Mouvement International pour le Loisir Scientifique et Technique
International Movement for Leisure Activities in Science and Technology
MILSET Europe
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3rd European Science Day for Youth
3rd May 2007 - http://esdy.milset.org
Scientific card: « The Gyroscope »
Most of us have already handled or played with spinning tops. Make it whirl, oscillate, what a pleasure! How attractive
they are with their colours, their music and their eccentric forms. They are as interesting for grown-ups, children and
young people.
Did you already go through the trouble of asking yourself about the physical elements of the spinning top? Why and how
it turns or oscillates? How does it stop? Does the size, texture, form, material of the spinning top influence its rotation?
The study of the motion of the spinning top allows us to approach many scientific concepts, such as:
- force (weight, mass, force of friction, couple,…)
- centre of gravity
- balance
- inertia of a body and moment of inertia
- circular motion
- kinetic moment
- angular moment
- axis of symmetry
- composition of colours
- magnetism
- …
Question
Why is a spinning top unable to balance on its point at rest, whereas launching it is enough to obtain a stable rotation?
It is difficult to answer this question since the stability of the spinning tops concerns general mechanics on a level which is
by no means elementary. We can nevertheless approach the explanation intuitively by approaching a phenomenon with
numerous applications. I will not say any more… Good reading!
Let us start by defining our subject:
The spinning tops
A spinning top is a toy intended to turn on itself for the longest time possible, in balance on its point. There are many
types of spinning tops, but the guiding principle is always the same :
-
a balanced mass (centre of gravity on the axis of rotation),
a great moment of inertia compared to the axis, (masses distributed far from the axis),
specific contact on the axis (or very near) with the ground (reduction in the effects of friction),
a system to set the top in rotation (stem, string…) allows to launch the spinning top. Once in rotation, the spinning
top behaves like a gyroscope.
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Let us look further into 2 interesting terms :
A – The moment of inertia
Which of the movements is harder?
The moment of inertia measures the resistance of a body subjected to a setting in
rotation. It is the analogue of Inertia that measures the resistance of a body
subjected to a linear movement
Empirical approach
Take a broom in your hand by the middle of the handle and make it turn as on the
figure opposite. It is easier to make the brush turn around the axis of the handle (1),
than around a transverse axis (2).
That is due to the fact that in the second case, the matter constituting the brush is further away from the axis of rotation.
As for a solid in rotation, the linear velocity of a point grows in proportion with this distance, it is necessary to
communicate a greater kinetic energy at more distant points. Therefore, the broom resistance against being turned
around a transverse axis will be greater than around the handle axis.
B – The gyroscope
Hey teacher! I have just found a site on the Web explaining what a spinning top is. The problem is that the
explanation comprises 2 terms which I did not understand! For the 1 st one, I could find a simple approach.
But on the other hand, I do not know what a gyroscope is. Can you explain it to me?
Gyroscope? mmm… yes it is an apparatus which allows… mmm… Good, let us start with a definition:
Gyroscope
Device made up of an animated spinning top of a fast
rotational movement around an axis, and a system of
suspension.
A gyroscope doubly suspended retains a fixed orientation
compared to a reference mark related to stars: it preserves its
initial orientation whatever the forces to which it is subjected.
Spinning top, rotation, reference mark related to stars… that doesn’t enlighten me much. I still don’t
understand why it is that a spinning top behaves like a gyroscope. The definition hasn’t taken me much
further!
I think a little historic and documented trip will help us to clarify all this. Fasten your seat belt and
listen to me for a few minutes, I can assure you it is well worth it!
Let's go!!
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The gyroscope, this old invention – it may recall happy memories to the oldest among us – is still in use in advanced
technology nowadays. Thanks to gyroscopes, planes, space rockets and – alas – missiles can navigate very
precisely, without drifting from their trajectory. Thanks to gyroscopes, choppers or segways (a means of
transport based on the principle of dynamic equilibrium... see figure below) can get stabilized, satellites can change
orientation, and it's also thanks to them that you can have fun with the gyroscopic joysticks of Wiimote on Wii or
Sixaxis on PS3.
Tell your parents or grandparents about gyroscopes, their faces will illuminate! They will tell you that as children,
they played with a spinning top called gyroscope, which seemed to defy gravity!
What does a gyroscope look like and who invented it?
The traditional gyroscope was invented by the physician of genius Léon Foucault (1819-1868) 150 years ago.
Foucault was researching on mechanical devices which would allow demonstrating or visualising terrestrial
rotation.
I heard about Mr Foucault in school. He seemed to be interested in a lot of things such as "Foucault's
currents"... He must have been some sort of Mac Gyver!
But how can you see the Earth's rotation? We spin with it, as well as every object on its surface! The only way
to become aware of its rotation would be to look at the Sun and the stars, wouldn't it?
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No it wouldn't! Foucault had noticed that some devices seemed to remain "stable" in space, in spite of
terrestrial rotation! There was the famous "Foucault's Pendulum" which looked exactly like the Professor
Calculus's one – except that it weighed several kilos and was hanging from the Pantheon’s cupola with
about twenty meters of rope.
During his experience, Foucault became aware that the plane in which the Pendulum oscillated revolved
360° in a 24 hours period! The obvious conclusion was that the Pendulum responded to the movement of the Earth's
rotation around itself. Foucault astounded the people of Paris when he invited them to his exhibition to "see the Earth
revolve!"
Then there was the Gyroscope (etymologically speaking, "that which demonstrates rotation") invented and named
by Foucault in 1852. This device was not only about to demonstrate the Earth's rotation but was discovered to remain
stable in relation to the entire cosmos and to generate totally incomprehensible forces!
