Question

The armature of a motor is accelerated uniformly from rest to a rotational velocity of 1800 rev/min in 10 seconds. the rotational acceleration of the motor is

Answer 1

The initial angular velocity of the motor is zero, while the final angular velocity is 1800 rev/min. Let's convert this into rad/s, keeping in mind that
$1 rev = 2 \pi rad$
$1 min = 60 s$
we have
$\omega_f = 1800 \frac{rev}{min} \cdot \frac{2 \pi rad/rev}{60 s/min}=188.4 rad/s$

And so now we can calculate the angular acceleration of the motor:
$\alpha = \frac{\omega_f - \omega_i }{t} = \frac{188.4 rad/s -0}{10 s}=18.8 rad/s^2$