139_Problem CHAPTER 9

139_Problem CHAPTER 9 - PROBLEM 9.114 A thin,...

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PROBLEM 9.114 A thin, semielliptical plate has a mass m . Determine the mass moment of inertia of the plate with respect to ( a ) the centroidal axis , BB ( b ) the centroidal axis CC that is perpendicular to the plate. SOLUTION First note mass mV t A ρ = == 2 ta b π  =   Also mass area I tI = area 2 m I ab = ( a ) Have 2 ,area xB B y I IA =+ or 2 3 4 82 3 BB b Ia b a b ππ =− or 3 2 64 1 8 9 BB b Then 3 ,mass 2 26 4 1 8 9 BB m b ab 2 2 16 4 1 4 9 mb 2 or 0.0699 BB I mb = W ( b ) Using Figure 9.12, 3 8 AA I
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