physics rotation and center mass

A giant swing at an amusement park consists of a 389-kg uniform arm 10.0 m long, with two seats of negligible mass connected at the lower end of the arm.(a) How far from the upper end is the center of mass of the arm? (b) The gravitational potential energy of the arm is the same as if all its mass were concentrated at the center of mass. If the arm is raised through a 41.7° angle, find the gravitational potential energy, where the zero level is taken to be 10.0 m below the axis. (c) The arm drops from rest from the position described in Part (b). Find the gravitational potential energy of the system when it reaches the vertical orientation. (d) Find the speed of the seats at the bottom of the swing. image.jpg

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