An electric fan with blades of length 0.4 m starts from rest. It...

Given, initial angular speed $\omega_0 = 0$
Final angular speed $\omega = 300 \text{ rpm}$
Time $t = 5 \text{ s}$
Radius of the circular path of the tip $R = 0.4 \text{ m}$

First, convert the final angular speed into $\text{rad s}^{-1}$:
$\omega = 300 \times \dfrac{2\pi}{60} \text{ rad s}^{-1} = 10\pi \text{ rad s}^{-1}$

Calculate the angular acceleration $\alpha$ using the first equation of rotational kinematics:
$\alpha = \dfrac{\omega - \omega_0}{t} = \dfrac{10\pi - 0}{5} = 2\pi \text{ rad s}^{-2}$

The tangential acceleration $a_t$ is related to angular acceleration by the formula:
$a_t = \alpha R$
$a_t = 2\pi \times 0.4 = 0.8\pi \text{ m s}^{-2}$

Answer: $0.8\pi \text{ m s}^{-2}$