Foucault PendulumA heavy bob swings back and forth in one plane. Do nothing else, wait, and that plane slowly turns — not because anything pushes it sideways, but because the floor underneath it is the thing rotating. Drag the room and watch the star-shaped trace it draws.Léon Foucault hung a 28 kg bob from the dome of the Panthéon in 1851. In the rotating frame the horizontal motion obeys x″ − 2Ωsinφ y′ + ω₀²x = 0 (and the mirrored equation for y) — the Coriolis cross-term. Writing w = x+iy collapses both into one solvable equation, w″ + 2iΩsinφ w′ + ω₀²w = 0, whose exact solution is a fast oscillation at ω₀ wrapped inside a slow rotation at exactly Ωsinφ — the sine of latitude is the whole reason it stalls at the equator and completes one full turn per day at the poles.