Use conservation of energy to determine the angular speed of the spool shown in the gure below after the 3.00-kg bucket has fallen 4.30 m, starting from rest. The light string attached to the bucket is wrapped around the spool and does not slip as it unwinds. rad/s 5.00 kg I : i l 3.00 kg A metal hoop lies on a horizontal table, free to rotate about a fixed vertical axis through its center while a constant tangential force applied to its edge exerts a torque of magnitude 1.75 x 10-2 N . m for 2.40 s. HINT (a) Calculate the magnitude of the hoop's change in angular momentum (in kg . m/s). kg . m2/s (b) Find the change in the hoop's angular speed (in rad/s) if its mass and radius are 0.290 kg and 0.140 m, respectively. rad/sA student holds a spinning bicycle wheel while sitting motionless on a stool that is free to rotate about a vertical axis through its center (see the gure below). The wheel spins with an angular speed of 19.1 rad/s and its initial angular momentum is directed up. The wheel's moment of inertia is 0.140 kg - m2 and the moment of inertia for the student plus stool is 2.60 kg - m2. (a) Find the student's nal angular speed (in rad/s) after he turns the wheel over so that it spins at the same speed but with its angular momentum directed down. rad/s (b) Will the student's final angular momentum be directed up or down? Up down A light rod of lengthl = 1.00 m rotates about an axis perpendicular to its length and passing through its center as in the figure below. Two particles of masses m1 = 4.55 kg and m2 = 3.00 kg are connected to the ends of the rod. (a) Neglecting the mass of the rod, what is the system's kinetic energy when its angular speed is 2.40 rad/s? J (b) Repeat the problem, assuming the mass of the rod is taken to be 2.05 kg. J