Kozhevnikov Evgeniy
The purpose of this work is to systematize the collected information and create a desktop demonstration installation of the Foucault pendulum.
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Regional competition for young researchers “Step into the future”
Topic: “Foucault Pendulum”
Completed:
Kozhevnikov Evgeniy Alexandrovich
9 "B" class MBOU "Secondary School No. 6"
Supervisor:
Davydova Irina Nikolaevna
Physics teacher MBOU "Secondary School No. 6"
Kolchugino
2012
Introduction 3
1.1. History of the creation of the Foucault pendulum 3
1.2. Foucault experiment 5
1.2.1. Experience Demonstration 5
1.2.2. Principle of operation of the pendulum 6
1.3. Biography of J.B.L. Foucault 6
1.4. Functioning Foucault pendulums 7
1.4.1. Operating pendulums in Russia and CIS countries 7
1.4.2. Operating pendulums in other countries 9
1.5. Interesting facts 11
2. Practical part 11
2.1. Pendulum models that you can make yourself 11
2.2. Pendulum model submitted to competition 13
Conclusion 14
References 15
Introduction
I learned about the existence of the Foucault pendulum from a 9th grade physics course (topic “Oscillations and Waves”). And then I watched the TV show “Galileo”, in which I saw a model of a pendulum made by the craftsmen of the program. And I decided to see if I could make such a working model myself. To do this, I collected and studied information from various sources: books, media, the Internet. The material was so interesting that I decided to systematize it and make a model myself.
The purpose of this work is to systematize the collected information and create a desktop demonstration installation of the pendulum. In the work, I presented material about the history of the creation of the pendulum, its first demonstration, the principle of operation, about various types of pendulum models created around the world, and I offer for the jury’s consideration a model of the pendulum made by myself.
I presented my work at a physics lesson in front of my classmates and at the school scientific and practical conference “Roads of Discovery” and was awarded a certificate for winning the “Applied Physics” category.
1.1 History of the creation of the Foucault pendulum
It turns out that not only Galileo loved to watch the swinging of the lamps in the cathedral. He passed this passion on to his student Vincenzo Viviani. In 1660, unlike Galileo, he drew attention to another feature of the oscillations of a pendulum on a long thread.
It turns out that the plane of their swing is constantly deviating, and always in the same direction - clockwise, if you look at the pendulum from top to bottom. And in 1664, a scientist from the city of Padua, Giovanni Poleni, connected this deviation with the rotation of the Earth - they say, the Earth rotates, but the plane of oscillation of the pendulum remains the same. So this is observed by people standing on Earth as a deviation of the swing plane of a pendulum.
But it turns out that this property of the pendulum was also known to the ubiquitous ancients. Indeed, the new is the well-forgotten old. This is what the Roman scientist Pliny the Elder, who lived in the 1st century, wrote about this in his “Natural History”. n. e.: “It is possible to arrange a compass without a magnet. To do this, you need to take a pendulum and make it swing in a certain direction. When the ship turns, the pendulum will maintain the direction given to it in its swings” (Fig. 1).
Rice. 1. Compass of Pliny the Elder on the ship Fig. 2. A rod clamped in a rotating
Patrone, does not change the plane of oscillation
It must be said that something in Pliny’s advice is questionable. First, Pliny could not have known about the compass; in Europe they learned about it much later, or at least they gave it that name. So much of what is attributed to Pliny could well have been contributed by the translator of his works from Latin in the 18th century. Secondly, it is impossible for the pendulum not to change the plane of its oscillations for so long; its suspension cannot be made ideal, and the air around it will cause interference. And thirdly, the rotation of the Earth will itself “deflect” the plane of oscillation of the pendulum, so that the ship “goes” in a circle. But one way or another, Pliny noticed that the pendulum retains the plane of its swing. And this property was brilliantly used by the French scientist Jean Bernard Leon Foucault (1819-1868), creating his famous pendulums. Since childhood, Foucault did not like to study; knowledge was difficult for him. But he had golden hands - he made toys, instruments, built a steam engine himself, and worked well on a lathe.
Foucault once noticed that if you clamp a long elastic steel rod in a machine chuck and make it vibrate (Fig. 2), the plane of oscillation will not change even with rapid rotation of the chuck. Having become interested in this phenomenon, Foucault first began to observe the behavior of the same rod in a rotating cartridge, and then, for convenience, decided to replace it with a pendulum.
