Eddy pendulum
A Foucault pendulum is a spherical pendulum that can oscillate freely in any vertical plane and capable of oscillating for a long time (hours). It is used to demonstrate the rotation of the Earth. It is named in honor of its inventor, Léon Foucault.
Foucault's Original Experiment
The first public exhibition of Foucault's pendulum took place in February 1851, in the meridian of the Paris Observatory. A few weeks later, the French physicist Léon Foucault made his most famous demonstration inside the Panthéon in Paris, when he suspended a 28 kg lead pendulum (a brass-coated cannonball) by a 67-meter cable. meters long that hung just below the center of the Pantheon's dome. The swing plane of the pendulum rotated to the right 11° per hour, making a complete circle in 32.7 hours. The original mounting used in 1851 in the Panthéon was transferred in 1855 to the Museum of Arts and Crafts in Paris. A second temporary installation was made at the Pantheon, in 1902, for the 50th anniversary of the original experiment.
During the museum's reconstruction in the 1990s, the original pendulum was temporarily displayed in the Panthéon (1995), but was later returned to the Museum of Arts and Crafts in Paris before its reopening in 2000. April 2010, the suspension cable of the pendulum snapped, causing irreparable damage to the pendulum and the museum's marble floor. An exact copy of the original pendulum had been swinging permanently since 1995 under the dome of the Pantheon in Paris until 2014, when it was dismantled during repair work on the building. In September 2017 the pendulum was back up and running again.
Physical - natural effects of the terrestrial rotation movement
With regard to planet Earth, the movement of the earth's rotation gives rise to a series of effects that are clarified and defined by the observation of the Foucault pendulum, an instrument that serves to demonstrate the movement of the earth's rotation and its physical consequences of said movement. These consequences or effects are those suffered by moving objects and the large fluid masses of the earth's surface (atmosphere and hydrosphere) in their displacements, movements that can also be defined as apparent, inertial, three-dimensional and asymmetric responses to the movement of the earth's rotation..
- It is an apparent and non-real effect. It is not the pendulum that deviates to the right (in the time sense) but it is the ground that turns in the anti-horn sense. By definition, the pendulum maintains the initial direction of the oscillations without diverting to losing strength and stopping. So the motion of the pendulum knocking down all the spheres in the pendulum circle over 12 hours is a demonstration of the actual effect of the double spin of that circle in the anti-horn sense (double twist during 24 hours). This is what happens in the Northern Hemisphere, while in the southern hemisphere, the Earth's surface revolves in a time sense, so the apparent deviation of the pendulum will be carried out in opposite direction (in an anti-horn sense).
- It's an inertial effect. The huge mass of the lower sphere compared to the height from the base point is that which explains, by inertia, that it may be oscillating for hours keeping the original direction. In this regard it should be clear that a magnet or rather electromagnet, located at the base of the pendulum, can perpetually turn the motion of swing of the pendulum.
- It's a three-dimensional effect. This is evident: all the bodies that move on the Earth's surface have volume and the Earth's rotation movement will act differently as the dimensions, size, mass and density and, on the other hand, with the interaction with other bodies that also move. For example, all storms formed by convection usually form clouds if atmospheric humidity in that place is enough and dust clouds in areas where the earth's surface is very dry. In turn, these clouds and that dust have a given cycle: clouds change shape and size when they rise due to the ascending air during the convection process. The formation and development of a tornado is an example of a three-dimensional process of meteorology that is not usually very well described. It has been said sometimes of a wet air column that descends from a large cloud and when it comes down it is turning more and more rapidly until it gets in touch with the ground, where it causes great destruction even though its turning radius is very small. The truth is that a tornado is initially formed by a decrease of cold and dry air from the upper edge of the cloud and descends to the front of the same rotating in a time sense but not seen because it is a cold and dry air until it reaches the ground at a high speed of rotation. On the ground is where a whirlpool (in time sense as we have said) forms that raises a lot of dust and debris from various objects by throwing them around. But immediately a funnel is formed in the anti-horn sense formed with warm and humid air that begins to ascend increasing in size and turning radius and, therefore, diminishing its speed, but forming with warm air that cools when ascending, forms an fun cloud that is not but the already developed phase of the tornado as can be seen in the respective article. The smooth winds in the equator, the equatorial current, the cold marine currents and to a greater or lesser degree, all the others originate as an inertial response of the earth's rotation movement. The same is true of jet currents (jet – stream), hurricanes and many other phenomena.
