Two small lead spheres (mass m) sit at the ends of a light rod suspended from a thin fiber. Two large lead spheres (mass M) are placed near — but not touching — the small ones, on opposite corners, so their gravitational pull twists the rod the same way on both ends. The fiber resists with a restoring torque proportional to the twist angle, so the system settles at an equilibrium where the two torques balance:
I·θ'' + b·θ' + κ·θ = τ, τ = 2·G·M·m·L / d²
equilibrium: θ_eq = τ / κ → G = θ_eq·κ·d² / (2·m·M·L)
Because G is tiny (6.674×10⁻¹¹ m³ kg⁻¹ s⁻²), the real twist is only a fraction of a degree — far too small to read by eye. Cavendish's trick, kept here, was an optical lever: a mirror on the fiber reflects a beam onto a distant scale, doubling the angle (2θ) and multiplying it by the beam's path length D, so a microscopic twist becomes a visible spot displacement s = D·tan(2θ).
- Mass M — heavier attracting spheres pull harder, increasing the equilibrium twist.
- Fiber stiffness κ — a softer fiber twists further for the same torque (more sensitive, slower to settle); a stiffer one is faster but less sensitive — the exact trade-off the real apparatus had to balance.
- Damping ζ — models air drag and internal fiber losses; ζ = 1 is critically damped (fastest settle with no overshoot), ζ < 1 rings before settling.
- Swap sides — moves the large spheres to the opposite corners, reversing the torque, exactly as Cavendish did to confirm the deflection really came from gravity and to average out any fiber zero-offset.
Physics time in this simulation runs 15× faster than real life — Cavendish's own apparatus took several minutes to settle after each swap, damped mainly by air resistance inside its wooden case.