A gizmo has a plumb-bob of mass m = 75 kg swinging in an arc of radius 40cm rotating circularly around a vertical axis. This is balanced balanced by a counter weight M = 100 kg via two pulleys and a rope of negligible mass suspended off the ground a height h = 30 cm. Due to friction the weight very slowly falls to the ground. Include on your scratch (show your work) an expression for the speed of the plumb-bob and it's moment of inertia. Calculate these if you can.

(a) what is the angle of the rope initially? deg from vertical

(b) What is the angle of the rope just before the counterweight hits the ground? angle? deg

(c) Make an expression for the velocity of the plumb-bob and it's moment of inertia when the counterweight is at height h?