- It's an asymmetrical effect. The asymmetry of the rivers is an example that is due to the asymmetric effect of the Earth's rotation movement. The rivers are asymmetrical in terms of its channel, its basin, the spolones or natural dikes of the channel, the tributaries and its confluences with the main river, the deposits of floods or sediments, the greater or less energy of its flow or the transport of sediments, the erosive power, the catch or river interception and the formation of residual rivers (sometimes also called).
Description and rationale
Let's first consider the device shown in the figure. If we rotate the platform while the pendulum is swinging, we will observe that the plane of the oscillations remains unchanged with respect to an inertial observer. This effect is due to the inertia of the pendulum mass. Since the two forces that act on it (its weight and the tension of the thread) are contained in the plane of the oscillations, these, once started, will always take place in the same plane. To change the plane of the oscillations would require a component of force normal to that plane.
On the contrary, it is obvious that the plane of the oscillations will not remain unchanged for an observer located on the rotating platform, who will obviously be a non-inertial observer; for this observer, the plane of the oscillations will precess around the vertical axis (axis of rotation) in the opposite direction to the rotation of the platform and with the same angular speed (of precession).
This property of the inalterability of the plane of the oscillations of the pendulum was used by the French physicist Bernard León Foucault (1819-68) to verify the movement of rotation of the Earth around its axis and to demonstrate that the Earth does not constitute an inertial referential. Foucault publicly performed his experiment in 1851, under the dome of the Panthéon in Paris, using a 28 kg mass suspended from a 70 m long thread. The period of a pendulum of that length is about 17 s. The suspension of the upper end of the thread allowed the pendulum to swing with equal freedom in all directions. A circular raft, filled with sand, about 3 m in radius, was arranged around the point on the ground directly below the point of suspension, so that a metal needle placed at the bottom of the pendulous mass swept the sand away at each point. oscillation. It was clearly seen that, in successive oscillations, the oscillation plane of the pendulum rotated clockwise. In one hour the oscillation plane of the pendulum rotated about 11°, and the circumference was completed in just over 32 hours.
Why does the swing plane of the pendulum rotate? It is easy to understand that, if the experiment had been carried out at the North Pole, it would be evident that the oscillation plane of the pendulum would remain fixed in an inertial referential, while the Earth would rotate under the pendulum at the rate of one revolution every 24 hours. Conversely, an observer situated "above" the Earth would see the oscillation plane of the pendulum rotate in the opposite direction to that of the Earth's rotation, making one turn every 24 hours. The situation is very different and much more difficult to analyze when we leave the North Pole and locate ourselves in a place on Earth with geographic latitude λ. Then, as we have already seen when describing Foucault's experience, the time taken by the plane of oscillation of the pendulum to rotate 360° is greater than necessary at the Pole. When the experiment is carried out in the equatorial zone of the Earth, the pendulum swings without changing, the effect does not occur.
Careful calculations allow us to relate the angular speed Ω of rotation of the plane of the pendulum's oscillations with the angular speed ω of rotation of the Earth:
(1)Ω Ω =ω ω without λ λ ♫{displaystyle Omega =omega sin {lambda }',}
where (90°-λ′) is the angle formed by the vertical of the place and the axis of rotation of the Earth. The apparent gravitational acceleration g* has the direction of the vertical of the place and since g* is only slightly deviated with respect to g (0° 6', maximum), the angle λ′ is very approximately equal to the geographical latitude of the place, that is, λ≈λ′. Obviously, the oscillation plane of the pendulum precesses in the laboratory referential with an angular velocity Ω given by expression (1). In the Northern Hemisphere the precession takes place in a clockwise direction (looking down).
