Platinum" A vertical support rod is xed at the center of a platform. A light string of length L is attached to the top of the support rod, and the other end of the string is attached to a sphere of mass m, as shown above. The platform rotates with an angular speed that can be varied. When the platform rotates with a constant angular speed a) (omega), the string makes an angle 6(theta) with the rod. Angler Annull' Wum Momentum :11 ' o 4' _ Graph .11. ' mm a (a) The platform rotates Wlth a constant angular speed. Which of the above graphs correctly shows the magnitude of the angular momentum of the platform as a function of time t about a vertical axis at the center of the support rod? Briey justify your answer. (b) The platform rotates with a constant angular speed. Is the net torque exerted on the platform about its center clockwise, counterclockwise, or zero? Explain your reasoning. (c) As the period of rotation becomes very small, what value does a gupproach? Without writing any equations or formulas, justify your answer. (d) A student derives an equation for the square of the period of revolution T of the sphere as a function of a? a? = (4a?) \"\"59 . Indicate whether this equation is consistent with your answer in part (c) and explain why. a (e) In a series of experimental trials, a group of students changes L and adjusts T to keep constant. They record L and T for each trial. If the students use the equation given in part (d), what quantities could they graph to yield a straight line whose slope could be used to nd the acceleration due to gravity, 3 ? (1) As the angular speed of the platform increases, does the period of revolution of the sphere increase, decrease, or stay the same? Briey explain your reasoning