Is the notion of angular velocity a relativistic invariant?
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.
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.
Why are you telling us to always go to other people's funerals,
otherwise they won't come to yours?
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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