Problem: A circular disk initially rotating at 9 radians/second accelerates uniformly to 18 radians/second while rotating through an angular displacement of 18.5 radians. How long does the acceleration require and what is its angular acceleration?
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Solution: From the two angular velocities and the fact that the angular acceleration is constant we conclude that the average angular velocity is ( 9 radians/second + 18 radians/second)/2 = 13.5 radians/second.
At this rate the time required to turn through 18.5 radians will be ( 18.5 radians)/( 13.5 radians/second) = 1.370 radians/second.
From the two velocities we can also determine that the change in velocity is 9 radians/second. To accomplish this change in 1.370 seconds requires an acceleration of ( 9 radians/second) / ( 1.370 seconds) = 6.569 radians.