The Foucault Pendulum

1. The Foucault Pendulum "You are invited to see the Earth turning …"

2. Jean Bernard LéonFoucault (1819-1868) Jean Bernard Leon Foucault, better known under the name of Leon Foucault, was a French physicist. Born in Paris on September 18, 1819 as a son of a bookseller. Died in Paris on February 2, 1868 of paralysis. In 1845 he made with Louis Fizeau (1819-1996) the first successful daguerreotype of the Sun. In 1850 he obtained the first accurate determination of the speed of light by using the rotating mirror technique. In 1851 he invented the Foucault pendulum which he used to measure the Earth's rotation. In 1852 he invented his gyroscope. In 1857 he improved the mirrors used in telescopes. The discoveries and inventions of Foucault do not only concern astronomy. He also known as the discoverer of the Foucault currents. This multitude of inventions, which are spread over two decades, were rewarded by many honours: “Officier de la Légion d‘Honneur”, member of the Office des Longitudes, foreign member of Royal Society and the Academies of Berlin and Saint-Petersburg, and finally member of the Academy des Science in 1865.

3. The experience of Foucault The pendulum of Leon Foucault is without doubt the most resounding experimental image of the XIX century. "You are invited to come to see the Earth turning.... Such are the words of Leon Foucault in 1851 to present his discovery and to make visible the rotational movement of the Earth around its axis. One century and half later, the invitation of Foucault remains still captivating and the rotating oscillations of the pendulum keep the same capacity of fascination.

4. Short history of the pendulum of Foucault The Foucault pendulum was constructed in 1851 in the cellar of the maternal house, 34 rue d’Assas in Paris where Leon Foucault had installed his working laboratory. For his first pendulum he used a small ball of 5kg suspended to a wire of two meters length. The very first presentation was done in the room “Méridienne” at the Paris observatory. The length of this pendulum was eleven meters. However, the first official public demonstration happened in the Pantheon, at the request of the President of the Republic, prince Bonaparte. For this great event, Foucault launched the invitation to come to see ‘turning the Earth’. He used a sphere of 28 kg fixed to a steel wire, actually a piano cord, having a length of 67 m and a diameter of 1,4 mm. Under the pendulum was a sand hillock where the pendulum came to chip and leave its changing traces. Thus common people could easily recognize the rotational movement of the Earth.

5. The pendulum of Foucault of the Centre Universitaire The imposing height of the hall of the Science Building of the Centre Universitaire was predestined to house the Foucault pendulum as important symbol of scientific achievement.

6. Suspension of the pendulum The pendulum is fixed on the iron-work of the hall of the Centre Universitaire.

7. The sphere The brass sphere, mass 32 kg, diameter 200 mm, is fixed at the end of a galvanized steel wire with 3 mm diameter and 16 m length.

8. Which is the direction of rotation? For observers at the Northern hemisphere, the direction of pendulum rotation is clockwise and for observers at the Southern hemisphere, rotation is opposite in direction. The observed rotational period of the pendulum (rotation angle of 360°) depends on the latitude. The pendulum located at the poles has a rotational period of 24 h, while at the equator the effect of rotation is not observed. At the Centre Universitaire, the rotational period of the pendulum is 31 h 25 min, this corresponds to a rotation angle of 274° per 24h.

9. The calculation of the period of oscillation The pendulum oscillation period T is given by the relation: osc l = distance between the fixation point and the centre of mass of the pendulum g = intensity of the gravitation field

10. Losses of energy of the pendulum To compensate the energy loss due to the friction of the air and the extensibilityof the cable, the basic idea is to increase the potential energy by raising the mass of the pendulum while passing its position of minimum deflection and to accelerate the ball by dropping the ball while passing the position of maximum deflection. The potential energy is transformed into kinetic energy. The amplitude of the raising movement is controlled by a computer. The up to 30 mm raising of the pendulum weight is performed with the assistance of an electro-magnet.

11. Compass card The "Compass card", which you see on the glass plate under the pendulum and on the screen of the computer on your right-hand side indicate the cardinal points. The arrow on the computer, as well as the laser beam in the sphere indicate the position of the pendulum relative to the cardinal points.