Pendulum suspension height to test the hourglass. Temples with foucault pendulums. The Spindle-Foucault pendulum proves that the Earth is at rest, and does not rotate at all, which is impossible in principle - both from mathematical considerations and from considerations of the gyroscope physics,

I don't know how many of the readers of this site have seen Foucault's pendulum live. There were many Foucault pendulums in the USSR. They were installed in cathedrals as anti-religious propaganda. And the longer the suspension was, the more impressive the pendulums looked. The longest in the Trinity Cathedral of the Pskov Kremlin, in the Church of St. John in Vilnius, in the Dominican Cathedral in Lviv. But the very best hung in St. Isaac's Cathedral in Leningrad, as much as 93 meters (it was hung after the city was renamed, it was removed exactly before the city was renamed again).

Those who have seen remember that this is such a hefty metal weight hanging on a thin thread, which swings over the floor in a big way, and the swing plane makes a full circle over time. These pendulums never stop, they are a living demonstration of the rotation of the Earth.

However, why does the pendulum need these pendulums? They can't do anything! Or can?...

The USSR has disappeared, no one needs science, and the pendulums have been removed. Pictured above is the Foucault pendulum in the Paris Pantheon. He was hung there in 1851 by Napoleon III and he still hangs there. Suspension length - 68 meters.

The principle of operation of the Foucault pendulum is rather confusing. The plane of its rotation is affected by both the geographical latitude of the place where it is installed and the length of the suspension (long pendulums rotate faster). A pendulum mounted on a pole will rotate in 24 hours. A pendulum mounted on the equator will not rotate at all, the plane will remain motionless. Foucault himself could not derive a sane rotation formula, this was done after him.

The question arises - how did Foucault guess to hang such a pendulum?
Here it seems like the case is to blame, but it seems like a pattern. In those days, artillery reached such accuracy that ballistics turned into a science. And then an anomaly was noticed - if the gun shoots exactly to the north, then if it is installed in the northern hemisphere, then the projectile will deviate to the right, and if in the southern hemisphere, then to the left.

Foucault was an original personality, and in order to prove that the rotation of the Earth is to blame, he came up with such an experiment with a pendulum.
That is, before Foucault, artillery technology did not reach such accuracy that the effect could be caught.
And after Foucault... If such an original as Foucault would not have been found, then surely the pendulum was built only when the theory was brought under it and the rotation of the plane would follow from the formulas. But then no one would need him and would not arouse such interest.
In reality, everything ended with the fact that in Rome, in the Vatican, in the Cathedral of St. Ignatius, the holy fathers hung the same pendulum, they were convinced of the effect - and the Catholic Church officially recognized the rotation of the Earth.

So, what practical significance could a pendulum as such have?
With it, you can approximately determine the geographic latitude. It is completely incomprehensible for the hitmen where, it is not clear where and it is not clear why.
But I remind you that the Foucault pendulum will work even in magical worlds, and no elves can do anything (the worlds where the planet did not rotate can be counted on the fingers of one hand - and in such worlds it is immediately clear that they are special).

In other cases, the Foucault pendulum has a very interesting role, which it also played in reality.
Namely, he broke the worldview of people.
And these things are very valuable, they shift the world from the point.
And there are few such things, except for the Foucault pendulum and , but I would recommend them to the hitman to implement in the first place, such things break the notorious inertia of thinking.

FOUCAULT PENDULUM, a device that visually demonstrates the rotation of the Earth. His invention is attributed to J. Foucault (1819-1868). At first, the experiment was performed in a narrow circle, but L. Bonaparte (who later became Napoleon III, the French emperor) became so interested that he suggested Foucault repeat it publicly on a grandiose scale under the dome of the Pantheon in Paris. This public demonstration, arranged in 1851, is 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. directions. Under the pendulum, a circular fence with a radius of 6 m was made with a center directly below the suspension point. Sand was poured over the fence so that with each swing, a metal point attached under the ball of the pendulum could sweep it away in its path. To ensure the launch of the pendulum without a lateral push, it was taken aside and tied with a rope. After the pendulum, after tying, came to a state of complete rest, the rope was burned out and the pendulum began to move.

A pendulum of this length makes one complete oscillation in 16.4 seconds, and it soon became clear that the swing plane of the pendulum rotates clockwise relative to the floor. With each subsequent swing, the metal tip swept the sand about 3 mm from the previous place. In an hour, the rocking plane turned more than 11°, and in about 32 hours it made a complete revolution and returned to its previous position. This impressive demonstration drove the audience downright into hysterics; it seemed to them that they felt the rotation of the Earth under their feet.

