# Foucault's pendulum?

I don't understand how it works and how it doesn't return to the same spot twice in succession.

Think first of the simplest case, Foucault's pendulum hung right on the north pole. I think you can see in this case it will take exactly 24 hours to return to its starting point, as the earth does a full revolution beneath it. You assume the earth is stable and say the pendulum swings around, when actually the earth is moving and the pendulum maintains its direction.

Now move it somewhere else, say New York City. The earth is still moving underneath it, but the motion is more copmlicated. The time to go through a full cycle gets longer the further south you go, to the equator, where it does not change.

There is a longer description at http://www.si.edu/resource/faq/nmah/pend... , but this is the basic idea. I hope that helps.
Suppose that you set up a pendulum at the north pole. The pendulum swings in an arc which is fixed in direction with respect to the stars. But the earth is turning under the pendulum, so the pendulum's arc appears to move. At lower latitudes than the north pole, the arc moves, but more slowly, as the arc path must be resolved into vector components based on the latitude. Since the component of arc rotation is zero at the equator, the Foucault effect is not observed there.
Foucault pendulum

Foucault's Pendulum in the Panthéon, Paris.The 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 friction. 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.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

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)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 [hide]
1 The dynamics of the Foucault pendulum
2 Foucault pendula in the world
5 References

 The dynamics of the Foucault pendulum

change of direction of the plane of swing of the pendulum in degrees per hour.
Red line: change of direction with respect to the Earth.
Blue line: change of direction with respect to the fixed stars.The diagram shows the change of direction 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 change of direction 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.

The blue line shows the change of direction with respect to the fixed stars. Close to the equator this change of direction of the plane of swing is dominated by the fact that the pendulum is being pulled along with the rotation of the Earth, therefore close to the equator the direction changes at a rate of 15 degrees per hour. Further away from the equator, precession of the pendulum due to the coriolis effect counteracts the effect of being pulled along with the Earth's rotation, resulting in a slower change of direction of the plane of swing.

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 )
 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].

Foucault Pendulum connections
Foucault Pendulum drive systems
Foucault Pendulum vector diagrams
Is the Coriolis force really responsible for the inertial oscillation?, Bull. Amer. Meteor. Soc., 74, 2179–2184; Corrigenda. Bulletin of the American Meteorological Society, 75, 261
How do we Understand the Coriolis Force? Bulletin of the American Meteorological Society 79, 1998, 1373-1385.
The Coriolis Effect: Four centuries of conflict between common sense and mathematics, Part I: A history to 1885 History of Meteorology 2 (2005)
Norman A. Phillips
An Explication of the Coriolis Effect, Bulletin of the American Meteorological Society: Vol. 81, No. 2, 2000, pp. 299–303.
What Makes the Foucault Pendulum Move among the Stars? Science and Education, Volume 13, Number 7, November 2004, pp. 653-661(9)
Classical dynamics of particles and systems, 4ed, Marion Thornton (ISBN 0-03-097302-3 ), P.398-401.
Categories: Articles with unsourced statements | Pendulum
It is possible to design such a pendulum that would return to the same place after a year, but it would require very precice measurement. The pendulum would have to be designed in such a way that the period of the pendulum was synchronized to the Earth's rotation. If the periods matchd exactly, then exactly one year after the start of the pendulum, the path of the pendulum would meet it's original starting point. That's a rather difficult thing to do though.

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