The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.27 radians?

After 24.3 seconds, the angular velocity is (24.3 s)*(1.27 radians/s^2) = 30.86 radians/s The angle through which it rotates in those first 24.3 seconds is 24.3 s times the mean velocity (15.43 radians/s), so it's 375.0 radians. In the next 44.2 seconds, it goes through 30.86*44.2 radians = 1364.0 radians, so the total angle covered in the 68.5 seconds is 1739 radians.

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