A circular museum laid out like a clock face. The hour hand visits one live experiment at a time; click a wedge or a number to jump to it. All twelve keep running.
Independent test: a separate RK4 integration of θ″ = −(g/L) sin θ is timed over four swings and compared with the exact period 2π√(L/g)/AGM(1, cos(θ₀/2)).
The science
Every wedge integrates its own equations of motion in real SI units (RK4 or small fixed steps). The 3D apparatus only shows the state. Gravity changes apply to all gravity-driven wedges.
1 Pendulum
θ″ = −(g/L) sin θ − cθ′; T ≈ T₀(1 + θ₀²/16 + 11θ₀⁴/3072), T = T₀ / AGM(1, cos(θ₀/2))
T₀ = 2π√(L/g) holds only for small angles. Damping is linear (air drag simplified).
2 Inclined plane
rolling: a = (5/7) g sin α (needs μ ≥ (2/7) tan α); slipping: a = g(sin α − μ cos α)
Solid sphere, I = ⅖mr². Energy is conserved while rolling; slipping converts it to heat.
3 Newton's cradle
Pairwise impulses with restitution e: after each collision v₁′ = v₁ − ½(1+e)(v₁−v₂). Several sweeps per time step carry the impulse along the chain. This is an idealised instantaneous-contact model; real cradles show small delays and a click.
4 Spring–mass
m x″ = −k x − c x′; ω_d = √(k/m − (c/2m)²)
The period does not depend on g or on the amplitude (linear spring).
5 Lever
I θ″ = g cos θ (m₁d₁ − m₂d₂) − cθ′
Balance at m₁d₁ = m₂d₂; mechanical advantage d₂/d₁. A beam pivoted at its centre of mass is neutrally stable, so it tips to the stops when unbalanced.
6 Ripple tank
v = √(g d), λ = v/f, nodal lines where |r₁ − r₂| = (m + ½)λ
Shallow-water (long-wave) speed; the surface is a sum of two circular waves with 1/√r spreading and edge absorption, not a full fluid solver.
7 Convex lens
1/f = 1/dₒ + 1/dᵢ, m = −dᵢ/dₒ
Thin-lens, paraxial approximation (no aberrations). The shown rays are drawn by geometry and their intersection is compared with the formula.
8 Bernoulli ball
F_drag = ½ρC_dA|u−v|(u−v), F_side = ½ρV ∂(u²)/∂n, u(s,n) = u₀/(1+s/z_h) · exp(−(n/b)²)
The jet is an empirical profile (decaying core, widening Gaussian), not a solved flow. Predicted hover height s = z_h(u₀/u_req − 1) neglects the small axial pressure-gradient force.
9 Buoyancy
F_b = ρ_f g V_sub; floats when ρ_b < ρ_f, submerged fraction ρ_b/ρ_f
Includes quadratic drag, added mass and the rise of the water level; surface waves are ignored.
10 Gyroscope
I₁θ″ = I₁φ′² sin θ cos θ − I₃ω₃φ′ sin θ + mgl sin θ; φ′ = (p_φ − I₃ω₃ cos θ)/(I₁ sin² θ)
Heavy symmetric top (Lagrange): slow precession Ω ≈ mgl/(I₃ω₃). Friction is neglected, so energy is conserved. The disc is drawn spinning 12× slower than reality.
11 Heat convection
Tracer parcels gain heat above the plate, lose it at the surface, and accelerate by Boussinesq buoyancy g β ΔT with viscous drag, plus a prescribed roll for continuity. Ra = gβΔT H³/(να) is real, the flow field is qualitative.
12 Static electricity
F = k q₁q₂ / r², tan α = F/(mg), F = kq²/(2L sin α)²
Two small charged spheres on threads; no charge leakage or induction effects.
Models and assets: Blender 5.2 (baked marble floor, apparatus), Three.js r160. Not a substitute for a lab.