PROBLEM 9.182 Prob. 9.167 For the component described in the problem indicated, determine (a) the principal moments of inertia at the origin, (b) the principal axes of inertia at the origin. Sketch the body and show the orientation of the principal axes of inertia relative to the x, y, and zaxes. SOLUTION From the solution to Problem 9.143 and 9.167 3234.10610 lb ft s50.12534.8760.96211 10 lb ft s0xyzxyyzzxIIIIII−−−−=×⋅⋅⋅⋅⋅⋅⋅⋅==(a) From Equation 9.55 000xxyxyyzIKIKIK−−=−or ()( ) ( )20xyzzxyI−−−−−=or ( )20zxyxy−−−−=Then 220 and 0yxyxyIIKKI−++−=Now 134.876
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