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**Problem:**

A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 12 rev/s; 69 revolutions later, its angular speed is 33 rev/s. Calculate (a) the angular acceleration, (b) the time required to complete the 69 revolutions, (c) the time required to reach the 12 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches 12 rev/s angular speed.

**My work:**

[tex]part (a):

\omega ^{2} = \omega ^{2}_{0} + 2 \alpha (\vartheta - \vartheta _{0}) \Rightarrow \frac{2 * \pi * (33^{2} rev/s - 12^{2} rev/s)}{2 * 69 sec} = 43.03 rad/s^{2}[/tex]

[tex]part (b):

\vartheta =\vartheta \frac{1}{2} (\omega _{0} + \omega)* t \Rightarrow \frac{2 * 69 sec}{12 rev/s + 33 rev/s} = 3.07 sec[/tex]

[tex]part (c):

\omega ^{2} = \omega ^{2}_{0} + 2 \alpha (\vartheta - \vartheta _{0}) \Rightarrow \frac{(33^{2} rev/s - 12^{2} rev/s)}{2 * 69 sec} = 6.85 rev/s^{2};[/tex]

[tex]\omega = \omega _{0} + \alpha * t \Rightarrow \frac{12 rev/s}{6.85 rev/s^{2}} = 1.75 sec[/tex]

[tex]part (d):

\omega ^{2} = \omega ^{2}_{0} + 2 \alpha (\vartheta - \vartheta _{0}) \Rightarrow \frac{(12^{2} rev/s - 0^{2} rev/s)}{2 * 6.85 rev/s^{2}} = 10.5 rev[/tex]

I think I did it correctly, but I would appreciate if I could have my work checked since it's the first time I've done angular acceleration. Thank you.