5) A frictionless rod of length L rotates counterclockwise in the with constant angular speed w at an angle a to the z axis. A bead of mass m, free to slide on the rod, leaves the origin with initial speed vo along the rod directed upward. Note that this is similar to problem 4) but with the rod at an arbitrary angle to the z axis instead of perpendicular to the z axis. Z y a) Find the equations of motion for the bead as seen by an observer co-rotating with the rod. b) Find initial speed vo if the bead just reaches the end of the rod. c) Find the magnitude of the normal force on the bead at the instant it reaches the end of the rod.