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# A flywheel at rest is to reach an angular velocity of 24 rev/s in 8 seconds with constant angular acceleration.

The total angle turned through during this interval is

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Initial Angular Velocity, $\omega _{0}=0$

Final Angular Velocity, $\omega=24rev/s=48\pi \ rad/s$

Time, t = 8 s

$\\\alpha =\frac{\omega -\omega _{0}}{t}\\ \alpha =\frac{48\pi }{8}=6\pi \ rad\ s^{-2}$

$\\\omega^{2} -\omega _{0}^{2}=2\alpha \theta \\ \theta =\frac{\omega^{2} -\omega _{0}^{2}}{2\alpha }\\ \theta =\frac{(48\pi )^{2}}{2\times 6\pi }\\ \theta =192\pi$

i.e. 96 revolutions

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