A Foucault pendulum suspended from the ceiling of a high tow

A Foucault pendulum suspended from the ceiling of a high tower located at the Earth’s equator is put in motion in a north-south plane. Explain what would be observed regarding any apparent deviation, or the lack thereof, of the pendulum from the north-south plane during a 24-hour period.

Solution

At either the North Pole or 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 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. At other latitudes, the plane of oscillation precesses relative to Earth, but slower than at the pole; the angular speed is proportional to the sine of the latitude,

   where latitudes north and south of the equator are defined as positive and negative, respectively. For example, a Foucault pendulum at 30° south latitude, viewed from above by an earthbound observer, rotates counterclockwise 360° in two days.

A Foucault pendulum at the north pole. The pendulum swings in the same plane as the Earth rotates beneath it.

In order to demonstrate the rotation of the Earth without the complication of the dependence on latitude, Foucault used a gyroscope . The gyroscope\'s spinning rotor tracks the stars directly. Its axis of rotation is observed to return to its original orientation with respect to the earth after one day whatever the latitude, not being subject to the unbalanced Coriolis forces acting on the pendulum as a result of its geometric asymmetry.