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281_Problem CHAPTER 9

# 281_Problem CHAPTER 9 - PROBLEM 9.186 For the component...

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PROBLEM 9.186 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. Problem 9.150 and 9.172 SOLUTION ( a ) From the solutions to Problem 9.150 3 2 14.32 10 lb ft s x I = × 3 2 18.62 10 lb ft s y z I I = = × From Problem 9.172 3 2 4.297 10 lb ft s , 0 xy zx xz I I I = = × = Substituting into Eq. (9.56) and using , , 0 y z xy zx yz I I I I I = = = ( ) ( ) ( ) ( ) 2 3 2 2 2 2 2 2 2 2 0 x y x y y xy x y y xy K I I K I I I I K I I I I + + + = ( ) ( ) ( ) ( ) ( ) 2 3 3 2 2 3 3 3 14.32 10 2 18.62 10 14.32 10 2 18.62 10 18.62 10 K K × + × + × × + × ( ) ( )( ) ( )( ) 2 2 2 3 3 3 3 3 2 4.297 10 14.32 10 18.62 10 2 18.62 10 4.297 10 0 K × × × × × = or 3 3 2 3 3 51.56 10 0.84305 10 0.004277 10 0 K K K × + × × = Solving: 2 1 0.010022 lb ft s K = or 3 2 1 10.02 10 lb ft s K = ×
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