18_Problem CHAPTER 9

18_Problem CHAPTER 9 - PROBLEM 9.15 Determine the moment of...

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PROBLEM 9.15 Determine the moment of inertia and the radius of gyration of the shaded area shown with respect to the x axis. SOLUTION At 12 , x ay y b = == 1 :o r b ybm a m a = = 3 2 3 r b ybk a k a Then 11 or ba yx xy ab 1 3 1 3 3 22 3 or x y a b    Now () 1 3 1 3 21 aa dA x x dy y y dy b b =− = 14 33 2 0 0 31 2 42 b b a a Ad A y y d y y y bb = ∫∫ ab ab ab = Then 1 3 1 3 x dI y dA y y y dy b b Now 71 0 34 0 0 3 2 10 4 b b xx yy y y Id I a d y a = 3 1 10 4 10 4 b a b or 3 1 10 x I ab = W And 3 1 10 1 2 1 5 x x ab I kb Aa b = 5 x b k = W
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This note was uploaded on 07/11/2011 for the course EGM 2511 taught by Professor Jenkins during the Spring '08 term at University of Florida.

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