Determine the moment of inertia I about axis O-M for the uniform slender rod bent into the shape shown. Plot I versus θ from θ = 0 to θ = 90° and determine the minimum value of I and the angle a which its axis makes with the x-direction. (Note: Because the analysis does not involve the z-coordinate, the expressions developed for area moments of inertia, Eqs. A /9, A /10, and A /11 in Appendix A of Vol. 1 Statics, may be utilized for this problem in place of the three-dimensional relations of Appendix B.) The rod has a mass ρ per unit length.

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y -M