# Question #a03f5

Feb 14, 2017

$26. \overline{6} {\text{ rad"cdot"s}}^{-} 2$

#### Explanation:

Expression connecting angular velocity $\omega$ and rpm is

$\omega = 2 \pi f$
where $f$ is revolution per second.

In the given problem
Initial angular velocity ${\omega}_{i} = 2 \pi \times \frac{1200}{60} = 20 \pi {\text{ rad"cdot"s}}^{-} 1$
Final angular velocity ${\omega}_{f} = 2 \pi \times \frac{3000}{60} = 100 \pi {\text{ rad"cdot"s}}^{-} 1$
Change in angular velocity $\Delta \omega = \left(100 - 20\right) \pi = 80 \pi {\text{ rad"cdot"s}}^{-} 1$
Average Rotational or Average Angular acceleration $\overline{\alpha} \equiv \frac{\Delta \omega}{\Delta t}$
Therefore we have Average Angular acceleration $\overline{\alpha} = \frac{80 \pi}{3}$
$= 26. \overline{6} {\text{ rad"cdot"s}}^{-} 2$