Is the notion of angular velocity a relativistic invariant?

R.H.

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On 2024-02-10 05:07:02 +0000, Richard Hachel said:

Is the notion of angular velocity a relativistic invariant?

In Special Relativity it is.

--
Mikko

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Le 10/02/2024 à 09:36, Mikko a écrit :

On 2024-02-10 05:07:02 +0000, Richard Hachel said:

Is the notion of angular velocity a relativistic invariant?

In Special Relativity it is.

Non, je pense que vous vous trompez.

La vitesse angulaire est un invariant relativiste.

Réfléchissez-y avec attention et après avoir pris trois tasses de
café.

C'est très contre-intuitif, je sais.

R.H.

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On 2/10/2024 8:38 AM, Richard Hachel wrote:

Non, je pense que vous vous trompez.

La vitesse angulaire est un invariant relativiste.

Réfléchissez-y avec attention et après avoir pris trois tasses de café. C'est très contre-intuitif, je sais.
R.H.

Why are you telling us to always go to other people's funerals,
otherwise they won't come to yours?

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On 2/10/24 2:36 AM, Mikko wrote:

On 2024-02-10 05:07:02 +0000, Richard Hachel said:

Is the notion of angular velocity a relativistic invariant?

In Special Relativity it is.

Actually it is not. Moreover, this is considerably more nuanced, so the
best response is: the question does not make sense.

Consider a disk in the x-y plane, rotating around the z axis with
angular velocity K in the inertial rest frame of its center. Mark the
edge of the disk with a dot, and an observer moving along the x axis
with relativistic factor γ will measure the dot moving in an ellipse, so "angular velocity" does not really apply [#]. If one ignores that, to
this observer the disk will have "angular velocity" K/γ (in addition to
its enormous linear motion along -x). There's nothing invariant here.

[#] One can say "angular velocity" does not apply to
elliptical motion, or one can say that it varies
depending on orientation. The choice depends on the
detailed meanings of words, not any physics or math.

Tom Roberts

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Le 10/02/2024 à 20:00, Volney a écrit :

Why are you telling us to always go to other people's funerals,
otherwise they won't come to yours?

Speaking of funerals, the question is very simple:
One day, a man was walking in the suburbs of Barcelona,
and he comes across an old lady who tells him that she is going to tell
him his fortune.
As he laughed about it, being very Cartesian, she said to him: "I'm going
to tell you your fortune, it will cost you five euros, and if you find
just one thing that isn't true, you won't have to pay." .
So he listens to the old lady who reveals her whole past to him and says
to him:
“You will marry a girl named Samantha-Maria Smith, village of Jaligny,
from whom you will have three children, and you will have a happy life.”
Arms drooping, he pays the old lady, and rushes home, then types on his computer:
"Samantha-Maria Smith. Jaligny".
Why is he doing this?
Because he is curious.
The computer responds:
Two possible answers.
1. Samantha-Maria Smith (1905-1997). Jaligny.
2. Samatha-Maria Smith (25 years old). Jaligny.
The guy then searches on his computer in which cemetery we could find the
grave of the first suitor.

He is curious.

But he's stupid.

R.H.

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Le 10/02/2024 à 21:04, Tom Roberts a écrit :

On 2/10/24 2:36 AM, Mikko wrote:

On 2024-02-10 05:07:02 +0000, Richard Hachel said:

Is the notion of angular velocity a relativistic invariant?

In Special Relativity it is.

Actually it is not. Moreover, this is considerably more nuanced, so the
best response is: the question does not make sense.

Consider a disk in the x-y plane, rotating around the z axis with
angular velocity K in the inertial rest frame of its center. Mark the
edge of the disk with a dot, and an observer moving along the x axis
with relativistic factor γ will measure the dot moving in an ellipse, so "angular velocity" does not really apply [#]. If one ignores that, to
this observer the disk will have "angular velocity" K/γ (in addition to
its enormous linear motion along -x). There's nothing invariant here.

[#] One can say "angular velocity" does not apply to
elliptical motion, or one can say that it varies
depending on orientation. The choice depends on the
detailed meanings of words, not any physics or math.

Tom Roberts

Thank you for your very interesting and intelligent response.

R.H.

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