234_Problem CHAPTER 9

234_Problem CHAPTER 9 - PROBLEM 9.163 Complete the...

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PROBLEM 9.163 Complete the derivation of Eqs. (9.47), which express the parallel-axis theorem for mass products of inertia. SOLUTION Have xy yz zx I xydm I yzdm I zxdm === ∫∫∫ (9.45) and x xx yyy zzz ′′ = += + (9.31) Consider xy I xydm = Substituting for x and for y ( ) ( ) xy I yy d m =+ + xydm y xdm x ydm xy dm ′′′ =+++ ∫∫ By definition xy I ′ ′ =
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