A Gyroscope consists very simply of a disc or ring which turns on itself at high speed. A spinning top is a
perfect example of a gyroscope.
FIG 1: Traditional gyroscope hanging in a structure which allows it to oscillate in every direction.
It's as simple as that? I thought it would be far more complicated!
Wait a little! It may be a very simple object in its conception, but its behaviour is extremely difficult to
understand!
Look at figure 1: in the centre, you can see the metallic gyroscope itself. This gyroscope is embedded in
double cardan structure. When the gyroscope turns around itself (after someone starts it by pulling on a rope
winded around its axis, or by accelerating its axis with an electric engine), a most curious phenomenon will
appear: the Gyroscope will stay pointed in its initial direction, whatever the movement of the structure which
contains it!!
Mmm...Yes, but I think the result would have been the same if the gyroscope had not been turning
around itself. The structure in which it is encased allows oscillations in every direction. If it is perfectly
conceived and well oiled, even when not spinning, the gyroscope has no reason to follow its movement, and
will retain its initial direction.
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Certainly, but not for long!!
A gyroscope which is not spinning will definitely drift, even if the structure it's hanging on is perfectly devised,
and will "forget" its initial direction. In particular if the structures move very slowly, it has every chance to
carry along the "dead" gyroscope with it! And thus would lose its initial orientation.
On the other hand, when the gyroscope spins very fast, it looks as if it's literally stowed to Space and it points in the
same direction with an extraordinary obstinacy!
In the same way, it is very hard to make a spinning top lose its balance when revolving, whereas when
motionless it has practically no equilibrium!!
Exactly! Whatever the movement of the structure it's hanging on, be it pitching, vibrating and moving
forward or backward, our "active gyroscope" will still point along the same vector!
Obviously, like all mechanical devices, the friction on the gyroscope's axis will finally stop the gyroscope
within a few hours and it will then lose its capacity to remain pointed in the same direction, if its movement is
not sustained.
Let's go back to Foucault: he observed that his gyroscope pointed exactly in the same direction every 24 hours, after
having revolved once in its casing!
Stupendous! You mean that the gyroscope remains stable in relation to the Earth and is not dragged along in
its rotation! In fact, the gyroscope had not changed orientation, but the Earth had revolved!
Actually it is even crazier than that! The gyroscope turning around itself is not only stable in respect to the
Earth, but also in relation to the farthest stars of the known Universe! It is a philosophical and scientific
"bomb"! I will try and explain. The Earth turns around itself, but also around the Sun. The Sun – and thus our
Solar System – has itself a well defined trajectory in our galaxy, the Milky Way. And this galaxy belongs to a
galactic cluster which has its own movement.
Well, when you activate your gyroscope, it retains absolute stability – or remains fixed – in relation to the movements of
all these clusters. We speak of cosmic stability.
Foucault simply remarked that the axis of the gyroscope he activated took back exactly the same orientation every 24
hours! In fact, it wasn't the gyroscope which had revolved, but the Earth itself!
Actually a gyroscope hanging in a double cardan can be used as a tridimensional compass, am I right?
Instead of pointing towards the North Pole, it remembers the direction it was first set on! But this
phenomenon of cosmic stability does not explain to me the increase in balance of a revolving spinning top.
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Aha! Let's now talk of the other important property of the gyroscope: the precession phenomenon!
What is this precession phenomenon? I really want to know more about
this!
OK ! Let's consider a simple cardan gyroscope:
It is simply a spinning top of which rotating axis is enclosed in a structure which mechanically isolates
it from the exterior.
Now, set this gyro into motion with a string you will wind around its axis and pull sharply!
Do you see this small plastic support? Put one of the gyro extremities on it while holding the other in your hand...this
is it!
And now: let go of the extremity you're holding!!!
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Do you really insist on it? It was a fine gyroscope you had there.
Don't be afraid, go on!
FANTASTIC!! Instead of falling, the gyro begins to revolve slowly laterally! I can't believe it! How can it be that
the gyro does not fall because of its weight? Gravity should make it topple over and instead, it goes on slowly
sideward!!!!
You just witnessed a Chris precession phenomenon. The gyroscope reacts very strangely to gravitational
flow when one of its extremities lies on a support.
I need an aspirin, quick! This device seems to defy gravity... what's going on Doc?
Actually, what you saw is the gyroscope's reaction to the terrestrial gravitational flow which tends to
make it revolve downwards in relation to its support. But the gyroscope immediately transforms this
tendency to fall in a sideward rotation!
When you try to make the rotating axis of a gyroscope turn, it doesn't let itself be pushed around! Instead
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of revolving where expected, it revolves in a plane at 90° from this impulse.
There are mathematical formulas to describe and predict this phenomenon, but in reality, nobody knows why this takes
place.
Precession occurs when you try to make the direction of the gyroscope rotation axis change.
Precession occurs in the wheels of cars, bikes, motorbikes and planes! It is also responsible for the changes in satellites
orientation.
This is the second strange property of a gyroscope.
If I understood well, when you push a chair forward, it topples over forward; it does not go left nor right. Still,
this is what occurs with a spinning top : if you push the rotating axis forward or backward, you'll be
surprised to see it move left or right depending on the direction of the axis’ rotation. We're dealing with the
precession phenomenon.
Exactly! Cosmic stability, precession...this gyroscope and this spinning top are really strange phenomena!
This card was prepared by:
http://www.jsb.be
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