A thin rod of given mass m. is attached to an hinge so that it can swing vertically. The length of the rod is given as f and the rotational inertial of the rod about one end is I = 11162. The rod is held in place at a given angle 9 with respect to the horizontal by an guy wire which we represent as an ideal string which connects the far end of the bar to the wall as shown. guy wire gravity hinge Part (a) Draw a careful and properly labeled Free-Body Diagram (FBD) that shows all of the forces on the thin rod. Also, draw a careful and properly labeled Extended Free-Body Diagram (XFBD) for the thin rod. In your diagrams, the unknown hingeforce should be represented by two components, Hg and H 1:, corresponding to the horizontal and vertical components respectively. Part (b) Calculate the magnitudes of both Hy and H\". Express your answers in terms of the given parameters. Explain. Hint: for this part use a coordinate system that is lined up with the Hinge Force components (not tilted). Another hint: si11(90 6) = sing 6) = cos 9. Part (c) Suppose the guy wire is cut so that the rod is suddenly free to begin to rotate on the hinge. What is the magnitude of the acceleration of the center-ofmass point of the rod just at the instant after the wire is cut? Express your answer in term of the given parameters. Explain your work. Hint: for this part use a coordinate system that is tilted so that it is aligned with the instantaneous direction of acceleration. Part ((1) After the wire is cut, the rod swings down and collides ush with the wall. What is tum-f, the angular speed of the rod at the instant just before it hits the wall? Express your answer in term of the given parameters. Explain your work