Compendium of fundamental governing equations in SI units
Every simulation chapter implements exact numerical integration of the governing differential and algebraic equations summarized below, allowing students and instructors to compare analytical predictions directly against live 3D telemetry:
| Discipline | Physical, Chemical or Biophysical Law | Governing Mathematical Equation | Key Variables & SI Units |
|---|---|---|---|
| Classical Mechanics | Conservation of Momentum & Inelastic Loss | m₁v₁ + m₂v₂ = m₁u₁ + m₂u₂, ΔQ = ½μ·Δv²(1 − e²) |
Mass m (kg), velocity v (m/s), restitution e |
| Rotational Dynamics | Rolling Kinetic Energy & Gyroscopic Precession | E_k = ½mv² + ½Iω², Ω_p = mgl / (I_s ω_s) |
Moment of inertia I (kg·m²), spin rate ω_s (rad/s) |
| Fluid Mechanics | Bernoulli's Principle, Torricelli's Law & Stokes Drag | P + ½ρv² + ρgy = const, v = √(2gh), F_d = 6πηrv |
Static pressure P (Pa), density ρ (kg/m³), viscosity η (Pa·s) |
| Thermodynamics | Ideal Gas Equation, RMS Speed & Carnot Efficiency | PV = νRT, v_rms = √(3RT/M), η = 1 − T_C/T_H |
Absolute temperature T (K), molar amount ν (mol) |
| Wave Optics | Snell's Law, Young's Double-Slit & Malus's Law | n₁ sin α = n₂ sin γ, Δy = λL/d, I = I₀ cos² θ |
Refractive index n, wavelength λ (nm) |
| Electromagnetism | Lorentz Force, Faraday Induction & RLC Resonance | F_L = |q|vB sin α, ℰ = −N dΦ/dt, ω₀ = 1/√(LC) |
Magnetic field B (T), inductance L (H), capacitance C (F) |
| Quantum Physics | Photoelectric Equation, Compton Shift & Bohr Levels | hc/λ = φ + eU_s, Δλ = λ_C(1 − cos θ), E_n = −13.6/n² eV |
Planck constant h (J·s), stopping voltage U_s (V) |
| Physical Chemistry | Gibbs Free Energy, Arrhenius Kinetics & Buffer pH | ΔG = ΔH − TΔS = −RT ln K, k = A e^{−E_a/RT}, pH = pK_a + lg([A⁻]/[HA]) |
Activation energy E_a (kJ/mol), equilibrium constant K |
| Electrochemistry | Nernst Potential & Faraday's Law of Electrolysis | E = E° + (RT/zF) ln([Ox]/[Red]), m = (M·I·t) / (z·F) |
Faraday constant F = 96 485 C/mol, current I (A) |
| Biophysics | Nernst Membrane Potential & Hagen-Poiseuille Flow | V_m = (RT/zF) ln([C]_o/[C]_i), Q = (πΔP·R⁴) / (8ηL) |
Vessel radius R (mm), volumetric blood flow Q (m³/s) |
Three-stage scientific inquiry architecture
Each of the 106 chapters guides learners through a structured three-stage experimental workflow designed for independent study and projector-based classroom instruction:
- Predictive hypothesis. Before running the apparatus, students analyze a conceptual or quantitative problem and commit to a testable physical hypothesis.
- Quantitative 3D experimentation. Learners vary physical parameters across core school and advanced university regimes, inspect real-time 3D force, velocity, field, and dipole vectors, and record live energy oscillograms.
- Analytical proof and lab report. The live KaTeX formula calculator substitutes the active slider values directly into the governing equations, solves inverse problems, shares exact parameter URLs for homework, and exports a clean printable laboratory report.
Curriculum organization and difficulty tiers
To support differentiated instruction across secondary school curricula such as Grades 8 to 11, GCSE, AP, and IB alongside introductory university courses, every simulation in the dropdown registry belongs to one of two curriculum tiers. The Core Curriculum tier covers foundational laws of mechanics, hydrostatics, ideal gases, geometric optics, atomic structure, acid-base pH, cell organelles, and Mendelian genetics. The Advanced Level tier covers gyroscopic precession, Michelson interferometry, Compton scattering, molecular orbital theory, Born-Haber cycles, Hodgkin-Huxley electrophysiology, and CRISPR-Cas9 gene editing.