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moment of inertia of a disk

I've asked this on Facebook before, but has anybody found (ideally those doing the Newtonian Dynamics exams in a few weeks), a concise explanation of derivations?

All I seem to find is people doing these formulas that, by apparently pulling numbers and constants out of their arse, ends up with a formula, but the logic behind it seems to have no explanation, where that be lecturers, PhD students, Youtube tutorial, etc...I can follow the proof, but why should we come to these conclusion in the first place?

How can something that is apparently so fundamental to understanding physics, have no bleeding explanation?!?!

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Moment of Inertia of a Disk

Here is a quick derivation of the value of the moment of inertia for a disk as rotated about a fixed axis through its center.

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