174_Problem CHAPTER 9

174_Problem CHAPTER 9 - PROBLEM 9.136 A square hole is...

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PROBLEM 9.136 A square hole is centered in and extends through the aluminum machine component shown. Determine ( a ) the value of a for which the mass moment of inertia of the component with respect to the axis , AA which bisects the top surface of the hole, is maximum, ( b ) the corresponding values of the mass moment of inertia and the radius of gyration with respect to the axis . AA (The density of aluminum is 3 2800 kg / m .) SOLUTION First note 2 11 mVb L ρρ == And 2 22 mVa L ( a ) Using Figure 9.28 and the parallel-axis theorem, have ( ) ( ) 12 AA AA AA II I ′′ =− () 2 1 12 2 a mb b m  =+ +  
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