The angular acceleration of a shaft is defined by the relation = 0.5, where is expressed in rad/s2 and in rad/s.

The angular acceleration of a shaft is defined by the relation α = − 0.5ω, where α is expressed in rad/s2 and ω in rad/s. Knowing that at t = 0 the angular velocity of the shaft is 30 rad/s, determine

(a) The number of revolutions the shaft will execute before coming to rest,

(b) The time required for the shaft to come to rest,

(c) The time required for the angular velocity of the shaft to reduce to 2 percent of its initial value