PAllen's latest activity

Note that if we change the mass assumption to be constant density in each element's local comoving frame, we get for an arbitrary...

To decouple an annulus from any hypothetical containing disc, we introduce ##\rho## which is simply ##M/\pi r^2## in post #1 convention...

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

If I am picking, for example, a finite set of approximating elements, I can certainly have the angular span of each be inversely...

I think this can be dispensed with. Just keep ##r d\phi## constant along a radial path. Also, @Ibix integral in the OP already keeps...

This would be the same as long as you have uniformly distributed rest mass per the COM inertial frame. To get any other result you have...

It’s possibly important to understand what M means. The construction of the integral means it summed from constituent rest masses.

I am simply describing a procedure to arrive at the final state starting from a rest state.

The proposed integral in the OP impies the following physical process: a disc of dust with uniform density in some inertial frame is...

I claim the integral in the OP, evaluated between specified r values below R corresponding to speed c, will always be finite, and no...

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

I don't believe this is correct, and you haven't made any attempt to demonstrate this part. The calculation for such an annulus with...

I think the implication is a similar phenomenon - the circumference of the rim grow unbounded, but this leads only to limiting area of 2...

So, if you do just treat the rim as one dimensional, with a linear mass distribution per the COM frame, you do get KE unbounded in the...

Qualitatively, what I am getting at is that as the rim speed approaches c, the number of small area elements of given measure (per a...