58.5Consider the sphere with the cavity to be made of a (i) solid sphere of radius and and mass asM, with its center of mass at 0z=, and (ii) a solid sphere the size of the cavity, with mass cM−and center of mass at 2az= −. The actual sphere with the cavity has a mass scMmM=−and center of mass. cmz3334474283scamM Maaπρπρ=−=−=87sMm=and 17cMm=From eqn. 8.3.2, III=+2222552aMaMI=+22131574 70aImamma=− =8.6The moment of inertia about one of the straight edges is 2zIRdv=∫where 222Rxy=+. From Appendix F … 2sindvrdr ddθθφ=φθr R yx z 22222
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