Question

During the spin-dry cycle of a washing machine, the motor slows from 90 rad/s to 30 rad/s while the turning the drum through an angle of 180 radians. What is the magnitude of the angular acceleration of the motor?

Answer 1

Answer:

The magnitude of angular acceleration of the motor is $20\ rad/s^2$.          

Explanation:

Given that,

Initial angular velocity, $\omega_i=90\ rad/s$

Final angular velocity, $\omega_f=30\ rad/s$

Angular displacement, $\theta=180\ rad$

Let $\alpha$ is the magnitude of the angular acceleration of the motor. It can be calculated using third equation of rotational kinematics as :

$\omega_f^2-\omega_i^2=2\alpha \theta\\\\\alpha =\dfrac{\omega_f^2-\omega_i^2}{2\theta}\\\\\alpha =\dfrac{30^2-90^2}{2\times 180}\\\\\alpha =-20\ rad/s^2$

So, the magnitude of angular acceleration of the motor is $20\ rad/s^2$.