Rotational Inertia of a Disk with Non-Uniform Mass Density

Derives the Rotational Inertia (a.k.a., Moment of Inertia or I) for disk of non-uniform mass density. For this example the axis is at the center of the disk and normal to it.
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[@MRF77]

Sir you're awesome! I have one request though, could you please upload some advanced physics videos in future? Like cocepts in electrodynamics from Griffith's book, or thermodynamics etc.?

[@unknownlegend660]

Exactly what I needed thank you!

[@athul_c1375]

very helpful

[@flurryofsnow]

Really wish I knew this.

[@goofyaaahhandle]

Thank you so much this helped a lot

[@elvishchouhan600]

Sir you are really amazing

[@satishbhatt2894]

sir why you didn't took the limits from r to R..why from 0 to R

[@lasseviren1]

I wanted the integral to start at r=0 and integrate all the way to r=R so that I got the I for the entire disk.

[@satishbhatt2894]

@@lasseviren1 thnkx sir i understood..i thought it was the disk which had a hole in its centre

[@rabri-ghewar]

How can we remove the 'C' in final answer

[@reveuse7871]

You don't have to remove it, it's just a positive constant.