The door will close automatically using torsional springs mounted on the hinges. If the to...

The door will close automatically using torsional springs mounted on the hinges. If the torque on each hinge is M = kθ, where θ is measured in radians, determine the required torsional stiffness k so that the door will close (θ = 0°) with an angular velocity ω = 2 rad/s when it is released from rest at θ = 90°. For the calculation, treat the door as a thin plate having a mass of 70 kg.