In the rotating Earth's reference frame, a freely-swinging pendulum experiences the Coriolis force:
where Ω = Ω sin(φ) ẑ is the vertical component of Earth's rotation at latitude φ. This causes the pendulum's plane of oscillation to precess with angular velocity:
Full precession period: T_prec = 24h / sin(φ)
At the North Pole (φ=90°), the plane rotates once per sidereal day (23h 56m). At Paris (φ=49°), once every ~32 hours. At the equator, no precession occurs. Léon Foucault demonstrated this in Paris, 1851, providing the first direct proof of Earth's rotation.