Foucault conducted his first experiments with the pendulum in the cellar of his house in Paris. He attached a two-meter long hardened steel wire to the top of the cellar vault and suspended a five-kilogram brass ball from it. Taking the ball to the side, fixing it with a thread near one of the walls, Foucault burned the thread, giving the pendulum the opportunity to swing freely. And within half an hour he witnessed the rotation of the Earth.
This happened on January 8, 1851. And a few days later, Foucault repeated his experience at the Paris Observatory at the request of its director, the famous French scientist Arago. This time the length of the wire was already 11 m. And the deviation of the swing plane of the pendulum was even more noticeable.
Foucault's experience was talked about everywhere. Everyone wanted to see the rotation of the Earth with their own eyes. It got to the point that the President of France, Prince Louis Napoleon, decided to stage this experiment on a truly gigantic scale in order to demonstrate it publicly. Foucault was given the building of the Parisian Pantheon with a dome height of 83 m.
1.2. Foucault's experience
1.2.1. Demonstration of experience
The first public demonstration was carried out by Jean Foucault in 1851 in the Paris Pantheon (Fig. 3): under the dome of the Pantheon, he suspended a metal ball weighing 28 kg with a point attached to it on a steel wire 67 m long; the pendulum mount allowed it to oscillate freely in all directions. directions, a circular fence with a diameter of 6 meters was made under the attachment point, a sand path was poured along the edge of the fence so that the pendulum, in its movement, could draw marks in the sand when crossing it. To avoid a side push when starting the pendulum, it was taken to the side and tied with a rope, after which the rope was burned.
The period of oscillation of the pendulum with such a suspension length was 16.4 seconds, with each oscillation the deviation from the previous intersection of the sand path was ~3 mm, in an hour the plane of oscillation of the pendulum rotated more than 11° clockwise, that is, in about 32 hours it completed a full revolution and returned to its previous position.
1.2.2. The principle of operation of a pendulum
The principle of operation of the Foucault pendulum is that for each oscillation it deviates about a given trajectory due to the rotation of the Earth around its axis; this effect is most noticeable at the poles of the planet and is not noticeable at all at the equator. The larger the pendulum, the more noticeable the deflection effect. If a working pendulum, or rather the frame, begins to rotate, then the pendulum maintains its position, the same happens with the Earth, it rotates under the pendulum and it seems that the pendulum changes the direction of its oscillations, but in fact the pendulum simply maintains its position, and the Earth rotates. Since the pendulum is not rigidly connected to its frame, the frame rotates with the ground, and the pendulum maintains its position.
1.3. Biography of J.B.L. Foucault
FOUCAULT Jean Bernard Leon (1819-1868), French physicist, famous for his experiments in optics and mechanics. Born September 18, 1819 in Paris. He received his primary education at home. At the insistence of his father, he studied medicine, but became interested in experimental physics. From 1845 - scientific columnist for the newspaper "Journal of Discussions" ("Journal des Dbats"), from 1855 - employee of the Paris Observatory, from 1862 - member of the Bureau of Longitudes. Basic research relates to optics, mechanics, electromagnetism. Together with A. Fizeau, he conducted a number of optical studies, the most famous of which was the observation of the interference of light with a large path difference. In 1849-1850 he measured the speed of light in air and water using a rapidly rotating mirror. These comparative measurements finally confirmed the wave nature of light. In 1851, using a pendulum (Foucault pendulum), he demonstrated the rotation of the Earth around its axis. In 1852 he invented the gyroscope, now widely used in technology and navigation. In 1855 he discovered the heating of conductive material by eddy induction currents (Foucault currents) and proposed a way to reduce them. He developed a precision method for making mirrors for large reflectors and proposed using lighter and cheaper glass mirrors coated with a silver film instead of metal ones. Foucault's other inventions included an automatic light regulator for an arc lamp, a photometer, and a polarizing prism suitable for use in the UV region. Foucault was a member of the Royal Society of London, the Berlin Academy of Sciences; For scientific achievements he was awarded the Copley Medal.
1.4. Functioning Foucault pendulums
1.4.1. Operating pendulums in Russia and CIS countries
On February 24, 2011, the pendulum model appeared inKyiv. It is installed in (Fig. 4). The bronze ball weighs 43 kilograms, and the length of the thread is 22 meters. The Kiev Foucault pendulum is considered the largest in the CIS and one of the largest in Europe.
