The angular speed of a motor increases from 600 rpm to 1200 rpm in 10 s. What is the angular acceleration of the motor

To find the angular acceleration of the motor, we can follow these steps:

Step 1: Convert the initial and final angular speeds from revolutions per minute (rpm) to radians per second (rad s^-1).
Recall the relation between angular speed in rpm ($N$) and angular speed in rad s^-1 ($\omega$):
$\omega =\frac{2\pi N}{60}$

Given:
Initial angular speed, $N_1=600\text{rpm}$
Final angular speed, $N_2=1200\text{rpm}$

Substituting the values to find initial angular velocity (${\omega }_1$):
${\omega }_1=\frac{2\pi \times 600}{60}=20\pi {\text{rad s}}^{-1}$

Substituting the values to find final angular velocity (${\omega }_2$):
${\omega }_2=\frac{2\pi \times 1200}{60}=40\pi {\text{rad s}}^{-1}$

Step 2: Calculate the angular acceleration ($\alpha$).
Angular acceleration is defined as the rate of change of angular velocity over time:
$\alpha =\frac{{\omega }_2-{\omega }_1}{t}$

Here, the time interval is $t=10\text{s}$.
Substituting the values of ${\omega }_1$, ${\omega }_2$, and $t$:
$\alpha =\frac{40\pi -20\pi }{10}$

$\alpha =\frac{20\pi }{10}=2\pi {\text{rad s}}^{-2}$

Therefore, the angular acceleration of the motor is 2π rad sec⁻².