When an automobile wheel is balanced, a small weight is added to the rim. Consider a similar problem for the thin rod. Assume a particle, of mass m1, is placed at a distance {10 in the body-fixed frame B " pG, b1, b2, b3q. Use (a positive angle as shown in the figure) to locate the particle. The quantity m1 is unknown. Assume that , , , and m (the mass of the thin rod) are known. Assume that m1 is placed to eliminate products of inertia (POIs). a) Derive a formula for m1 in terms of m, , and (perhaps) . b) Assume that " " 45 deg and give a value for m1 in terms of m. c) Derive a formula for Ixx of the rod plus the mass m1 in terms of m and . Assume that " " 45 deg