PROBLEM 9.79 Determine for the quarter ellipse of Problem 9.67 the moments of inertia and the product of inertia with respect to new axes obtained by rotating the xand yaxes about O(a) through o45 counterclockwise, (b) through o30 clockwise. SOLUTION From Figure 9.12: ()()3216xIaaπ=48a=()3216yI=42a=From Problem 9.67: 412xyIa=First note 444115228216xyIIaaaππ+=+=438216Iaa−=−=−Now use Equations (9.18), (9.19), and (9.20). Equation (9.18): cos2sin 2xxyxyxyIIIIθ′
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