Problem #3 In the following problem. any vector calculations should be done in reference to the coordinate system to the right. Ea} A rod with length L and mass M is supported as shown. The crosssection of the rod is square. with each side in the cross section having length a. The rod is rotated slightly away from the vertical and released. Starting from Newton's second law for rotation. derive a formula giving the angular frequency of the pendulum motion in terms of L and M. You may use that the moment ofinertia with respect to the support is iMLE. {This problem is entirely out of Physics EA. but you will need to know how to do this when you get to part {ell}. {b} The mass of the rod is 2.13 kg. and the oscillation period is LSD s. What is the length? {c} How, N turns of a current carrying wire are wrapped around the rod. A massless battery attached to the rod drives current I through the coils. The direction of current is such that the magnetic moment points away from the pivot {in a generally downward direction}. The rod is subject to a magnetic field of strength 3 pointing downward. Starting from Newton's second law for rotation, derive a symbolic expression for the angular frequency of the pendulum. in terms of L, M, a. N, I and B. {d} Suppose that B 2.5 T, i 51} A, a 4.1:} cm, and the period oftlie motion is now Ill} s. [low many turns were wrapped around the rod? till I ll [\"1le {at and {h} pants to} and [d1