PeroK's latest activity

Note that we can get a similar paradox by considering a length of elastic material that stretches out until instantaneously it has a...

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...

You can, but perhaps you can't meaningfully have the boundary of the dust cloud moving at ##c##. In one sense you can, because the...

Dust is not a continuous distribution of matter.

There's an ambiguity over which limit to take first. Even if the physical model is not valid, there's a question over the validity of...

Sure, if you do the integral first and then take the limit as the velocity tends to ##c##. But, if you consider the construction of the...

A one-dimensional ring is fundamentally unphysical. Integration involves the limit of finite rings or annuluses, which is where the...

Consider the outer portion of the disk. For each ##n##, consider the annulus with inner radius ##r_n = R(\frac {n-1}n)##. The mass of...

Yes, as @anuttarasammyak also wrote. Sorry I missed that. So the reason why K diverges computationally in this case, is that the rest...

Yes, but here one of the limits is due to actual physics (KE of the rim particles of constant finite rest mass going to infinity), while...

See also the recent thread about the electric field of an infinite, uniformly charged plate.

Mathematically, it's that the sequence or sum diverges. Swapping the order of limits is not always reliable. See the simple example for...

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...

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

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