How is the spinner related to the laws of conservation in physics, to the alternation of day and night, to the North Star and to the heavenly bodies known as pulsars?
Author: Zvi Atzmon, young Galileo
It can be said that the Hanukkah holiday is based on three things: Chanukahs, donuts and spinners. But if you want the entire Torah of Hanukkah on one leg only, you can say: a spinning wheel. Why a spinning wheel? Because the spinner stands (or rather - rotates) on one "leg".
Why does the spinning wheel start spinning?
We hold the spinner handle between our fingers and spin. Why did the spinning wheel start spinning? The movement of our fingers forced it to turn. But why does it continue to spin for quite a few minutes after it has been released from our fingers, which in the meantime may have already moved on to holding a doughnut? The answer is: conservation of angular momentum. The angular momentum depends on the speed of rotation - the angular momentum of a spinning top that spins slowly is smaller than the angular momentum of a similar spinning top that spins quickly; In mass - the angular momentum of a lead spinning top is greater than the angular momentum of a light plastic spinning top; And in the distribution of the mass in relation to the axis of rotation - if most of the mass is close to the axis of rotation, the angular momentum is relatively small; If the mass is mostly at the circumference, far from the axis of rotation, the angular momentum is large. The angular momentum is a vector, which means that apart from the numerical value, it also has a direction; The direction of the angular momentum vector is along the axis of rotation. This quantity, the angular momentum, is a conserved quantity. Therefore, if the spinning wheel turned (and thus had angular momentum) and our fingers released it, it tends to continue spinning at the same speed and in the same direction (the direction of the axis of rotation). As long as the spinner rotates, it has angular momentum and the direction of rotation tends to be preserved, and therefore the spinner remains upright.
Why does the spinning top stop spinning?
Why, after all, after a few minutes does the spinner fall on its side and stop? Because an external force acts on it, and this slows it down, the friction. There is friction between the spinner's foot and the floor, the table or the palm (where the spinner is turned), and there is friction between the spinner and the air. An astronaut who left the space station on the first candle of Hanukkah and spins a pinwheel in space will also find it spinning on the eighth candle of Hanukkah because there is no friction in space.
This is also the explanation for the continued rotation of the great spherical "spindle" on which we live - the Earth. The earth rotates on its axis (an imaginary line that connects the north pole to the south pole and passes through the center of the earth), and therefore there is day and night - the half of the earth facing the sun has day, while the other half is at night. The earth rotated on its axis in the very distant past, and therefore - thanks to the conservation of angular momentum - it also rotated on its axis in the days of the Maccabees and a hundred years ago, and will continue to rotate next year as well. Although in the distant past the rotation was faster (and therefore the day was shorter), and due to various factors the rotation speed is getting smaller and smaller, but the change is so slow that in human life, and in all of written history, this has no real expression.
Why does the spinning wheel oscillate?
When you look at the spinning top while it is still spinning, you can see that the axis of rotation itself is not fixed, but tilts this way and that and oscillates. The change of direction of the axis is much slower than the rotation of the rotor on its axis. This slow oscillation of the axis of rotation itself is called precession, and originates from the influence of external forces, such as the Earth's gravity.
The Earth's axis of rotation also oscillates slowly in a wobbly motion. Therefore, the earth's axis is not always oriented in the same direction in the sky. Nowadays, further along the rotation axis of the earth, the north star is located in the sky, which helps us to orientate at night in a field or desert. Because of the accretion, in the past there were other stars located further along the Earth's axis. In the days of the Maccabees, the earth's axis was directed not towards the North Star, but towards the star whose scientific name is Kochov (one of the stars of the "Little Chariot"). So if the Maccabees wanted to surprise the Greeks at night, they could navigate their way according to the north star of their day - the star star.
How does size affect rotation rate?
