I've tried to find the moment of inertia of a cylinder rotating about an axis parallel to its base (i.e about the 'End diameter') as one can see here . But when I checked my results with different references ,I've found that it's incorrect!.I need a help to figure out where I did it wrong.
since I=∫x2.dm
dm=ρ.dv
dv=r.dθ.dr.dh
ρ=MπR2H
M:cylinder total mass. H:total height of cylinder. R:the radius of the cylinder.
The distance of each infinitesimal element from the axis of rotation would be :
√r2+h2
Therfore,
I=2MR2HR∫0H∫0r(r2+h2)dhdr
and this gives a result of : M H23+M R22
Which is obviously wrong since the second term should be multiplied by a factor of 1/2.
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