Opened on June 12, 2011Moscow Planetarium , where an operating Foucault pendulum with a thread length of 16 meters and a ball mass of 50 kilograms is installed (Fig. 5).
Opened on February 8, 2012Novosibirsk Astrophysical Complex , which includes a Foucault tower with a pendulum whose thread is 15 meters long.
A working Foucault pendulum with a thread length of 20 meters is available inSiberian Federal University (Krasnoyarsk ).
A working Foucault pendulum, weighing 12 kilograms and a thread length of 8.5 meters, is available in the Volgograd Planetarium.
A functioning Foucault pendulum is currently in the St. Petersburg Planetarium. The length of its thread is 8 meters.
FOUCAULT PENDULUM, a device that clearly demonstrates the rotation of the Earth. Its invention is attributed to J. Foucault (1819–1868). At first, the experiment was carried out in a narrow circle, but L. Bonaparte (who later became Napoleon III, the French emperor) was so interested that he invited Foucault to repeat it publicly on a grand scale under the dome of the Pantheon in Paris. This public demonstration, organized in 1851, is commonly called the Foucault experiment.
Under the dome of the building, Foucault suspended a metal ball weighing 28 kg on a steel wire 67 m long. Unlike a clock pendulum, which can only swing in one plane, the Foucault pendulum had the upper end of the wire fixed in such a way that it could swing equally freely in all directions. A circular fence with a radius of 6 m was made under the pendulum with the center directly under the suspension point. Sand was poured onto the fence so that with each swing, a metal tip attached under the pendulum ball could sweep it away in its path. To ensure the launch of the pendulum without a side push, it was taken to the side and tied with a rope. After the pendulum, after being tied, came to a state of complete rest, the rope was burned and the pendulum began to move.
A pendulum of this length makes one complete swing in 16.4 s, and it soon became clear that the plane of swing of the pendulum rotates clockwise relative to the floor. With each subsequent swing, the metal tip swept away sand approximately 3 mm from the previous place. In an hour, the swing plane rotated by more than 11°, and in about 32 hours it made a full revolution and returned to its previous position. This impressive display had the audience downright hysterical; it seemed to them that they could feel the rotation of the Earth under their feet.
To find out why a pendulum behaves this way, consider a ring of sand. The northern point of the ring is 3 m from the center, and given that the Pantheon is located at 48°51º north latitude, this part of the ring is 2.3 m closer to the earth's axis than the center. Therefore, when the Earth rotates 360° within 24 hours, the northern edge of the ring will move in a circle of smaller radius than the center, and will travel 14.42 m less per day. Therefore, the difference in speed between these points is 1 cm/min. Likewise, the southern edge of the ring moves 14.42 m per day, or 1 cm/min, faster than the center of the ring. Thanks to this speed difference, the line connecting the northern and southern points of the ring always remains directed from north to south.
At the earth's equator, the northern and southern ends of such a small space would be at the same distance from the earth's axis and, therefore, move at the same speed. Therefore, the surface of the Earth would not rotate around a vertical pillar standing at the equator, and the Foucault pendulum would swing along the same line. The rotation speed of the swing plane would be zero, and the time for a complete revolution would be infinitely long. If the pendulum were installed exactly on one of the geographic poles, it would turn out that the swing plane rotates exactly 15° every hour and makes a full rotation of 360° in 24 hours. (The surface of the Earth rotates 360° per day around the earth's axis. )
We have witnessed how once again the church and the state, opposing or, conversely, finding complete mutual understanding, clearly demonstrate this to their citizens and parishioners with such broad gestures that they cause a wave of protest movement in both. The raised and widely debated status of St. Isaac's Cathedral, the pendulum in the cathedral, as an anti-religious argument, the resumed services and the ongoing educational work of the museum-monument bring confusion and discord between the restless residents of the city. What is the essence of the dispute?
St. Isaac's Cathedral under Tsarism
Architect Auguste Montferrand and the construction of his brainchild, the new, fourth in a row,The cathedral built on the same site in honor of Isaac of Dalmatia was controlled by Emperor Nicholas himself I . The design work that began in 1818, making corrections to the original version and the construction of the temple itself continued 40 years.
The ceremonial consecration of the cathedral on May 30, 1858 was attended by the family of Emperor Alexander II. The majestic building amazed with its size and beauty both outside and inside. The troops were lined up in parade. For the people, stands were erected on two adjacent squares. It was a great holiday for all of St. Petersburg.
