137_Problem CHAPTER 9

137_Problem CHAPTER 9 - PROBLEM 9.113 The quarter ring...

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PROBLEM 9.113 The quarter ring shown has a mass m and was cut from a thin, uniform plate. Knowing that 1 12 2 , rr = determine the mass moment of inertia of the quarter ring with respect to ( a ) axis , AA ( b ) the centroidal axis CC that is perpendicular to the plane of the quarter ring. SOLUTION First note mass mV t A ρ = == ( ) 22 21 4 tr r π =− Also mass area I tI = () area 4 m I = ( a ) Using Figure 9.12, ( ) 44 , area 2 1 16 AA I Then ( ) , mass 2 1 16 4 AA m
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