270_Problem CHAPTER 9

# 270_Problem CHAPTER 9 - PROBLEM 9.183 Prob 9.147 and 9.151...

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PROBLEM 9.183 Prob. 9.147 and 9.151 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 Problem 9.147: 32 9.8821 10 lb ft s x I = ×⋅ 11.5344 10 lb ft s y I = 2.1878 z I = From Problem 9.151: 0.48776 xy I = 1.18391 10 lb ft s yz I = 2.6951 10 lb ft s zx I = ( a ) From Equation 9.56 ( ) ( ) 2 2 2 xyz x yy zz xx x KI I I I I I I I III K −+ + + + + −−− () 222 20 x y z x yz y zx z xy xy yz zx III II II I I −− = Substituting ( ) ( ) ( ) { 33 2 9.8821 11.5344 2.1878 10 9.8821 11.5344 11.5344 2.1878 KK  + ×+ +  ( ) ( ) } 22 2 6 2.1878 9.8821 0.48776 1.18391 2.6951 10 K +− ×
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