To find out why the pendulum behaves this way, consider a sand ring. 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 by 360 ° within 24 hours, the northern edge of the ring will move in a circle of a smaller radius than the center, and will pass 14.42 m less per day. Therefore, the difference in the velocities of these points is 1 cm/min. Similarly, the southern edge of the ring is moving 14.42 meters per day, or 1 cm/min, faster than the center of the ring. Due 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, moving at the same speed. Therefore, the surface of the Earth would not revolve around a vertical column standing at the equator, and Foucault's 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 set exactly at one of the geographic poles, then it would turn out that the swing plane rotates exactly 15 ° every hour and makes a complete rotation of 360 ° in 24 hours. (The surface of the Earth rotates 360 ° per day around the earth's axis. )

Recall that the Foucault pendulum is an experimental device with which you can visually observe the daily rotation of the Earth. It is a rather long (in the original design of Jean Foucault, the length was 67 m) steel wire, on which a load is suspended. Over time, the plane of oscillation of the pendulum changes, slowly turning in the direction opposite to the direction of the Earth's rotation, and the geographical position (latitude) of the device affects the rate of change.

It is very difficult to imagine a plane that is stationary relative to the stars and, accordingly, rotating relative to the Earth. The Earth is too big, its apparent “flatness” is too familiar to us, and it is completely impossible to feel the rotation on ourselves. Foucault's pendulum clearly demonstrates the effect of daily rotation, but even looking at it, it is not always easy to understand and accept its "testimony".

Plate; three forks; wine cork; lime or any other object of similar parameters, easily pierced with a needle; two sewing needles; spool of thread; salt.

And imagine the situation: your son comes up to you and asks: dad, I read about some kind of Foucault pendulum, which proves that the Earth is spinning, and did not understand anything. Can you explain to me in a simpler way? Of course, you answer and build a pendulum model right in the kitchen.

limes and needles

You can build a model from almost anything, you can make it more beautiful, bigger, more photogenic. We chose to use simple items that can be found in just a few minutes in almost any kitchen. You don't even need to go to the store.

If we rotate the plate evenly (for example, by placing it on a spinning disk), the tip of our pendulum will describe a figure on the salt, similar to the figure described by a real Foucault pendulum.

So, a plate, three forks, two needles, a cork, some kind of load (lime, potato, small apple), a spool of thread, salt. The plate plays the role of the Earth, and the table on which it stands is a fixed coordinate system in which the Earth rotates (in other words, stars). From all this it is easy to build the structure shown in the first photo. The most difficult thing is to choose the length of the thread so that the tip of the needle barely touches the surface of the plate. It is very important to keep the centering, that is, to make sure that the tip of the needle comes out of the very middle of the fruit, which is used as a load.

Then we start the system - it is best to pull the load to the side and let it go. The pendulum starts to swing. If we rotate the plate around the axis, it will be found that the pendulum does not rotate with it, but continues to oscillate in a constant plane! Salt in this case is used for clarity - when you turn the plate, the tip of the needle draws a new trajectory.

The longer the thread, the longer the pendulum will oscillate with sufficient amplitude to make it interesting to observe the experiment from the side.

Now it is enough to imagine that the plate is very large - with a diameter of the Earth. And it rotates, as Galileo used to say, on its own, just as we rotate the plate with our hands. And Foucault's pendulum, descending from the dome of the Moscow Planetarium or the Paris Pantheon, writes out an intricate figure, constantly changing the plane of oscillation relative to the Earth. More precisely, it is the Earth that changes its position relative to the pendulum. Like a plate.

Let's walk through the Foucault pendulum - the only visual evidence of the "correct" rotation of the Earth.

This is a common pendulum that we have seen many times in wall/grandfather clocks. But only a special suspension allows it to spin. For some reason, the design of this suspension is not available on the Internet. Here are just the creators of the pendulum in Kyiv complained about the complexity of the work: a creative team of 10 people worked on the creation of the pendulum during the year(http://www.mpravda.com/?lang=ru&pubId=51956- this information has already been deleted).

We had a pendulum in St. Isaac's Cathedral from 1931 to 1986: the ball was suspended under the dome on a cable of 93 meters. The biggest in the world!

