A variable torque is applied to a rotating wheel at time t = 0 and causes the clockwise...

A variable torque is applied to a rotating wheel at time t = 0 and causes the clockwise angular acceleration to increase linearly with the clockwise angular displacement θ of the wheel during the next 30 revolutions. When the wheel has turned the additional 30 revolutions, its angular velocity is 90 rad/s. Determine its angular velocity ω₀ at the start of the interval at t = 0.