Sunday, 12 August 2018

homework and exercises - Moment of inertia of a cylinder about its base


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

where


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=2MR2HR0H0r(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.




No comments:

Post a Comment

Understanding Stagnation point in pitot fluid

What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...