Laws & Proofs

Physical laws, formulas and axioms — statement, why it holds, and a step-by-step proof where one exists.

1. Th
   Archimedes' principle

   $F_A = \rho_{\text{fluid}}\, g\, V_{\text{submerged}}$ — the buoyant force on an object immersed in a fluid equals the weight of the fluid it displaces.TheoremProvedFluid mechanics
2. Th
   Newton's first law (inertia)

   An object remains at rest or in uniform straight-line motion unless acted on by a force, or as long as the net force acting on it is zero.TheoremProvedNewtonian mechanics
3. Th
   Newton's third law (action-reaction)

   When object A exerts a force on object B, object B simultaneously exerts a force on A that is equal in magnitude, same line of action, but opposite in direction.TheoremProvedNewtonian mechanics
4. Th
   The Faraday–Lenz law of electromagnetic induction

   $\varepsilon = -N\dfrac{d\Phi}{dt}$ — the EMF induced in a closed loop is proportional to the rate of change of magnetic flux $\Phi$ through it ($N$ is the number of turns); the minus sign (Lenz) shows the induced current always opposes the change that created it.TheoremProvedElectricity and magnetism
5. Th
   The first law of thermodynamics

   $\Delta U = Q - A$ — the change in a system’s internal energy equals the heat it absorbs minus the work it performs.TheoremProvedThermal physics
6. Th
   The Heisenberg uncertainty principle

   $\Delta x \, \Delta p \geq \hbar/2$ — the product of the uncertainties in a particle’s position and momentum can never be smaller than the fixed bound $\hbar/2$.TheoremProvedQuantum mechanics
7. Th
   The second law of thermodynamics

   The entropy of an isolated system never decreases over time; heat does not spontaneously flow from a colder body to a hotter one without external work.TheoremProvedThermal physics