Find out the moment of inertia of a semicircle, Mechanical Engineering

Find out the moment of inertia  of a semicircle:

Find out the M. I. of a semicircle ABM around its periphery AB and also around centroidal axes x and y as illustrated in Figure.

492_Find out the moment of inertia  of a semicircle.jpg

Solution

The position of centroid C of the semicircle is already calculated earlier. It is

                                      x¯ =  4 a /3 π ≈ 0.424 a

I(AB) for semicircle =  1/2 [I AB  for full circle] = π a 4 / 8

 IGY +  A (x¯)2  =  I ( AB) for semicircle =  (½) I (AB) for full circle

∴ I y =  π a /8 -  (π a2 /2)(0.424)2 a2

I y  = a4  (0.3927 - 0.2824)

I y  = 0.1103 a 4

Posted Date: 1/29/2013 1:30:04 AM | Location : United States







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