We can interpret the result expressed by (1) as follows:
- in a place of the Earth, latitude λ, the soil behaves like a rotating platform with a angular velocity Ω = ωz = ω sen λ
(vertical component of the angular velocity of the Earth) so that the precession movement of the Foucault pendulum is the one that corresponds to that angular velocity. In this way, the time taken by the plane of oscillation of the pendulum to make a complete turn is
(2)T=2π π ω ω without λ λ =24without λ λ hours{displaystyle T={frac {2pi }{omega sin {lambda }}}}{frac {24}{sin {lambda }}}{text{horas}}}}}}}
and the angle rotated in an hour θ θ {displaystyle theta ,} is the function of the latitude of the place:
(3)θ θ =15orwithout λ λ {displaystyle theta =15^{o}sin {lambda },}
The Foucault pendulum experience is an effective proof of the Earth's rotation. Even if the Earth were and had always been covered in clouds, Foucault's experiment would show that the Earth is rotating. Likewise, this pendulum allows determining the latitude of the place without resorting to astronomical observations.
Geometric phase
Foucault's pendulum has been reinterpreted as a particular case of the universality of the concept known as geometric phase, which on the other hand is related to parallel transport, which is illustrated in the figure, and to the Gauss-Bonnet theorem, which relates the curvature of a surface to its Euler characteristic.
In this sense, it is essential to take into account that the period of rotation of the Earth is much longer than the period of oscillation of the pendulum. Specifically, the change in direction of the force of gravity experienced by the pendulum—in the Earth's reference frame—is slow enough to satisfy the adiabatic theorem, so that there is no effective exchange of energy between the two oscillations.
Relevant Foucault pendulums
United States
In New York City (40º North latitude) at the entrance of the United Nations building. It was inaugurated in 1955. It has a golden sphere of about 90 kg suspended from the ceiling about 22.5 m above the ground by a stainless steel wire so that it can oscillate in any plane. The oscillation plane deviates continuously clockwise so that it completes one revolution in 36 hours 45 minutes.
Hungary
Hungary has more than 30 Foucault pendulums. The first such pendulum was made in 1880 by Adolf Kunc in Szombathely.
Spanish-speaking countries
Mexico
- The Manuel Gómez Morín Educational and Cultural Center in Santiago de Querétaro, in Querétaro, Mexico, has a Foucault pendulum of 28 m in total length, with a bronze mass (64 cm in diameter and a weight of 280 kg) suspended from a steel cable. Its period is 9.3sec, turning 360 degrees every 66.79 hours or 5.38 degrees/hour.
- In the National Library of Science and Technology "Víctor Bravo Ahuja" of the National Polytechnic Institute of Zacatenco, Mexico, it was placed in December 2016.
- The Sinaloa Science Center has a pendulum located at the main entrance, suspended with a 17-metre cable from a dome. The dial weighs 400 kilograms and its oscillation period is approximately 8.3 seconds and remains in motion by a magnetic mechanism, which offsets the loss of energy by friction. This pendulum is located at the entrance of the museum and has copper bars that the dial melts to better observe the movement of the pendulum.
- The Military School of Engineers, completed and inaugurated by President Enrique Peña Nieto on July 6, 2018, has a Péndulo de Foucault in the Academic Building.
Spain
- The Museum of Science in the Coruña has one of the oldest pendulums of Foucault in Spain, five floors high.
- In Madrid the Royal Astronomical Observatory located next to the Parque del Buen Retiro has a pendulum of Foucault.[chuckles]required]
- In Barcelona in the CosmoCaixa Barcelona, in its entrance hall. He was the first to settle in Spain in 1980.
- In Santander there is a pendulum of Foucault in the main hall of the CIC building, in the Cantabria Science and Technology Park (PCTCAN). It has a length of 17 meters and 120 kilograms of mass in the sphere.
- In Huelva there is a pendulum of Foucault in the Galileo Galilei building of the University of Huelva.
- In Granada there are three specimens of these pendulums: One at the Higher Technical School of Road Engineering, Canals and Ports of the University of Granada, another at the Faculty of Sciences in the physics building of the University of Granada, and another at the Parque de las Ciencias de Granada.
- In Valencia at the Príncipe Felipe Science Museum of the City of Arts and Sciences there is another Foucault pendulum exposed to the public.
- In Salamanca in the Trilingual Building of the Faculty of Sciences of the University of Salamanca, where the Degree in Physics is taught.
- In Valladolid, at the Museum of Science, where it is suspended from an 11-metre-long cable and formed by an 80-kg-weight dial.
