Question

an electric fan goes from rest to 2200 rpm in 4.1 s. part a what is its angular acceleration? express your answer with the appropriate units. α = value units incorrect; try again enter your answer using units of angular acceleration. previous answers request answer provide feedback

Explanation:

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

The initial angular speed $\omega_0 = 0$ rad/s (starts from rest). The final angular speed $\omega$ in rad/s: First, note that $1\ \text{rev}= 2\pi\ \text{rad}$ and $1\ \text{min}=60\ \text{s}$. So, $\omega=2200\ \text{rpm}=\frac{2200\times2\pi}{60}\ \text{rad/s}=\frac{220\pi}{3}\ \text{rad/s}$.

Step2: Use the formula for angular acceleration

The formula for angular acceleration is $\alpha=\frac{\omega - \omega_0}{t}$. Substitute $\omega=\frac{220\pi}{3}\ \text{rad/s}$, $\omega_0 = 0$ rad/s and $t = 4.1\ \text{s}$ into the formula. Then $\alpha=\frac{\frac{220\pi}{3}-0}{4.1}=\frac{220\pi}{3\times4.1}\ \text{rad/s}^2\approx56.6\ \text{rad/s}^2$.

Answer:

$\alpha\approx56.6\ \text{rad/s}^2$