THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Mode
An allowed standing-wave pattern of a bounded system, labelled by an integer.
Moment arm
The perpendicular distance from a rotation axis to the line of action of a force. Torque = force × moment arm.
moment of inertia
The rotational analogue of mass: I = Σ m_i · r_i² (or ∫ r² dm for a continuous body).
momentum
Mass times velocity (a vector, p = m·v); conserved in any closed system.
Motional EMF
The EMF induced in a conductor moving through a magnetic field, driven by the magnetic part of the Lorentz force on free charges inside the conductor. Equals (v × B) · ℓ for a straight rod of length ℓ moving with velocity v in field B.
Mutual inductance
The coupling between two separated coils: M = Φ₁₂/I₂, the flux that coil 2's current produces through coil 1 per unit coil-2 current. The operating principle of every transformer.
Navier-Stokes equations
The PDEs governing viscous fluid flow. Nonlinear, exact, and generally unsolved — smoothness in 3D is a Millennium Problem.
Near-field zone
The region r ≪ λ surrounding an oscillating source where the field resembles a time-varying instantaneous quasi-static field (amplitude ∝ 1/r³ for a dipole) that stores and returns energy rather than radiating it. Also called the induction zone or reactive zone.
Newton's laws of motion
The three laws — inertia, F = ma, and equal-and-opposite reaction — that launched classical mechanics in 1687.
Newtonian fluid
A fluid whose shear stress is strictly proportional to its velocity gradient, with viscosity independent of shear rate.
Node
A point on a standing wave that never moves.
Noether's theorem
Every continuous symmetry of a physical system's action gives rise to a conserved quantity.
Non-abelian gauge theory
A gauge theory whose gauge group is non-commutative, so the gauge fields themselves carry charge under the group and the field strength tensor acquires a self-interaction term. Yang-Mills 1954 introduced the construction; QCD and the weak force are non-abelian; QED is the abelian exception.
nonlinear dynamics
Study of systems where output is not proportional to input; chaos, solitons, turbulence.
normal modes
Independent oscillation patterns of a coupled system; any motion is their superposition.
Null interval
A separation between two events with invariant interval s² = 0 — meaning a light signal exactly connects them. The world-lines of photons are null curves; the light-cone of any event is the locus of null-separated points; null separations sit on the boundary between timelike and spacelike.
Numerical aperture
NA = n sin θ_max. For a fibre, NA = √(n_core² − n_cladding²) gives the sine of the maximum acceptance half-angle. For a microscope objective, NA determines the diffraction-limited resolution λ/(2·NA).
Obliquity
The tilt angle between a planet's rotation axis and the perpendicular to its orbital plane.
Ohm's law
V = IR. For a metallic conductor at fixed temperature, the current through it is proportional to the voltage across it, with the proportionality constant R being the resistance.
p-polarization
An EM wave incident on an interface with its electric field parallel to the plane of incidence (German parallel). Also called TM (transverse magnetic) polarisation. Reflection coefficient passes through zero at Brewster's angle.
parabola
Conic section given by a quadratic in one variable; the trajectory of a projectile under gravity alone.
parallel-axis theorem
For any axis parallel to one through the centre of mass, I = I_CM + M·d² (also called Steiner's theorem).
Permittivity
The constant ε in D = εE that characterises how a medium permits the establishment of an electric field. SI unit: farad per metre.
Perpendicular axis theorem
For a planar body, I_z = I_x + I_y — the moment about an axis perpendicular to the plane equals the sum of moments about two in-plane axes.
phase portrait
Plot of position versus velocity showing the trajectory of a dynamical system.
Phase space
The 2N-dimensional space of (position, momentum) pairs in which every classical state is a single point.
Phase velocity
The speed v_p = ω/k at which an individual crest of a sinusoidal wave moves. Can exceed c; carries no information.
Phasor
A complex number representing the amplitude and phase of a sinusoidal quantity. Turns linear differential equations for AC circuits into algebraic equations: V = IZ in the frequency domain.
Plane wave
An EM wave whose phase is constant on planes perpendicular to the propagation direction k. Written E(r,t) = E₀ cos(k·r − ωt + φ), with ω = c|k| in vacuum. The simplest solution of the wave equation.
Poisson bracket
The antisymmetric bilinear {f, g} = Σ (∂f/∂q·∂g/∂p − ∂f/∂p·∂g/∂q). Every observable evolves as df/dt = {f, H}.