PROBLEM 9.162 Thin aluminum wire of uniform diameter is used to form the figure shown. Denoting by m′the mass per unit length of wire, determine the products of inertia ,xyI,yzIand zxIof the wire figure. SOLUTION First compute the mass of each component. Have mmLmLL′==Then 151122mmmRmRππ′′=( )2421RR′−322mmRmR′′Now observe that because of symmetry the centroidal products of inertia, ,,xyyzII′′′′and ,zxI′ ′of components 2 and 4 are zero and ( )( )( )( )113300xyyzII==( )( )550==Also 122 34450xxyyyzz===Using the parallel-axis theorem [Equations (9.47)], it follows that xzzxIfor components 2 and 4.
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