101_Problem CHAPTER 9

101_Problem CHAPTER 9 - PROBLEM 9.85 For the quarter...

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PROBLEM 9.85 For the quarter ellipse of Problem 9.67, determine the orientation of the principal axes at the origin and the corresponding values of the moments of inertia. SOLUTION From Problem 9.79: 44 82 xy I aI a π == Problem 9.67: 4 1 2 xy I a = Now, Equation (9.25): 4 1 2 2 2 tan 2 xy m a I II aa θ ππ    =− 8 0.84883 3 Then 2 40.326 and 220.326 m = °° or 20.2 and 110.2 m = W Also, Equation (9.27): 2 2 max, min 22 xy I I +− + 1
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