299_Problem CHAPTER 9

299_Problem CHAPTER 9 - PROBLEM 9.197 Determine the moments...

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PROBLEM 9.197 Determine the moments of inertia of the shaded area shown with respect to the x and y axes. SOLUTION Have ( ) ( ) ( ) 123 x xx x I III =+− where () 3 4 1 14 22 12 3 x I aa a == Now 4 23 8 AA BB I Ia π and ( ) ( ) 2 2 2 AA xz I IA d =+ or 2 42 2 3 4 82 3 xx a II a a ππ    4 8 89 a =− Then 2 2 2 2 24 2 2 84 2 3 a IIA d a = + + 4 45 38 a 3 3 3 2 2 3 2 3 a d a = + 4 a =− + Finally 44 4 5 4 5 33 8 3 8 x I a  + +   4 or 4 x I a = W Also ( ) ( ) ( ) yy y y I where () () ( ) 1 32 2 4 11 6 2 12 3 y I a = 2 a + 4 16 3 y I a ∴= W
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