172_Problem CHAPTER 9

172_Problem CHAPTER 9 - PROBLEM 9.135 The cups and the arms...

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PROBLEM 9.135 The cups and the arms of an anemometer are fabricated from a material of density ρ . Knowing that the moment of inertia of a thin, hemispherical shell of mass m and thickness t with respect to its centroidal axis , GG is 5 ma 2 /12, determine ( a ) the moment of inertia of the anemometer with respect to the axis , AA ( b ) the ratio of a to l for which the centroidal moment of inertia of the cups is equal to 1 percent of the moment of inertia of the cups with respect to the axis . AA SOLUTION ( a ) First note 2 arm arm 4 mV d l π ρρ == × and cup cup dm dV = ( )( )( ) 2c o s at a d πθ θ = Then 2 2 cup cup 0 o s md m a t d ρθ =∫ [] 2 2 0 2s i n = 2 2 πρ = Now ( ) ( ) ( ) anem. cups arms AA AA AA II I ′′ =+ Using the parallel-axis theorem and assuming the arms are slender
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