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267_Problem CHAPTER 9

267_Problem CHAPTER 9 - PROBLEM 9.182 Prob 9.167 For the...

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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 z axes. SOLUTION From the solution to Problem 9.143 and 9.167 3 2 3 2 3 2 3 2 34.106 10 lb ft s 50.125 10 lb ft s 34.876 10 lb ft s 0.96211 10 lb ft s 0 x y z xy yz zx I I I I I I = × = × = × = × = = ( a ) From Equation 9.55 0 0 0 0 0 x xy xy y z I K I I I K I K = or ( ) ( ) ( ) ( ) 2 0 x y z z xy I K I K I K I K I = or ( ) ( ) ( ) 2 0 z x y xy I K I K I K I = Then ( ) 2 2 0 and 0 z x y x y xy
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