dt}

A changing magnetic flux induces an electromotive force.

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Lenz's Law

Advanced
ε∝−dΦBdt\varepsilon \propto -\frac{d\Phi_B}{dt}

Induced current opposes the change in flux that produced it.

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Ampère's Law

Advanced
∮B⃗⋅dl⃗=μ0I\oint \vec{B} \cdot d\vec{l} = \mu_0 I

A magnetic field circulates around an electric current.

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Kirchhoff's Current Law

Intermediate
∑Iin=∑Iout\sum I_{in} = \sum I_{out}

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

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Kirchhoff's Voltage Law

Intermediate
∑V=0\sum V = 0

The sum of voltages around any closed loop is zero.

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Lens Maker's / Thin Lens

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

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

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Snell's Law

Intermediate
n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2

Light bends when passing between media of different refractive index.

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Mass–Energy Equivalence

Intermediate
E=mc2E = mc^2

Mass and energy are equivalent and interconvertible.

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Planck–Einstein Relation

Advanced
E=hfE = hf

The energy of a photon is proportional to its frequency.

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Heisenberg Uncertainty Principle

Advanced
Δx Δp≥ℏ2\Delta x \, \Delta p \ge \frac{\hbar}{2}

Position and momentum cannot both be known with unlimited precision.

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Newton First Law

Basic
∑F=0⇒constant v\sum F = 0 \Rightarrow \text{constant } v

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

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Newton Third Law

Basic
FAB=−FBAF_{AB} = -F_{BA}

Every action has an equal and opposite reaction.

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Conservation of Energy

Basic
Etotal=constantE_{total} = \text{constant}

Energy cannot be created or destroyed, only transformed.

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Conservation of Momentum

Intermediate
∑pi=∑pf\sum p_i = \sum p_f

Total momentum is conserved without external forces.

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Conservation of Charge

Intermediate
∑q=constant\sum q = \text{constant}

Total electric charge in an isolated system is conserved.

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First Law of Thermodynamics

Intermediate
ΔU=Q−W\Delta U = Q - W

Change in internal energy equals heat added minus work done.

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Second Law of Thermodynamics

Advanced
ΔSuniverse≥0\Delta S_{universe} \geq 0

Total entropy of an isolated system never decreases.

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Hooke Law

Basic
F=−kxF = -kx

Elastic restoring force is proportional to displacement.

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Faraday Law of Induction

Advanced
ε=−dΦBdt\varepsilon = -\frac{d\Phi_B}{dt}

A changing magnetic flux induces an EMF.

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Lenz Law

Intermediate
induced current opposes change\text{induced current opposes change}

Induced currents oppose the change producing them.

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Archimedes Principle

Intermediate
Fb=ρVgF_b = \rho V g

Buoyant force equals the weight of displaced fluid.

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Pascal Principle

Intermediate
ΔP=transmitted equally\Delta P = \text{transmitted equally}

Pressure applied to a confined fluid transmits undiminished.

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