The direction of the precession

[Luigi Fortunati]

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.

[Luigi Fortunati]

The movie
https://youtu.be/1sLbkfHXIDA
inspired my reflections.

In the movie it is initially explained that it is the impulses of the
particles of the wheel that determine the precession and it certainly
is.

But there is a part of the explanation that did not convince me.

The professor says that the impulses are all equal, but if that were
the case, the impulse of each particle would be equal and opposite to
that of the diametrically opposite particle, so that, in the end, the
summation of rightward impulses would be exactly counterbalanced by the
summation of those going to the left.

In such conditions, is it not contradictory that the precession goes to
the right (or to the left) if the impulses on the right are always
equal and opposite to those on the left?

[Luigi Fortunati]

I've been thinking a lot about what the video teacher says
https://www.youtube.com/watch?v=1sLbkfHXIDA&t=1399s
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?

[Lou]

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.
I bet if your wheel was made of a very flexible rubber it would
not preccess, or preccess very little as the wheel shape would
distort instead to compensate for the different speeds of the
different points on its circumference as it rotated.

[Luigi Fortunati]

Lou il 05/03/2023 12:34:17 ha scritto:
> 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.

I translate the words of the professor: "Let us consider the wheel as
made of separate particles moving in a circle around the axis and fix
our attention on one of them. For example this particular particle. Its
mass is m1, the distance from the axis is r1. It moves in this way with
velocity v1, perpendicular to the radius vector. We write its angular
momentum. The angular momentum is L1 equal to the momentum m1, v1
transverse by r1 (L1=(m1* v1)*r1).
...
We have calculated the angular momentum of the particle. We could do
the same for this, or this, or this, and so for any particle of the
wheel. And, having done this, the total angular impulse of the wheel is
found by adding together all these different angular impulses".

> 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.

You too make the same mistake as the teacher in the video: consider
only the rotation of the wheel on its axis.

I have updated my animation
https://www.geogebra.org/m/sssuefav
adding a side view where there is another rotation highlighted with red
dashed line.

It is clearly seen that the wheel, descending by gravity, is forced to
incline following the red circumference line whose radius is the arm
AB.

This inclination is the cause of the precession and, in fact, if the
wheel did not incline, it would descend in perfect vertical, without
going either to the right or to the left.

Obviously, it depends on the principle of conservation of angular
momentum, as in the case of the ice skater who rotates faster when
bringing her arms towards her body and slower when moving them away.

In my animation, the upper half of the wheel (moving away from the axis
of rotation) slows its rotation to the right (like the skater spreading
her arms) and the lower half (moving towards the axis of rotation) it
accelerates its rotational motion to the left like the skater narrowing
her arms.

As a result, the wheel moves to the left.

If the rotation is counterclockwise, the reverse occurs and the

precession goes to the right.

All of this can be used to establish an alternative method to the
right-hand rule: the direction of precession always goes to the same
side as the particles at the bottom of the wheel.

In the clockwise spinning wheel, its bottom particles go to the left
and the precession also goes to the left, in the counterclockwise one,
for the same reason, the precession goes to the right.

[Sylvia Else]

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
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.

Sylvia.

[Lou]

On Tuesday, 7 March 2023 at 17:19:09 UTC, Sylvia Else wrote:
> On 16-Jan-23 9:03 pm, Luigi Fortunati wrote:=20
> > One possible explanation for the direction of the precession is that of=
=20
> > my simulation=20
> > https://www.geogebra.org/m/ry8zxkwj=20
> >=20
> > Gravity affects impulses in diametrically opposite ways if the directio=
n=20
> > of 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=
=20
> > maximum, 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=
=20
> > the wheel (going to the left) that prevails and the precession goes to=
=20
> > the 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=
=20
> precession. But there is not. As the axis of rotation of a spinning=20
> object changes, so does its angular momentum, and the rate of change of=
=20
> angular momentum has to be proportional to the applied torque. So the=20
> precession is in the direction required to make that true.=20
>=20
This statement seems illogical to me. You say: =E2=80=9CAs the axis of rota=
tion=20
of a spinning object changes, so does its angular momentum=E2=80=9D
I assume you mean precession when you say =E2=80=98axis of rotation changin=
g=E2=80=99=20

Isnt that putting the cart before the horse? Because my understanding is th=
e opposite.
In that (for any rotating point on the wheel) it=E2=80=99s the angular mome=
ntum ( via Gravity
vector changing ) which changes. Which results in a change of the axis of r=
otation.


> Sylvia.

[Sylvia Else]

[[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]]

On 08-Mar-23 10:12 pm, Lou wrote:
> On Tuesday, 7 March 2023 at 17:19:09 UTC, Sylvia Else wrote:

> This statement seems illogical to me. You say: "As the axis of rotation

> 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.

For a rigid object whose rate of rotation is not changing, the axis of
rotation and angular momentum are tied together - neither can change
without the other changing. There is no sense in which a change to one
causes the change to the other.

Sylvia.

[Sylvia Else]

On 10-Mar-23 7:37 am, Sylvia Else wrote:
> [[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]]
>

This seems to related to some Thurderbird setting. I've fiddled with
it but made no progress (I've manually inserted newlines into this).

Perhaps others know the solution, but is it actually problem with
modern news readers?

Sylvia.

[[Mod. note -- In general "meta-discussions", i.e., discussions about
how the newsgroup operates, are forbidden by our newsgroup charter.
But I think it's reasonable to make an exception here, since this is
a fairly common problem. To answer the author's question, yes, over-long
lines are still a problem: windows are of finite width, and not everyone
uses software which auto-rewraps long lines, and when software does this
it doesn't always result in a very readable result. (For example, I
often see auto-rewrapped quoted lines with "> > >" in the middle of
text, because the auto-rewrapping software doesn't know the semantics
of "> " quote markers.
-- jt]]