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But the uniform COM frame density follows necessarily from any simple (i.e. not including stress energy of holding the disc together)...

This is a nice simplification for further discussion, that changes the main questions not at all. This would be computing the total...

There is such a thing as null dust in the literature. :wink: But it's not intended to cover this kind of case. I think @Demystifier...

The conducting electrons interact with lattice atoms. It turns out that the lowest energy state of such interactions realizes when...

There is one more way to look at the problem, to avoid the continuum distribution of matter in the radial direction. Consider ##N##...

We have two limits here. The first is the limit involved in the definite integral of a continuous mass distribution across a disk. We...

Do you mean a hoop with zero or non-zero extension in the radial direction? In the case of a realistic non-zero extension, it's not...

Exactly. To understand it quantitatively, one has to focus on the contribution of the integral near the ##r=R## region. For that...

The word 'ether' has had several meanings throughout the history of science. For example, regarding your question, look at what Einstein...

That's irrelevant, because the KE is computed in the laboratory frame (not in the disk frame), where the spatial geometry is Euclidean.

Compute the integral in the interval ##[R-\epsilon R,R]## for small ##\epsilon##, it should explain what's going on.

In your formula K=M for ##\omega R=1##. I think that even the rim part speed reaches light speed, its element contribution is...

Ahh, just found a translated version! 🙌🏼...

That's a physical inevitability. Nevertheless, the kinetic energy of a spinning disk tends to infinity as the speed of rotation tends to...

Here is a demonstration: