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The Foucault pendulum or Foucault's pendulum is a simple device named after French physicist Léon Foucault, conceived as an experiment to demonstrate the Earth's rotation.

If a long and heavy pendulum suspended from the high roof above a circular area is monitored over an extended period of time, its plane of oscillation appears to change spontaneously as the Earth makes its 24-hourly rotation. Foucault introduced his pendulum in 1851 in the first experiment to give simple, direct evidence of the Earth's rotation, which he further demonstrated in 1852 with a gyroscope experiment. Foucault pendulums have become popular in science museums and universities.

Foucault was inspired by observing a thin flexible rod on the axis of a lathe, which vibrated in the same plane despite the rotation of the supporting frame of the lathe. The first public exhibition of a Foucault pendulum took place in February 1851 in the Meridian of the Paris Observatory. A few weeks later, Foucault made his most famous pendulum when he suspended a 28-kilogram (62 lb) brass-coated lead bob with a 67-metre-long (220 ft) wire from the dome of the Panthéon, Paris.

, so with each oscillation, the pendulum rotates by about Foucault reported observing 2.3 mm of deflection on the edge of a pendulum every oscillation, which is achieved if the pendulum swing angle is 2.1°.

At either the Geographic North Pole or Geographic South Pole, the plane of oscillation of a pendulum remains fixed relative to the distant masses of the universe while Earth rotates underneath it, taking one sidereal day to complete a rotation. So, relative to Earth, the plane of oscillation of a pendulum at the North Pole (viewed from above) undergoes a full clockwise rotation during one day; a pendulum at the South Pole rotates counterclockwise. When a Foucault pendulum is suspended at the equator, the plane of oscillation remains fixed relative to Earth. A "pendulum day" is the time needed for the plane of a freely suspended Foucault pendulum to complete an apparent rotation about the local vertical. For example, a Foucault pendulum at 30° south latitude, viewed from above by an earthbound observer, rotates counterclockwise 360° in two days. Using enough wire length, the described circle can be wide enough that the tangential displacement along the measuring circle of between two oscillations can be visible by eye, rendering the Foucault pendulum a spectacular experiment: for example, the original Foucault pendulum in Panthéon moves circularly, with a 6-metre pendulum amplitude, by about 5 mm each period.

When the disk is turned, the plane of oscillation changes just like the one of a Foucault pendulum at latitude φ. Parallel transport of polarization vectors along such sphere gives rise to Thomas precession, which is analogous to the rotation of the swing plane of Foucault pendulum due to parallel transport along a sphere S2 in 3-dimensional Euclidean space.

The motion of a pendulum, such as the Foucault pendulum, is typically analyzed relative to an Inertial frame of reference, approximated by the "fixed stars."

To model the Foucault pendulum, we consider a pendulum of length L and mass m, oscillating with small amplitudes.

Wolfe, Joe, "A derivation of the precession of the Foucault pendulum". "Foucault's Pendulum" by Jens-Peer Kuska with Jeff Bryant, Wolfram Demonstrations Project: a computer model of the pendulum allowing manipulation of pendulum frequency, Earth rotation frequency, latitude, and time. Foucault pendulum model Exposition including a tabletop device that shows the Foucault effect in seconds. "On the Theory of Foucault's Pendulum, and of the Gyrostatic Pendulum". "Foucault Pendulum Experiment by Kamerlingh Onnes and degenerate perturbation theory". "Foucault Pendulum at the South Pole: Proposal For an Experiment to Detect the Earth's General Relativistic Gravitomagnetic Field" (PDF). "A simple geometric model for visualizing the motion of a Foucault pendulum".

Quick Facts

• Foucault introduced his pendulum in 1851 in the first experiment to give simple, direct evidence of the Earth's rotation, which he further demonstrated in 1852 with a gyroscope experiment.
• A "pendulum day" is the time needed for the plane of a freely suspended Foucault pendulum to complete an apparent rotation about the local vertical.
• So, relative to Earth, the plane of oscillation of a pendulum at the North Pole (viewed from above) undergoes a full clockwise rotation during one day; a pendulum at the South Pole rotates counterclockwise.
• When a Foucault pendulum is suspended at the equator, the plane of oscillation remains fixed relative to Earth.
• A few weeks later, Foucault made his most famous pendulum when he suspended a 28-kilogram (62 lb) brass-coated lead bob with a 67-metre-long (220 ft) wire from the dome of the Panthéon, Paris.

Source material: Wikipedia - "Foucault pendulum". Adapted and summarized for DiscoverScroll. Original contributors are credited through the linked Wikipedia article. Read original on Wikipedia. CC BY-SA 4.0. Changes were made from the original.