a) Show that the polar radius of gyration kO of the

Chapter 9, Problem 9.26

(choose chapter or problem)

(a) Show that the polar radius of gyration \(k_{O}\) of the semiannular area shown is approximately equal to the mean radius \(R_{m}=\left(R_{1}+R_{2}\right) / 2\) for small values of the thickness \(t=R_{2}-R_{1}\). (b) Determine the percentage error introduced by using \(R_{m}\) in place of \(k_{O}\) for the following values of \(t/R_m:\ 1\), \(\frac{1}{2}\), and \(\frac{1}{10}\).

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