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(a) Determine by direct integration the polar moment of inertia of the area shown with respect to point O. (b) Using the result of part a, determine the moments of inertia of the given area with...

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(a) Determine by direct integration the polar moment of inertia of the area shown with respect to point O.
(b) Using the result of part a, determine the moments of inertia of the given area with respect to the x and y axes.


Answered Same Day Dec 24, 2021

Solution

Robert answered on Dec 24 2021
120 Votes
b)By Symmetry we have Ix1=Iy1 and Ix2=Iy2
But Since we have
Ix=Ix1+Ix2 and Iy=Iy1+Iy2
J=Ix+Iy
J=2Ixx
Substituting from first part we have
Ixx=1/8R(R2^4-R1^40
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