- In Becerril de Campos, in San Pedro Cultural, a pendulum of Foucault is displayed along with other elements for the study of astronomy.
- In Castellón, in the lobby of its Planetarium.
- In Orense, in the lobby of the Faculty of Sciences.
- In Santiago de Compostela, in the lobby of the Faculty of Physics.
Chili
- In the city of Valdivia. Located at a latitude of almost 40° South, it was the most southern in the world until 2012. It is located on the Avenida costanera Arturo Prat, opposite the Center for Scientific Studies (CECs) to which it belongs. It is part of the walk of the so-called “Scientific Coast” on the banks of the Valdivia River. It was created by the Spanish physicist Miguel Cabrerizo in 2007. It consists of a chrome lead sphere of 100 kg weight, hanging from a steel wire of 13 meters long supported by a steel structure ripped by the lamp of an old lighthouse of the centuryXIX, which was in disuse and currently has a system of solar panels for lightning energy. The pendulum has a 7-second oscillation period. Its apparent turn is 10° in every hour, completing a rotation every 36 hours. In addition, this turn makes anti-hour sense, the other way around that is located in the northern hemisphere.
- In the city of Puerto Montt (Latitude: 41° 30' S) It is located in the new units of the San Francisco Javier College Its manufacture was carried out by the engineer Gonzalo Arroyo of the Federico Santa María Technical University. It is a chrome sphere of 115 kilos, a length of 19.5 meters with a oscillation period of 8.7 seconds. Its design includes a device to compensate for friction with air and between mechanical parts so that it does not stop.
- In the city of Santiago (33o Sur) there are two.
In 1970, a pendulum was installed at the Natural History Museum. It has a 12 m high suspension cable and a mass of 45 kg.
El Segundo belongs to the Faculty of Physical Sciences and Mathematics of the University of Chile. It is located in the central hall of the Central Library. He had the advice of Miguel Cabrerizo. It was inaugurated on November 3, 2017. It is a steel ball 30 centimeters in diameter filled with lead with a weight of 100 kilograms, hung from the skylight by an 18-meter steel cable. The swing plane of the pendulum rotates approximately 8 degrees per hour, counterclockwise, taking just over 43 hours to complete one full turn.
Argentina
- In the city of Buenos Aires (Latitude: 34o Sur) there are two pendulums, both in the context of the University of Buenos Aires.
- Located in Hall II (destinated to the Faculty of Exact and Natural Sciences) of University City. The project was executed by the Faculty of Exact and Natural Sciences and opened in November 2004. It consists of a casting sphere, an iron and carbon alloy, of 30 cm in diameter that weighs 90 kg. It has a height of almost 27 meters and a period of oscillation of a little more than 10 seconds. Physical law predicts that the plane of oscillation should rotate contrary to the clock needles at a rate of 8.5 degrees/hour. Checked on several occasions, the law is met with an error less than 10%, the standard error that the most famous pendulums have. The pendulum stops at 6 or 7 hours after it has been put into operation as, at the time of its inauguration, it has no energy recovery device.
- Located in the Museum of Science and Technology, at the headquarters of the Faculty of Engineering of Las Heras Avenue.
- City of La Plata (Latitude 34o Sur), located in the Teatro Argentino, installed in 2011, is one of the largest installed in South America and the only one that looks within a lyric theater. It was designed and built by the Faculty of Astronomical Sciences of the National University of La Plata (UNLP). It is a bronze sphere that suspended from the ceiling to the theatre's foyer, which allows anyone who stops to observe it, to avoid the rotation of the planet. It is almost 18 meters long, the dial is approximately 40 cm in diameter and more than 200 kilos of mass. The disc where the blades are is 120 mm in diameter and the height of the entire suspension set is less than 200 mm.
- City of Cordoba (Latitude 31° South) in the center of scientific interpretation Square Heaven and Earth in the Parque Las Tejas. The interpretation centre, opened in September 2017, is an initiative of the National University of Córdoba and the Government of the Province. The pendulum is 12 meters high
Models of Foucault's pendulum
Foucault pendulum model 1. | Foucault pendulum model 2. | Foucault pendulum model 3. |