One possible explanation for the direction of the precession is that of
my simulation
https://www.geogebra.org/m/ry8zxkwj
Gravity affects impulses in diametrically opposite ways if the direction
of rotation changes.
If the rotation is clockwise, the impulses of the right side of the
wheel are strengthened by the force of gravity and those of the left
side are slowed down.
Consequently, in the lower part of the wheel the impulses are at their maximum, and in the upper part they are at a minimum.
Therefore, it is the direction of the impulses from the lower part of
the wheel (going to the left) that prevails and the precession goes to
the left.
It goes without saying that if the rotation is counterclockwise, the
exact opposite occurs and the precession goes to the right.
I've been thinking a lot about what the video teacher says https://www.youtube.com/watch?v=1sLbkfHXIDA&t=1399sI don’t speak Italian so could not watch the video with confidence
and I have come to the conclusion that (if I am not mistaken) there is
an error in what he says.
But this mistake (if it is a mistake) is not the only one he makes...
Towards the third minute, the professor states that the wheel is made
up of particles and that each particle has an impulse L1=(m1*v1)*r1,
due to the rotation of the wheel on itself.
This is correct but it is also incomplete, because, in addition to this rotation, there are also others: those around the two axes that support
the wheel.
And if the rotations are more than one, the impulses are also more than
one.
Moreover, if the impulse due to the rotation of the wheel on itself
were unique, the sum of the impulses of all the particles of the wheel
would be null because these impulses are symmetrical and, therefore,
they would cancel each other with those diametrically opposite.
Consequently, in that case, there would be no justification for
precession.
Instead, in the rotation with respect to the support rods, the impulses
are not symmetrical and, therefore, justify the directions that the precession takes.
In short, the video professor's mistake (in my opinion) is that he
considers only one rotation (which justifies nothing) and neglects all
the others.
To clarify what these other rotations are, I have prepared the
simulation
https://www.geogebra.org/m/sssuefav
where the path of particle E is much greater than that of the opposite particle Z.
In your opinion, do the particles of the wheel in the video follow a
single rotation (that of the wheel on itself, as the professor says) or
do they also follow the other rotations that I highlighted in my
simulation?
I don't speak Italian so could not watch the video with confidence
as to what the message is. I don't know what he is saying
nor can read the out of focus chalk marks.
But your simulation animation seems to confirm exactly why it
preccesses and which direction it must take, rather than rule it out.
To start with when the wheel rotates freely your two particles
take very different path lengths. From your animation I measured
E as being 17.5 cm And Z as being 25.5 cm. (And incidentally
E&Z both only take 1 path each . Not multiple paths!)
The reason for the precession seems simple. Let's study the 1/4 rotation paths of each particle as E moves from 3:00 to 6:00 and Z moves
from 9:00 to 12:00
E starts off moving downwards. It has gravitational pull G added to rotational momentum R.
So it speeds up.
Z on the other hand starts off moving upwards. It also
has gravitational pull G and rotational momentum R. But although R
is the same for both Z and E,..G on the other hand is opposite to
the direction of each. In the sense that G pulls on Z reducing its speed whilst G pulls on E increasing its speed.
To compensate for these different velocities of E and Z ....Z travels
less distance because it has a slower velocity. And E travels a
greater distance as it has a greater velocity. To compensate
without distorting its shape the wheel preccesses.
As your animation confirms.
One possible explanation for the direction of the precession is that of
my simulation
https://www.geogebra.org/m/ry8zxkwj
Gravity affects impulses in diametrically opposite ways if the direction
of rotation changes.
If the rotation is clockwise, the impulses of the right side of the
wheel are strengthened by the force of gravity and those of the left
side are slowed down.
Consequently, in the lower part of the wheel the impulses are at their maximum, and in the upper part they are at a minimum.
Therefore, it is the direction of the impulses from the lower part of
the wheel (going to the left) that prevails and the precession goes to
the left.
It goes without saying that if the rotation is counterclockwise, the
exact opposite occurs and the precession goes to the right.
On 16-Jan-23 9:03 pm, Luigi Fortunati wrote:=20=20
One possible explanation for the direction of the precession is that of=
n=20my simulation=20
https://www.geogebra.org/m/ry8zxkwj=20
=20
Gravity affects impulses in diametrically opposite ways if the directio=
=20of rotation changes.=20
=20
If the rotation is clockwise, the impulses of the right side of the=20 wheel are strengthened by the force of gravity and those of the left=20 side are slowed down.=20
=20
Consequently, in the lower part of the wheel the impulses are at their=
=20maximum, and in the upper part they are at a minimum.=20
=20
Therefore, it is the direction of the impulses from the lower part of=
=20the wheel (going to the left) that prevails and the precession goes to=
=20the left.=20
=20
It goes without saying that if the rotation is counterclockwise, the=20 exact opposite occurs and the precession goes to the right.=20
You seem to be suggesting that there is some mystery to the direction of=
precession. But there is not. As the axis of rotation of a spinning=20=20
object changes, so does its angular momentum, and the rate of change of=
angular momentum has to be proportional to the applied torque. So the=20 precession is in the direction required to make that true.=20This statement seems illogical to me. You say: =E2=80=9CAs the axis of rota= tion=20
=20
Sylvia.
On Tuesday, 7 March 2023 at 17:19:09 UTC, Sylvia Else wrote:
On 16-Jan-23 9:03 pm, Luigi Fortunati wrote:This statement seems illogical to me. You say: "As the axis of rotation
One possible explanation for the direction of the precession is that ofYou seem to be suggesting that there is some mystery to the direction of
my simulation
https://www.geogebra.org/m/ry8zxkwj
Gravity affects impulses in diametrically opposite ways if the direction >>> of rotation changes.
If the rotation is clockwise, the impulses of the right side of the
wheel are strengthened by the force of gravity and those of the left
side are slowed down.
Consequently, in the lower part of the wheel the impulses are at their
maximum, and in the upper part they are at a minimum.
Therefore, it is the direction of the impulses from the lower part of
the wheel (going to the left) that prevails and the precession goes to
the left.
It goes without saying that if the rotation is counterclockwise, the
exact opposite occurs and the precession goes to the right.
precession. But there is not. As the axis of rotation of a spinning
object changes, so does its angular momentum, and the rate of change of
angular momentum has to be proportional to the applied torque. So the
precession is in the direction required to make that true.
of a spinning object changes, so does its angular momentum"
I assume you mean precession when you say 'axis of rotation changing'
Isnt that putting the cart before the horse? Because my understanding
is the opposite.
In that (for any rotating point on the wheel) it's the angular momentum
( via Gravity
vector changing ) which changes. Which results in a change of the axis rotation.
Sylvia.
[[Mod. note -- Please limit your text to fit within 80 columns,
preferably around 70, so that readers don't have to scroll horizontally
to read each line. I have manually reformatted parts of this article.
-- jt]]
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