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Home > The Foucault's pendulum > The Foucault's pendulum of the "arts et métiers" museum from Paris

 

 

The Foucault's pendulum which was exhibited during the International exhibition of Paris in 1855, is now in the chorus of the church "Saint Martin des champs" in Paris.
The Foucault's pendulum makes it possible to highlight the rotation of the Earth on itself by only terrestrial means.

 

 


The Foucault's pendulum in the Museum's chapel

 



The first experiments of the Foucault's pendulum was experimented at Paris in 1851

In January 1851, Leon Foucault installed in his cellar in the Arras street in Paris a pendulum. This pendulum constitued of a of 2 m (6,56 feet) long wire supporting a 5 kg weight. Leon Foucault observed a small movement of the oscillation plan of the pendulum.

In February it renews its experiment with a 11 m pendulum at the observatory of Paris. The oscillations of the pendulum were longer and the deviation was more visible. Because Louis Napoleon Bonapartre had been informed of Foucault's works, he asks him to carry out the pendulum experiment in a prestigious place : the Pantheon of Paris.
The experiment took place on March 31, 1851.
The sphere was 28 Kg and the wire was 67 m (219,8 feet) long.

 

Constitution of the pendulum in the "Arts et Métiers" Museum

The sphere :

  • steel, brass, lead .
  • diameter = 18 cm. (0,59 foot) 1 foot = 0,3048 m
  • mass = 25 Kg.

The wire :

  • steel.
  • lenght = 18 m (59 feet) 1 foot = 0,3048 m
  • has used since 1855.

 

The sphere of the Museum

 

The oscillation period of the Foucault's pendulum of the museum is 8,5 s and is apparent complete rotation occurs in 31,78 h = 31. 47 min at the latitude 48° 50 '.
The pendulum describes an ellipse revolving at the angular velocity .


Note: This movement of ellipse can't be seen because the ellipse is very flattened. However an elipsoid oscillation cab sometimes been observed with the pendulum of the museum. This may probably comes from a nonregular throw. This is not the movement in ellipse describes higher.
.



 

Animation carried out by Philippe Morin 2001

 

 

The pendulum is subjected to two forces:

Le pendule est soumis à deux forces :

  • The gravity force
  • The Coriolis force

The oscillations in the terrestrial reference frame, are carried out in a xOy plan according to the following equations :

 

 

with

g : gravity.
l
: wire's lenght.
: angular velocity.
: latitude of the place.

 

Fundamental principles of the Foucault's pendulum

 

1. The plan of the pendulum oscillation is fixed compared to the Earth.
2. The apparent movement of the pendulum occurs in the direction of the needles of a watch in the northern hemisphere and the contrary direction in the southern hemisphere. This movement is apparent because the pendulum doesn't rotates, but the Earth does.
3. The pendulum is not related to the terrestrial reference frame because its point of anchoring is specific.
4. The period of the pendulum is independent of the mass of the sphere.

 


point of anchoring for system

 

Explanation of the pendulum movement for a pendulum localised at the geographical North Pole

- If the pendulum is at the geographical North Pole, the wire will be placed in the axis of rotation of the Earth.
- the Earth rotates in the contrary direction of the needles of a watch of 23 h 56' 4,091" = 86164 S = 1 sideral day (the sidereal day is the time of the rotation of the Earth compared to remote and fixed stars).
- If the pendulum is not related to Earth, it will oscillate in the same plan.
- However, the pendulum will seem turn in the direction of the needles of a watch for a person who is related to Earth and who observes the pendulum.

 

Animation of an half-oscillation of the pendulum at the North Pole

  • It acts of a sight of the top, in the axis of rotation of the Earth.
  • The pendulum oscillates in a fixed plan, while Earth carries rotates in approximately 24 h

(the durations of the évenements are not respected)

Animation carried out by Philippe Morin 2001

 

At the equator, on the other hand, the plan oscillation of the pendulum does not move.

Example: If the experiment were carried out in Cayenne in Guyana which is located at approximately 4° 56 ' North, the pendulum will have a complete rotation in the direction of the needles of a watch in 278. 19 min !

At the geographical South Pole, it will turn in 1 sideral day, in the contrary direction of the needles of a watch.

The time of rotation of the pendulum depends on the latitude and is given by the relation:

 


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