If a Saturn star, a real, large star collapses under its own gravity, its atoms collapse, and it can change into a star built entirely of neutrons. The volume of such a star is infinitely smaller than the volume of the original star. If the original star rotated, it had angular momentum. Reducing its dimensions greatly reduced the distance of its mass from the axis of rotation. For the angular momentum to be conserved, the rotation speed of a star whose dimensions have shrunk must increase greatly. Such a star, which originally completed one rotation for our number of days, for example, will after its collapse complete a rotation, for example, every half a second. If it emits radio radiation in a certain direction, we will receive a pulse of radio transmission every rotation, in our example - every half second, regularly. Such stars have indeed been detected in radio telescopes and are called pulsars (according to English acronyms for "pulsating radio stars").
Unfortunately, Hanukkah spinners don't suddenly shrink and increase their rate of rotation - that would have been nice. But thanks to them and thanks to the laws that govern them, we can better understand the universe and also guess how the Maccabees navigated their way in dark nights.
The article appeared in the December issue of Young Galileo – Monthly for curious children
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7 תגובות
"If the system didn't rotate first."
But spinning relative to what?
You have two systems as you described. Each takes a picture of the other and claims that it is stationary and the other is rotating. So which of them if you break the rod has kinetic energy and which does not?
The interesting thing is that there is an answer. But you wouldn't be able to tell from the photos alone.
Israel
Let's imagine a flat, two-dimensional universe. In the universe there are two particles of equal mass. Let's assume they are connected by a massless rod and the rod rotates at a constant speed around an axis at its center. If we break the rod, the particles will move in opposite directions and we will get a reference point, which is the position where the axis was. Now - we see that the system has kinetic energy. If the system did not rotate first, we would see that the system has no kinetic energy and the particles would remain at a constant distance between them.
If you reverse the arrow of time in both cases, you will see that they are different. In these examples it is allowed to reverse the arrow of time.
What I'm trying to say is that the starting conditions of the two cases are different, so in practice there is no paradox. To reach a spinner in empty space, you have to build the system. There is no God who "creates" the spiral suddenly.
You are a young man.
In 75 the only institute I might have been to was the Wingate Institute in some fitness series in the army.
I still don't understand how there would be centrifugal force without other masses in the universe. Relative to why the round then? Why exactly does one spinning top spin and another doesn't? Or maybe the masses themselves are arranged relative to time space?
Israel
I was in a "science seekers club" or something like that in high school. We were two weeks in the summer (74 or 75 I think) at the Weizmann Institute, in a group of 5 children and we were busy with holograms. So it was something innovative and complicated…. Teller visited the Weizmann Institute and we had a meeting with him where he told us a little and we asked a few questions. I wanted to understand how a gyroscope keeps its direction in space, and this was his answer.
Happy holiday miracles.
Have you met Teller? Wow! Book, book, expand.
But Einstein claims that even in a universe empty of matter the rotation is absolute and the measurement of centrifugal force. I have never been able to understand his claim, because there is no doubt that the rotation is correlated with the distant stars, and if they are stationary from the point of view of the observer, then there is no centrifugal force either. So how does it work out?
Israel
Happy holiday!!
I had the chance to meet Edward Teller and ask him exactly this question. His answer was Mach's answer - and if the spinner was alone in the universe then there is no meaning at all to spin around an axis. So that convinced me….
But here an important question arises regarding the rotation of the rotor and its angular momentum: rotation relative to what?
Because momentum by its very nature is mass multiplied by speed. In linear momentum the velocity is relative: the body has momentum only relative to a specific coordinate system, and this momentum is different in another system and zero relative to a system that is at rest relative to the body.
Angular momentum, on the other hand, is absolute: a spinner has an angular momentum that does not depend on the axis system. Each spinner, whether in the land or in space, has an absolute momentum in its strength and direction that can also be measured by the magnitude of the centrifugal force acting on the spinner.
But relative to what does the spinning wheel spin?
Mach claims: relative to the other masses in the universe. Einstein holds: relative to space-time. Newton - relative to the divine spirit.
So what's the answer, sub sub sub?