Foucault’s Pendulum in the World and at the

Gdańsk University of Technology

Bogusław KuszFaculty of Technical Physics and Applied MathematicsGdańsk University of Technology

History Jean Bernard Léon Foucault wanted to become a

doctor, but ... he was fainting at the sight of blood. He became interested in inanimate matter achieving significant success in astronomy, chemistry and the physics of electricity and magnetism. He is best-known as the author of an experiment proving that Earth rotates on its axis. In the cellar of his home Foucault suspended a bob (5 kg) on a two-metre wire and noticed that the plane of oscillations of the pendulum was regularly rotating. He repeated the experiment publicly in 1851 suspending a pendulum with a 67-metre wire in the Panthéon in Paris. The spectators could see that the Earth’s rotation under the pendulum resulted in a continuous change of the plane of pendulum oscillations. Foucault encouraged people to participate in the experiment saying:

“Come and see how the Earth is rotating”.

Foucault’s Pendulum

                  

              If the Foucault pendulum were placed on a pole, the plane of its oscillations would make a full revolution in ca. 24h (23h 56min ), i.e. the time which is needed by Earth to make one compete revolution on its axis. Time T of one complete revolution of the plane of the pendulum oscillations on geographic latitude q can be calculated from the following formula:

T = 24h/ sin q (for Gdańsk T is equal to approx. 30h)Hence, when the pendulum is placed not on a pole, but somewhere at an intermediate geographic latitude, the time needed for a complete revolution of the plane of the pendulum oscillations will be longer. No revolution of the plane of oscillations with respect to the Earth will be observed on the equator.

Problems related to the pendulum motion:

1. The resistance of air and the internal friction of suspension result in a continuous loss of energy which in consequence is the reason why the pendulum stops. The “pendulum’s life” may be prolonged by increasing the pendulum weight and length. Another way to maintain the oscillations is to supply the lost energy, e.g. by applying another force in addition to the force of gravity.

2. During long operation of the pendulum, any lack of symmetry in the suspension system, and even movement of air, may lead to disturbance of motion. The pendulum starts moving in an elliptic motion which in consequence can either accelerate or slow down the expected change of the direction of oscillations.

B B

B

free forced from beneath parametric forced from the top

Ways of maintaining pendulum oscillations.

Foucault pendulums around the world

Foucault pendulum at the Smithsonian Museum. 108 kg 16 m

Univ. of Louisville 25m 59 kg

South Pole (winter 2001)

33m 25kg

Franklin Institute Philadelphia

27 m 80 kg

Centre Universitaire

de Luxemburg

32 kg 16 m

MacNaughton Physical Sciences Building University of Guelph

“Small” Foucault Pendulum

Pendulums in Poland

The wire of the pendulum spheroid in Krakow is 46.5 metres long and the spheroid is 25 kg in weight. The first demonstrations of the Foucault Pendulum in Krakow took place in 1949, almost 100 years after the first public exhibition in the Panthéon in Paris. Venue - St Mary's Church

www.stronamiasta.com

Frombork - Radziejowski Tower. The pendulum steel rope is 28 m long, and the bob is 46.5 kg in weight(pendulum without stimulation)

Institute of Physics, Nicolaus Copernicus University, Toruń

16 m 29 kg (stimulated pendulum)

In 1837 Poisson published a dissertation in which he was trying to prove that artillery shells fired horizontally on the northern hemisphere should deflect eastwards as a result the Earth’s rotation. He also noticed that the Earth’s rotation should affect the motion of pendulums, however, in his opinion, the effect was too small to be observed. Poisson’s considerations were based on earlier (1831) calculi of his student Coriolis who, in his doctoral dissertation, dealt with accelerations in rotating coordinate systems. Foucault knew Poisson’s work and he shared his views as to the minor effect of the deflection of the plane of pendulum oscillations, however, after a series of experiments, he understood that the pendulum had the property of accumulating small deflections into one large deflection following many oscillations. He conducted his first experiments in the cellar of his home with a pendulum 2 m long and 5 kg in weight. The public exhibition, mainly for his colleague scientists, took place in the Paris Observatory on 3 February 1851 with a 11 m pendulum. Foucault invited his guests with the words printed on a banner outside the Panthéon in Paris - the "temple" of the most outstanding minds in France - "Vous êtes invités à venir voir tourner la Terre..." which means: “You are invited to come and see how the Earth is rotating”. The exhibition was a great sensation and Prince Louis Napoleon Bonaparte, future Napoleon III, asked Foucault to show the experiment to the wide public. It took place on 26 March 1851 with a pendulum - a 28 kg cannon ball suspended with a 67 m wire from the dome of the Panthéon in Paris. The experiment was a sensation for the spectators of the world exhibition w Paris and triggered off a huge number of similar experiments around the world.

SELECTED LARGE PENDULUMS

Foucault’s Pendulums are installed worldwide at numerous locations that are important for culture, science or politics. The following table contains a selection of the most interesting installations. Length L is rounded up to full metres, and weight W - to fill kilograms.

Information -http://www.phys.uni.torun.pl/phys/WAHADLO/wahadlo-w.html

Location L[m] W[kg]

Panthéon, Paris 67 28

Oregon Convention Center in Portland 27 408

Museum of Science and Industry, Chicago 20 300

National Museum of American History, Washington, DC 21 105

Radziejowski Tower, Frombork 28 47

UNO, New York 23 91

Institute of Physics, Toruń 16 29

Gdańsk University of Technology 26 64

Interesting Web Sites

• www.calacademy.org/products/pendulum • www.phys-astro.sonoma.edu/people/ students/baker/SouthPoleFoucault.html • www.physics.uoguelph.ca/foucault/foucault1.html • www.abc.net.au/surf/pendulum/default.htm • www.phys.uni.torun.pl/phys/WAHADLO/wahadlo-w.html • stalker.republika.pl/foucault_teksty.htm • plus.maths.org/issue9/xfile • www.frombork.art.pl/Ang23.htm • fi.edu/time/Journey/Pendulum/tfi_pendulum.html