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 mand thickness twith respect to its centroidal axis ,GG′is 5ma2/12, determine (a) the moment of inertia of the anemometer with respect to the axis ,AA′(b) the ratio of a to lfor 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 2armarm4mVdlπρρ==×and cupcupdmdV=( )( )( )2cosatadπθθ=Then 22cupcup0osmdmatdρθ=∫2202sin=22πρ=Now ( ) ( ) ( )anem.cupsarmsAAAAAAIII′′′=+Using the parallel-axis theorem and assuming the arms are slender
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