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. This view looks straight down on the apparatus from above, so the arm's rotation reads directly as an angle in the plane of the page. Drag to pan the view, scroll (or pinch) to zoom.