Foucault pendulum

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This article is about the physics experiment and implement. For the novel by Italian philosopher Umberto Eco, see Foucault's Pendulum.
Foucault's Pendulum in the Panthéon, Paris.
Foucault's Pendulum in the Panthéon, Paris.

A Foucault pendulum, or Foucault's pendulum, named after the French physicist Léon Foucault, was conceived as an experiment to demonstrate the rotation of the Earth; its action is a result of the Coriolis effect. It is a tall pendulum free to oscillate in any vertical plane and ideally should include some sort of motor so that it can run continuously rather than have its motion damped by air resistance. The first Foucault pendulum exhibited to the public was in February 1851 in the Meridian Room of the Paris Observatory, although Vincenzo Viviani had already experimented with a similar device in 1661. A few weeks later, Foucault made his most famous pendulum when he suspended a 28-kg bob with a 67-metre wire from the dome of the Panthéon in Paris. In 1851 it was well known that the Earth moved: experimental evidence included the aberration of starlight, stellar parallax, and the Earth's measured polar flattening and equatorial bulge. However Foucault's pendulum was the first dynamical proof of the rotation in an easy-to-see experiment, and it created a justified sensation in both the learned and everyday worlds.

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

At either the North Pole or South Pole, the plane of oscillation of a pendulum remains pointing in the same direction with respect to the fixed stars, while the Earth rotates underneath it, taking one sidereal day to complete a rotation. When a Foucault pendulum is suspended somewhere on the equator, then the plane of oscillation of the Foucault pendulum is at all times co-rotating with the rotation of the Earth. What happens at other latitudes is an intermediate between these two effects.

At the equator the equilibrium position of the pendulum is in a direction that is perpendicular to the Earth's axis of rotation. Because of that, the plane of oscillation is co-rotating with the Earth. Away from the equator the co-rotating with the Earth is diminished. Between the poles and the equator the plane of oscillation is rotating both with respect to the stars and with respect to the Earth. The direction of the plane of oscillation of a pendulum with respect to the Earth rotates with an angular speed proportional to the sine of its latitude; thus one at 45° rotates once every 1.4 days and one at 30° every 2 days.

n = degrees per day

φ = Latitude

n = 360^\circ \sin \phi

Foucault pendulum at the Musée des arts et métiers (Paris); pegs are placed around and are knocked down as the pendulum swing plane veers. This is the original bob from the 1851 Panthéon pendulum
Enlarge
Foucault pendulum at the Musée des arts et métiers (Paris); pegs are placed around and are knocked down as the pendulum swing plane veers. This is the original bob from the 1851 Panthéon pendulum
Foucault pendulum at the Franklin Institute (Philadelphia)
Enlarge
Foucault pendulum at the Franklin Institute (Philadelphia)

Many people found the sine factor difficult to understand, which prompted Foucault to conceive the gyroscope in 1852. The gyroscope's spinning rotor tracks the stars directly. Its axis of rotation turns once per day whatever the latitude, unaffected by any sine factor.

A Foucault pendulum is tricky to set up because imprecise construction can cause additional veering which masks the terrestrial effect. The initial launch of the pendulum is critical; the traditional way to do this, without imparting any unwanted sideways motion, is to use a flame to burn through a thread which is temporarily holding the bob in its starting position. Air resistance damps the oscillation, so Foucault pendulums in museums usually either incorporate an electromagnetic or other drive to keep the bob swinging or are restarted regularly and in fact may have a launching ceremony as an added show.

The Foucault pendulum that hangs in the rotunda of the Lexington Public Library in Lexington, Kentucky in the United States is the largest ceiling clock in the world.[citation needed]

Contents

[edit] The dynamics of the Foucault pendulum

Precession in degrees per hour of the plane of swing of the pendulum. Red line: precession with respect to the Earth. Blue line: should be removed.
Precession in degrees per hour of the plane of swing of the pendulum. Red line: precession with respect to the Earth. Blue line: should be removed.

The diagram shows the precession of the plane of swing of a Foucault pendulum as a function of latitude. The horizontal axis is the latitude: from 90 degrees latitude (at the north or south pole) to 0 degrees latitude (at the equator). The vertical axis shows the rate of precession in degrees per hour; positive numbers indicate precession in the direction which the fixed stars appear to rotate (clockwise in the northern hemisphere, and counterclockwise in the southern hemisphere).

The red line shows the precession with respect to the Earth of a Foucault pendulum. At the pole the pendulum precesses (with respect to the Earth) through an entire circle in one sidereal day.

For example: A Foucault pendulum located on the southern hemisphere at 30 degrees latitude will take two days to precess through an entire circle with respect to the Earth, precessing counterclockwise with respect to the Earth at a rate of 7.5 degrees per hour.

The precession of the plane of swing at 30 degrees latitude. The view is from very high above the north pole. The oval represents a circle that appears distorted because it is viewed at a 60 degrees angle. The line inside the oval is the trace of the plane of swing over the surface that the pendulum is suspended above. On the left the view as seen from a non-rotating point of view, on the right the co-rotating-with-the-Earth point of view. ( Double sized version of this animation )
The precession of the plane of swing at 30 degrees latitude. The view is from very high above the north pole. The oval represents a circle that appears distorted because it is viewed at a 60 degrees angle. The line inside the oval is the trace of the plane of swing over the surface that the pendulum is suspended above. On the left the view as seen from a non-rotating point of view, on the right the co-rotating-with-the-Earth point of view. ( Double sized version of this animation )

[edit] Foucault pendula in the world

Further information: List of Foucault pendula

There is an abundance of Foucault pendula in the world, mainly at universities, science museums and planetariums. The experiment has even been carried out at the South Pole [1].

[edit] See also

[edit] External links

[edit] References

  • Classical dynamics of particles and systems, 4ed, Marion Thornton (ISBN 0-03-097302-3 ), P.398-401.
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