The door will close automatically using torsional springs mounted on the hinges. If the torque on each hinge is M=ktheta, where thetais measured in radians, determine the required torsional stiffness kso that the door will close (theta=0degrees)with an angular velocityw=2.5rad/swhen it is released from rest at theta=90degrees. For the calculation, treat the door as a thin plate having a mass of 90kg.