All pendulums rotated in accordance with the Coriolis displacement (not per day, but according to the sine of the latitude of the area - 32 hours in Paris). But here is an interesting quote from the site " Mechanics of the inercoid"(those who wish can study the calculations):

... if we proceed from the Coriolis acceleration, then the speed of the relative rotation of the pendulum at each point of the trajectory will be twice as high as follows from the relative calculation, which cannot be in principle. The Coriolis force in this case clearly gives the wrong result.

And I have an explanation for this twice as fast rotation: the rotation of the pendulum symbolizes the rotation of the plane of rotation of the pendulum, but when the Earth rotates 180 degrees, this plane will coincide with the starting one, only the movement in it will be in the opposite direction (look at the figure at the beginning text and rotate the observer 180 degrees - the projectile flies in the same plane, but away from him). Thus, the plane of rotation of the pendulum per day (at the pole) should scroll twice. So where did those 32 hours in Paris come from then? Fake constructors came up formally using a standard formula.

We know how pendulum clocks work: they are "charged" by a weight, without which the oscillations would quickly die out due to friction. There is no weight in Foucault pendulums. What "twirls" them?

But the main thing: the pendulum rotates. This means that the pendulum presses on the suspension, causing it to rotate. After all, if the suspension makes the pendulum rotate, then this is already a scam. How can we understand without knowing the construction?

And according to the same grandfather clock! And there the pendulum swings, but on a fixed suspension - on an axis. This means that the Coriolis force must always act on the right side of the axle, well, like a railroad rail. And grind the axle on one side. Which should lead to a quick breakdown of this axis. Have you ever heard of such a breakdown? But the original Foucault pendulum in Paris was smashed in 2010, accidentally touching the cable (power to the rotating motor?)?!

I thought for a long time how the suspension is arranged to demonstrate this fake, until I saw a wonderful video:

First, starting from the 50th second (clearly at the 55th) the cord is visible. And he is not stretched, but a wave. Is it a sheath that hides the cord inside so you can't see it spinning?

Secondly, a very remarkable effect: at 1.13 the pendulum moves away from us and hits the target, and at 1.17 it is already moving towards us and does NOT hit the target (at 1.19 it hits even more). Is it like this? With each swing, the pendulum turns slightly (should).

Those. if touched in one direction, then when moving back, it should hurt even more.

This can only be if it swings not in a plane, as we are told, but along a curve. Moreover, it is tucked at the moment of maximum deviation to the camera.

I would say that the ball of the pendulum, leaning towards us, hits a curved surface (something like a Möbius strip). Thus, each time the ball hits not perpendicularly, but at a certain angle, changing the angle of reflection. Hence, some curvature of the trajectory.

Actually, the gif from Wiki demonstrates exactly this fact.

It seems that the mystery of the suspension of the Foucault pendulum has been solved.

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For experimental demonstration of the daily rotation of the Earth, many universities, planetariums and libraries use the Foucault pendulum. I will tell about the temples in which this experience was demonstrated or is being demonstrated now.

Pantheon, Paris
The French physicist Jean Bernard Léon Foucault (1819-1868) first demonstrated his experiment on January 8, 1851. In the cellar of his house in Paris, the physicist performed an experiment with a pendulum 2 meters long. The experiment aroused great interest and already in March of the same year it was carried out publicly under the dome of the Pantheon in Paris.

In the building of the Pantheon, the scientist hung a metal ball weighing 28 kilograms on a steel wire 67 meters long. A point was fixed at the bottom of the metal ball. The mount allowed the pendulum to oscillate freely in all directions. Before launching, the pendulum was taken aside and tied with a rope, which was then burned through - this made it possible to avoid a lateral push. The pendulum swung over a fenced area with a diameter of 6 m. A sandy path was poured along the diameter of the area, and the pendulum, when moving with its tip, drew marks on the sand. After a few minutes, it could be seen that the plane of the pendulum's swing had changed.

In about 32 hours, the pendulum made a complete revolution and outlined the trajectory of its rotation on the sand. With the help of this experiment, the daily rotation of the Earth was clearly demonstrated. The experience can be made even more spectacular by placing an object near the edge of the pendulum's trajectory, which will be knocked down after a while.

How, then, does the change in the plane of the pendulum's oscillation prove the rotation of the Earth? According to the laws of physics, the pendulum does not change the plane of its swing. But sand or objects placed for the experiment rotate together with the Earth's surface in the course of its daily circular motion and at some point find themselves in the plane of the pendulum's swing.