Soon the building was transferred to the hands of the Ministry of Internal Affairs and since 1883 was in dual subordination: to the Orthodox department - in “economic terms”, to the Ministry - in “technical and artistic terms”. Repeated requests from the metropolitans of both capitals to transfer St. Isaac's Cathedral to the sole control of the clergy were answered with a decisive refusal.
Until 1928, St. Isaac's Cathedral, freed from expensive church valuables, belonged to different communities of parishioners. In June, the contract with the next parish was terminated, services were stopped, and the building was transferred to the use of Glavnauka. On April 12, 1931, a museum of anti-religious propaganda was opened here.
The building began to serve exclusively secular functions. After restoration, an observation deck was opened at the top. Every Soviet citizen could now admire the beauty of Leningrad from the heights of St. Isaac's Cathedral. Pendulum in the cathedral, installed as a scientific instrument to prove the fact that the Earth rotates on its axis, has aroused great interestcity residents and their guests. Few people were excited by the fact that for its installation, the figure of a dove, the image of the Holy Spirit, was removed from the inside of the dome.
On the night of April 12, 1931, 7,000 spectators gathered to watch its first launch, watching with interest and noisily arguing in anticipation of the result: whether the matchbox hit by the ball would fall or not. The sciencetriumphed over religion: “It revolves,” and Foucault pendulum in St. Isaac's Cathedralproved this beyond doubt.
What is a Foucault pendulum?
The first such experiment was carried out in 1851 by the Frenchman Jean Foucault. After trial runs in the basement of the house, he demonstrated his experience under the dome of the Pantheon in the presence of the future Emperor Napoleon IIIand with the permission of the Pope.
When a pendulum weighing 28 kg was launched along the geographical meridian into free oscillation on a wire 67 meters long, its metal tip outlined the pouredsand all around. It was clear that each subsequent arrival of the tip shifted several millimeters relative to the previous one. After some time, it became obvious that the plane of the pendulum’s oscillation was turning. In one hour the angle of rotation was 11 degrees.
Foucault pendulum in St. Isaac's Cathedralweighing 54 kg and a cable length of 98 meters rotated the oscillation plane by 13 degrees in an hour.
Pendulum in the cathedral
In the eighties of the last century, the Orthodox Church began to regain its influence. Control has ceasedfor citizens visiting churches and performingchurch sacraments. On holidays, top officials attended services in the capital's cathedral.
As a sign of its loyalty to the church, the state paid attention to St. Isaac'sCathedral. Pendulum in the cathedraldismantled under a plausible pretext: breakdown of the suspension system. This was in 1986, and four years later services resumed here.
Foucault's physics device, sacrificed for the sake of peace and harmony between two powerful power structures, the state and the church, lies in the museum's vault. Where the pendulum hung in St. Isaac's Cathedral in St. Petersburg, the dove flies again.
In 2015, the clergy raised for the third time (twice before the revolution) the question of transferring St. Isaac's Cathedral to the church. There were many publications, debates and speeches by citizens “for” and “against”. Finally, in January 2017, the governor of St. Petersburg announced the authorities’ decision: “The issue of transferring St. Isaac’s Cathedral to the use of the Russian Orthodox Church has been resolved, but the building will fully retain its museum and educational function.”
What will be next?
Everyone understood the statement differently. Museum workers regarded this as the liquidation of the museum. Protests by museum supporters and religious processions by opponents took place. Thus, when the Foucault pendulum was removed from St. Isaac's Cathedral, and the authorities announced their decision, this did not bring final clarity either about the ownership or purpose of the building.
To date, neither side has a final understanding of the status of the cathedral. It seems that, having expressed its readiness to transfer “Isaacia” into the hands of the church, the government has not received an official application for this from the Russian Orthodox Church since January of this year. Museum employees do not know what to do: pack exhibits or unpack what has already been collected. The media periodically raise this issue with the museum's management, but both the former and Yuri Mudrov, who took office in June, seem to have a poor idea of their future.Citizens protest periodically.
For now, we can only confidently say that today services are held in the building every day and there is a museum right there “Saint Isaac's Cathedral". Pendulum in the cathedral seems to continue to sway.
Foucault's pendulum - what is it and what is it eaten with?
For conducting an experiment with a pendulum, Jean Foucault was awarded the Legion of Honor, the highest award in France.
