A crane is made from a long, horizontal arm with mass m = 2.30 104 kg and length L = 54.0 m. The crane arm is supported by a vertical tower positioned halfway along the arm as shown in the figure below. The arm is free to rotate horizontally about the axis of the tower. L Mc m M L2 Part 1) The crane lifts a mass M = 1760 kg at the end of the arm on one side of the tower. To keep the crane balanced, a counterweight of mass 6640 kg is placed on the arm on the opposite side of the tower to mass M. How far from the tower should the counterweight be placed such that the centre of mass for the arm and both masses is directly over the tower? Mc = x = m Part 2) What is the moment of inertia of the crane about the axis of the tower? I = kg m Part 3) A net torque of magnitude = 5180 N m is applied to the crane. If the crane starts at rest, what is its angular velocity after t = 30.0 s? @= rad s-1 S