The longer the thread on which the metal ball is suspended, the greater the rotation made in one period. Accordingly, when demonstrating the work of the Foucault pendulum in very tall buildings, for example, in temples, the rotation of the Earth will be more noticeable, and the experiment itself will be more spectacular.

The photo shows a modern copy of Foucault's pendulum and a stone statue of an Egyptian cat. (A photo)

Fukusaiji, Nagasaki
In the Japanese city of Nagasaki on the island of Kyushu, there is an unusual Buddhist temple complex. Fukusaiji was founded by Chinese monks from Fujian Province in 1628, but it was destroyed in an atomic explosion on August 9, 1945. The monastery was restored in memory of those who died in 1979. Every day at exactly 11-02, during the explosion of the atomic bomb, the temple bell rings.

The shape of the temple-mausoleum is similar to a giant tortoise, on the shell of which there is a large white statue of the goddess of mercy Kannon. The sculpture, 18 meters high and weighing 35 tons, is made of aluminum alloy.

In the temple, a Foucault pendulum is hung over the remains of 16,500 who died during World War II. The 25-meter cable is inside the statue.

The photograph shows the interior of the temple. The rope of the Foucault pendulum emerges from a golden hole in the vault and descends behind a metal railing on the floor.

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Basilica of San Petronio, Bologna
Perhaps the most suitable place to demonstrate Foucault's pendulum was the Italian "city of sciences", where the oldest university in Europe (1088) was founded. The Cathedral of Bologna, dedicated to the patron saint of the city, the holy bishop Petronius, was built over several centuries, starting in 1390. The basilica impresses with its size: the length of the building is 132 meters, the width is 60 meters, the height of the vaults is 45 meters.

The cathedral demonstrates not only Foucault's experience (pictured in the background). Professor of astronomy at the University of Bologna Giovanni Domenico Cassini (1625-1712) in 1665 marked inside the cathedral, on the floor, a meridian 66.8 m long, on which one can observe the movement of the sun's ray through a hole in the roof of the temple and mark days and months.

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Church of St. John, Vilnius
The only Foucault pendulum in Lithuania is located in the Catholic church. Named after St. John the Baptist and St. John the Evangelist, the church was built in the 18th century according to the design of Johann Christoph Glaubitz (1700-1767). You can see the pendulum at the Museum of Science, going up to the second floor of the 68-meter bell tower.

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Sophia Cathedral, Vologda.
In Russia during the Soviet era, the first display of Foucault's experience was prepared by the State Museum, the Union of Militant Atheists, and the Society of Local History. The demonstration took place during the anti-Easter campaign of 1929 in the St. Sophia Cathedral in Vologda. An anti-religious exhibition was arranged in the building, and the pendulum became one of its exhibits. An 18-meter thread was suspended from metal ties in the interior. (Photograph 1917-1950)

St. Isaac's Cathedral, St. Petersburg
On Easter night from April 11 to 12, 1931, Jean Foucault's pendulum was demonstrated in St. Isaac's Cathedral. Thousands of spectators witnessed the scientific triumph. A bronze ball suspended from the dome was set in motion to visually demonstrate the rotation of the Earth. The length of the thread was 98 m - the longest in the history of the demonstration of experience.

The pendulum was removed in 1986, and a sculpture of a dove, a symbol of the Holy Spirit, was returned to the center of the dome, where the cable used to be attached. Now Foucault's pendulum is stored in the basement of St. Isaac's Cathedral, in the memorial exposition "To Remember".

The journal "Museum World" (No. 10, 2016) says that back in 1901 in the Cathedral of St. Isaac of Dalmatia demonstrated the experience of Jean Foucault. But not in the center, under the dome, but in the vault of the side arch.

View of the Decembrists Square and St. Isaac's Cathedral. 1930-1936

Exposition of the State Anti-Religious Museum in the building of St. Isaac's Cathedral. Leningrad, 1931
Schoolchildren at the model explaining the experiment with the Foucault pendulum. State Anti-Religious Museum. 1930s
Exposition of the State Anti-Religious Museum. 1930s A model that helped to understand the essence of the experience.

In the same article, the location of the experiment is also indicated demolished in Soviet times Andrew's Cathedral in Kronstadt. Experience in it was demonstrated at the end of the first decade of the 20th century.