The door will close automatically using torsional springs mounted on the hinges. If the torque on each hinge is M = k(theta), where theta is measured in radians, determine the required torsional stiffness k so that the door will close (theta = 0) with an angular velocity w = 2.4 rad/s when it is released from rest at theta = 90 degrees . For the calculation, treat the door as a thin plate having a mass of 82 kg.