Flywheel Rotation: Calculate Total Angle After 48.7s

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The discussion revolves around calculating the total angle of a flywheel after 48.7 seconds, starting from rest with a constant angular acceleration of 1.33 rad/s² for 23.5 seconds. The initial angular velocity is calculated to be 31.26 rad/s after the acceleration phase. Participants are asked to help determine the angle unwound during both the acceleration and the constant speed phases. The initial calculation of 1522.1 rad is questioned as incorrect. The thread emphasizes the need for accurate calculations in angular motion.
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The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.33 rad/s2. It accelerates for 23.5 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 48.7 s after it begins rotating.
\omega = \omega _ o + \alpha t
\omega = 0 + 1.33(23.5)
\omega= 31.26
31.26 = \Delta \theta / \Delta t
Solving for \theta gave me 1522.1 rad
which wasn't right.. can someone please help me?
 
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Find the angle unwound during its acceleration.
Find the angle unwound during the rest of the time while its at a constant rotation speed.

Add.
 
I'm stupid :-p
Thanks
 

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