Question

part a
what is its angular acceleration?
express your answer with the appropriate units.
an electric fan goes from rest to 2200 rpm in 4.1 s.
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Explanation:

Step1: Convert initial and final angular - speeds to rad/s

The initial angular speed $\omega_0 = 0$ (since it starts from rest). The final angular speed $\omega$ in rad/s: First, convert 2200 rpm to rad/s. We know that 1 revolution = $2\pi$ radians and 1 minute = 60 s. So $\omega=2200\times\frac{2\pi}{60}\text{ rad/s}\approx2200\times\frac{2\times3.14}{60}\text{ rad/s}\approx230.38\text{ rad/s}$.

Step2: Use the angular - acceleration formula

The formula for angular acceleration $\alpha=\frac{\omega-\omega_0}{t}$. Substitute $\omega_0 = 0$, $\omega\approx230.38\text{ rad/s}$, and $t = 4.1\text{ s}$ into the formula. Then $\alpha=\frac{230.38 - 0}{4.1}\text{ rad/s}^2\approx56.2\text{ rad/s}^2$.

Answer:

$56.2\text{ rad/s}^2$