A fan is turned off, and its angular speed decreases from 10.0 rad/s to 6.3 rad/s in 5.0 s. what is the magnitude of the angular acceleration of the fan?

Angular acceleration can be defined as the change in the angular velocity over time.

Angular acceleration can be calculated using the following rule:

Angular acceleration = change in angular velocity / time

where:

change in angular acceleration = 6.3 - 10 = - 3.7 rad/sec

time = 5 sec

Substitute in the above equation to get the angular acceleration as follows:

angular acceleration = (-3.7) / 5 = - 0.74 rad/sec^2

Note that the negative sign is only an indication that the the speed is decreasing (deceleration)

Since the question is only asking for the magnitude, therefore, the answer would simply be 0.74 rad/sec^2