Bead on a rotating rod (modified from taylor 7.21) the center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a horizontal plane with constant angular velocity w. consider a bead with mass m that is free to move frictionlessly along the rod. find the position of the bead as a function of time using the polar coordinate r as your generalized coordinate. (a) before doing any calculation, discuss what you think functional behavior of the position will be. (b) before doing any calculation, what special cases will you want to check at the end to see if your acceleration is correct? what do you expect the acceleration to be for those special cases? (c) using a lagrangian approach, find the position of the bead as a function of time using the polar coordinate s as your generalized coordinate (d) discuss whether your answer is sensible: the scalar/vector nature of your answer, dimensions, functional behavior (including at least one plot), and check some special cases, including the ones you mentioned in part 2b.