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Mechanics

Newton's First Law

An object at rest will remain at rest, and an object in motion will remain in motion unless acted upon by a net external force.

F = 0

Newton's Second Law

The net force on an object is equal to the mass of the object multiplied by its acceleration.

F = m a

Newton's Third Law

For every action, there is an equal and opposite reaction.

Thermodynamics

First Law of Thermodynamics

Energy cannot be created or destroyed, only transformed from one form to another.

ΔU = Q - W

Second Law of Thermodynamics

The total entropy of an isolated system always increases over time.

Third Law of Thermodynamics

As a system approaches absolute zero, the entropy of the system approaches a minimum value.

Entropy

Entropy is a measure of the disorder or randomness in a system.

S = \frac{Q}{T}

Electromagnetism

Coulomb's Law

The force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

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

Faraday's Law

A change in magnetic flux induces an electromotive force in a conductor.

ε = - \frac{dΦ_B}{dt}

Quantum Mechanics

Wave-Particle Duality

Particles such as electrons exhibit both particle-like and wave-like properties.

λ = \frac{h}{p}

Heisenberg Uncertainty Principle

It is impossible to simultaneously know the exact position and momentum of a particle.

Δx Δp \geq \frac{ħ}{2}

Schrödinger Equation

Describes how the quantum state of a physical system changes with time.

iħ \frac{∂ψ}{∂t}