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?

The magnitude of the angular acceleration of the motor is  .

Given data:

The initial angular speed of the motor is, .

The final angular speed of the motor is, .

The angle turned by the motor drum is, .

Here we can use the concept and fundamentals of rotational motion. We can apply the third rotational equation of motion to obtain the angular acceleration of the motor as,

Thus, we can conclude that the magnitude of the angular acceleration of the motor is  .

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The magnitude of angular acceleration of the motor is .          

Explanation:

Given that,

Initial angular velocity,

Final angular velocity,

Angular displacement,

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

So, the magnitude of angular acceleration of the motor is .