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.

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20 10 30 0, rev a, rad/s2