As steam is slowly injected into a turbine, the angular acceleration of the rotor is observed to increase linearly with the time t. Knowing that the rotor starts from rest at t = 0 and that after 10 s the rotor has completed 20 revolutions, write the equations of motion for the rotor and determine (a) the angular velocity at t = 20 s, (b) the time required for the rotor to complete its first 40 revolutions.