A thin, light rod of length 2.0m is pivoted without friction at one end so that it may rotate in a vertical plane. Two small masses are rigidly attached to the rod:
• Mass m1=0.30kg is fixed at a distance 0.50m from the pivot.
• Mass m2=0.60kg is fixed at a distance 1.50m from the pivot, on the opposite side of the rod from m1 (that is, one mass lies above and the other below the horizontal line through the pivot when the rod is horizontal).
Initially the rod is held exactly horizontal and then released from rest. Neglect air resistance. A positive angular displacement corresponds to counter-clockwise rotation.
(a) Determine the rotational inertia of the system (rod plus both masses) about the pivot. Treat the rod as having negligible mass and each small mass as a point particle.
(b) Calculate the net torque about the pivot due to gravity at the instant the rod is released. Clearly indicate the sign of each torque term and the resulting net torque.
(c) Using your results from parts (a) and (b), compute the initial angular acceleration of the rod. State the direction of the resulting motion.
(d) Qualitatively describe how the magnitude of the net torque on the system will change as the rod begins to rotate away from the horizontal position. Justify your answer without additional calculations.