158_Problem CHAPTER 9

158_Problem CHAPTER 9 - PROBLEM 9.127 A thin steel wire is...

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PROBLEM 9.127 A thin steel wire is bent into the shape shown. Denoting the mass per unit length of the wire by , m determine by direct integration the moment of inertia of the wire with respect to each of the coordinate axes. SOLUTION First note 1 12 2 2 33 3 dy xa x dx  =−   Then 22 2 33 3 2 11 dy x ax dx += + 2 3 a x = For the element shown 2 1 dy dm m dL m dx dx ′′ ==+ 1 3 a md x x = Then 1 3 1 3 0 0 a a a m x m a x m a x  =∫ = =   Now 1 3 1 3 3 2 0 a x a I ydm a x m dx x = 5 14 1 2 3 3 3 1 3 2 0 a a ma ax x d x x +− 8 4 4 2 3 3 3 3 0 3933 2428 a a x x +
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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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