It gets its name from the name of a French physicist-astronomer and is used to experimentally demonstrate the daily rotation of the Earth. The first experiment with a pendulum was carried out by Jean Foucault in the basement of a house at night, in January 1851. He attached a two-meter long hardened steel wire to the top of the cellar vault and suspended a 5-kilogram brass ball from it. Taking the ball to the side, fixing it with a thread near one of the walls, Foucault burned the thread, giving the pendulum the opportunity to swing freely. And within half an hour he witnessed the rotation of the Earth. At the next stage of his experiment, the scientist took a load already weighing 28 kg and suspended it from the top of the dome on a wire 67 m long. Jean Foucault attached a metal point to the end of the load. The pendulum oscillated over a round fence, along the edge of which sand was poured. With each swing of the pendulum, a sharp rod attached to the bottom of the weight dropped sand approximately 3 mm from the previous location. After a couple of hours, it became clear that the swing plane of the pendulum was turning clockwise relative to the floor. In an hour, the plane of oscillation rotated more than 11 degrees, and in about 32 hours it made a full revolution and returned to its previous position. Foucault thus proved that if the surface of the Earth did not rotate, the pendulum would not show a change in the plane of oscillation. After the experiment was repeated in a narrow circle of people, the future French Emperor Napoleon III invited Foucault to repeat the experiment publicly under the dome of the Pantheon in Paris.
Geography of pendulums
The plane of rotation of the pendulum is affected by the latitude of the place where it is installed. If, for example, it is placed at the North or South Pole, it will make a revolution in 24 hours. And a pendulum mounted on the equator will not rotate at all. Another factor is the length of the suspension. Long pendulums rotate faster.
After the experiment of the French astronomer, the Foucault pendulum began to be used all over the world. Existing devices are designed according to the same principle and differ from each other only in technical parameters and the design of the sites on which they are installed.
From 1931 to 1986, a 98 m long Foucault pendulum could be seen in St. Isaac's Cathedral in St. Petersburg. During the excursion, visitors could observe the experiment: the plane of rotation of a pendulum suspended under the dome was rotated, and the rod knocked down a matchbox on the floor away from the plane of rotation. In 1986, the pendulum was removed and placed in the basement of St. Isaac's Cathedral due to a malfunction of the suspension mechanism. A dove, the original inhabitant of this place, was placed on a hook under the dome. For 30 years, the Foucault pendulum was in storage, but last year it was taken out again. A single demonstration of his work was planned for Cosmonautics Day, and then it became part of the museum exhibition. Director of the St. Isaac's Cathedral State Municipal Enterprise Nikolai Burov suggested that the city authorities display the pendulum on the square in front of the cathedral, but this initiative did not find support. By the way, the pendulum hanging in St. Isaac's Cathedral was the largest in the world. The length of its thread is 98 m, and the bronze pendulum weighs 54 kg.
Today in our country, in addition to the Novosibirsk planetarium, the operating Foucault pendulum can also be viewed in the Moscow planetarium (there is a pendulum with a thread length of 16 m and a ball mass of 50 kg), and the Siberian Federal University (thread length is 20 m). Right now, pendulums are swinging in the St. Petersburg (string length - 8 m) and Volgograd (weighing 12 kg and string length 8.5 m) planetariums, as well as in the atrium of the seventh floor of the Fundamental Library of Moscow State University, at the Volga Federal University in Kazan. Another Foucault pendulum is located in Barnaul at Altai State Technical University. I.I. Polzunov at the Department of Experimental Physics. The length of its thread is 5.5 m.
The largest Foucault pendulum in the CIS and one of the largest in Europe was installed at the Kiev Polytechnic Institute. The bronze ball weighs 43 kg and the length of the thread is 22 m.
There are about 20 models of Foucault pendulums in the world, including in the USA, France, Romania, Australia, Kuwait and other countries. Giant pendulums of this kind are now common exhibits in some major museums, including the Smithsonian Museum in Washington and the Science Museum in London. The headquarters of the United Nations in New York also has its own pendulum, and the tallest active Foucault pendulum in the world is located in the Oregon Convention Center, its thread is 27.4 m long.
It’s possible to repeat the astronomer’s experience at home
The editors of the magazine “All about New Buildings” studied ways to make a Foucault pendulum at home. The above options can be useful, for example, for visually demonstrating to children the daily rotation of the Earth.
