281_Problem CHAPTER 9

281_Problem CHAPTER - PROBLEM 9.186 For the component described in the problem indicated determine(a the principal moments of inertia at the

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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 32 14.32 10 lb ft s x I 18.62 10 lb ft s yz II == × From Problem 9.172 4.297 10 lb ft s , 0 xy zx xz I × = Substituting into Eq. (9.56) and using , , 0 y z xy zx yz I I I = () ( ) ( ) ( ) 2 32 2 2 2 22 2 2 0 xy x yy x y x x y KII KI IK I I I I  −+ + + =   ( ) ( ) ( ) 2 33 2 2 3 3 3 14.32 10 2 18.62 10 14.32 10 2 18.62 10 18.62 10 KK −− −× + × + × × ( ) ( )( ) 2 3 3 3 2 4.297 10 14.32 10 18.62 10 2 18.62 10 4.297 10 0 K  × × ×=   or 2 3 3 51.56 10 0.84305 10 0.004277 10 0 K −−− + × × = Solving: 2 1 0.010022 lb ft s K =⋅ or 1 10.02 10 lb ft s K = ×⋅ W 2 2 0.018624 lb ft s K
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This note was uploaded on 07/11/2011 for the course EGM 2511 taught by Professor Jenkins during the Spring '08 term at University of Florida.

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