215_Problem CHAPTER 9

215_Problem CHAPTER 9 - PROBLEM 9.153 Determine the mass...

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PROBLEM 9.153 Determine the mass products of inertia I xy , I yz , and I zx of the cast aluminum machine component shown. (The density of aluminum is 2700 kg/m 3 .) SOLUTION Have al mV ρ = Then () 3 1 3 kg 2700 0.350 0.100 0.030 m m m  ×   2.8350kg = 3 2 3 kg 2700 0.200 0.100 0.050 m m m × 2.7000kg = 2 3 3 3 kg 2700 0.025 0.100 m m m π 0.53014kg = First note that symmetry implies 0 ′′ === xy yz zx III for each component Now uv u v I Im u v =+ where 0 = uv I ( )( )( ) 2.8350kg 0.175m 0.050m xy x y = ( )( )( ) ( )( )( ) 2.7000kg 0.100m 0.050m 0.53014kg 0.080m 0.050m +− ( ) 32 3
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