Option 1. Tie a string to a pencil with a small round weight, such as a nut. Place a ruler on the table and, holding the pencil horizontally, push the pendulum so that it swings along the ruler. Next, you need to gradually rotate the pencil in a horizontal plane. Turning the pencil will not affect the pendulum; it will still swing along the ruler. During this experiment there should be no wind or draft that could affect the pendulum.
Option 2. You can turn the stool upside down and attach a wooden stick or metal tube at the ends of its two legs, diagonally, and tie a pendulum exactly in the middle of this structure. Make it move so that the plane of its swing passes between the legs of the stool. Slowly rotate the stool around its vertical axis. Now the pendulum is swinging in a different direction. In fact, it still swings the same way, and the change occurred due to the rotation of the stool itself, which in this experiment plays the role of the planet Earth.
Option 3. Take a wooden board 50–60 cm long, 12–15 cm wide and 2–3 centimeters thick. Attach a U-shaped stand made of narrow wooden slats to it. The height of the stand should be about 30–40 cm. Drill a vertical hole in the middle of the top crossbar and insert a piece of wire into it, bending the upper end to hold it in the hole. Bend the lower end of the wire with a hook, the pendulum will be suspended from it. This hook should rotate freely in its socket. Using a thin cord, hang some heavy weight (a large nut or a ball from a bearing, wrapped in fabric) from the hook. Swing the pendulum so that its swing does not exceed the length of the stand. By rotating the stand around its vertical axis counterclockwise, you will thereby repeat in miniature the rotation of the Earth from west to east. Thus, the model of the Earth rotates, and the pendulum continues to oscillate in the plane in which it was launched.
FOUCAULT PENDULUM, a device that clearly demonstrates the rotation of the Earth. Its invention is attributed to J. Foucault (1819–1868). At first, the experiment was carried out in a narrow circle, but L. Bonaparte (who later became Napoleon III, the French emperor) was so interested that he invited Foucault to repeat it publicly on a grand scale under the dome of the Pantheon in Paris. This public demonstration, organized in 1851, is commonly called the Foucault experiment.
Under the dome of the building, Foucault suspended a metal ball weighing 28 kg on a steel wire 67 m long. Unlike a clock pendulum, which can only swing in one plane, the Foucault pendulum had the upper end of the wire fixed in such a way that it could swing equally freely in all directions. A circular fence with a radius of 6 m was made under the pendulum with the center directly under the suspension point. Sand was poured onto the fence so that with each swing, a metal tip attached under the pendulum ball could sweep it away in its path. To ensure the launch of the pendulum without a side push, it was taken to the side and tied with a rope. After the pendulum, after being tied, came to a state of complete rest, the rope was burned and the pendulum began to move.
A pendulum of this length makes one complete swing in 16.4 s, and it soon became clear that the plane of swing of the pendulum rotates clockwise relative to the floor. With each subsequent swing, the metal tip swept away sand approximately 3 mm from the previous place. In an hour, the swing plane rotated by more than 11°, and in about 32 hours it made a full revolution and returned to its previous position. This impressive display had the audience downright hysterical; it seemed to them that they could feel the rotation of the Earth under their feet.
To find out why a pendulum behaves this way, consider a ring of sand. The northern point of the ring is 3 m from the center, and given that the Pantheon is located at 48°51º north latitude, this part of the ring is 2.3 m closer to the earth's axis than the center. Therefore, when the Earth rotates 360° within 24 hours, the northern edge of the ring will move in a circle of smaller radius than the center, and will travel 14.42 m less per day. Therefore, the difference in speed between these points is 1 cm/min. Likewise, the southern edge of the ring moves 14.42 m per day, or 1 cm/min, faster than the center of the ring. Thanks to this speed difference, the line connecting the northern and southern points of the ring always remains directed from north to south.
At the earth's equator, the northern and southern ends of such a small space would be at the same distance from the earth's axis and, therefore, move at the same speed. Therefore, the surface of the Earth would not rotate around a vertical pillar standing at the equator, and the Foucault pendulum would swing along the same line. The rotation speed of the swing plane would be zero, and the time for a complete revolution would be infinitely long. If the pendulum were installed exactly on one of the geographic poles, it would turn out that the swing plane rotates exactly 15° every hour and makes a full rotation of 360° in 24 hours. (The surface of the Earth rotates 360° per day around the earth's axis. )