Foucault pendulum
If a long and heavy pendulum suspended from the high roof above a circular area is monitored over an extended period of time, its plane of oscillation appears to change spontaneously as the Earth makes its 24-hourly rotation.
The pendulum was introduced in 1851 and was the first experiment to give simple, direct evidence of the Earth's rotation.
[2] The first public exhibition of a Foucault pendulum took place in February 1851 in the Meridian of the Paris Observatory.
A few weeks later, Foucault made his most famous pendulum when he suspended a 28-kilogram (62 lb) brass-coated lead bob with a 67-metre long (220 ft) wire from the dome of the Panthéon, Paris.
[2] Foucault explained his results in an 1851 paper entitled Physical demonstration of the Earth's rotational movement by means of the pendulum, published in the Comptes rendus de l'Académie des Sciences.
He wrote that, at the North Pole:[3] ...an oscillatory movement of the pendulum mass follows an arc of a circle whose plane is well known, and to which the inertia of matter ensures an unchanging position in space.
If these oscillations continue for a certain time, the movement of the earth, which continues to rotate from west to east, will become sensitive in contrast to the immobility of the oscillation plane whose trace on the ground will seem animated by a movement consistent with the apparent movement of the celestial sphere; and if the oscillations could be perpetuated for twenty-four hours, the trace of their plane would then execute an entire revolution around the vertical projection of the point of suspension.The original bob used in 1851 at the Panthéon was moved in 1855 to the Conservatoire des Arts et Métiers in Paris.
[4] During museum reconstruction in the 1990s, the original pendulum was temporarily displayed at the Panthéon (1995), but was later returned to the Musée des Arts et Métiers before it reopened in 2000.
[8] At either the Geographic North Pole or Geographic South Pole, the plane of oscillation of a pendulum remains fixed relative to the distant masses of the universe[citation needed] while Earth rotates underneath it, taking one sidereal day to complete a rotation.
When a Foucault pendulum is suspended at the equator, the plane of oscillation remains fixed relative to Earth.
[10][11] For example, a Foucault pendulum at 30° south latitude, viewed from above by an earthbound observer, rotates counterclockwise 360° in two days.
A Foucault pendulum requires care to set up because imprecise construction can cause additional veering which masks the terrestrial effect.
Heike Kamerlingh Onnes (Nobel laureate 1913) performed precise experiments and developed a fuller theory of the Foucault pendulum for his doctoral thesis (1879).
By a perturbation analysis, he showed that geometrical imperfection of the system or elasticity of the support wire may cause a beat between two horizontal modes of oscillation.
Notably, veering of a pendulum was observed already in 1661 by Vincenzo Viviani, a disciple of Galileo, but there is no evidence that he connected the effect with the Earth's rotation; rather, he regarded it as a nuisance in his study that should be overcome with suspending the bob on two ropes instead of one.
Air resistance damps the oscillation, so some Foucault pendulums in museums incorporate an electromagnetic or other drive to keep the bob swinging; others are restarted regularly, sometimes with a launching ceremony as an added attraction.
Besides air resistance (the use of a heavy symmetrical bob is to reduce friction forces, mainly air resistance by a symmetrical and aerodynamic bob) the other main engineering problem in creating a 1-meter Foucault pendulum nowadays is said to be ensuring there is no preferred direction of swing.
As early as 1836, the Scottish mathematician Edward Sang contrived and explained the precession of a spinning top.
When the disk is turned, the plane of oscillation changes just like the one of a Foucault pendulum at latitude φ.
[16] Spin of a relativistic particle moving in a circular orbit precesses similar to the swing plane of Foucault pendulum.
"[20] These stars, owing to their immense distance from Earth, exhibit negligible motion relative to one another over short timescales, making them a practical benchmark for physical calculations.
While fixed stars are sufficient for physical analyses, the concept of an absolute reference frame introduces philosophical and theoretical considerations.
Newtonian absolute space Cosmic microwave background (CMB) Mach's principle and distant masses General relativity and spacetime To model the Foucault pendulum, we consider a pendulum of length L and mass m, oscillating with small amplitudes.
In a reference frame rotating with Earth at angular velocity Ω, the Coriolis force must be included.
