A flywheel is required to start from rest, accelerate uniformly, reach a maximum angular speed ωmax, and then decelerate uniformly with the same magnitude of angular acceleration back to rest. The total angular displacement during the entire motion is 25 revolutions and the total time taken is 10s. The angular acceleration during the speeding-up phase has constant magnitude α, and the magnitude of angular deceleration during the slowing-down phase is also α.
(i) Show that the time taken to accelerate is equal to the time taken to decelerate.
(ii) Derive expressions for ωmax and α in terms of the total time and total angular displacement.
(iii) Calculate the numerical values of ωmax and α.