The time taken by the gyroscope to come to rest is 51.85 seconds.
The initial rate of the gyroscope is 28 rad/s and the angular acceleration is 0.54 rad/s², it is required to stop the gyroscope.
So, we can use the this equation here,
W' = W + at
W' is the final rate of gyroscope,
W is the initial rate of gyroscope,
a is the angular acceleration,
t is the time taken by the gyroscope.
So, putting values,
0 = 28+(-0.54)t
t = 51.85 seconds.
So, it will take 51.85 seconds for the gyroscope to come to rest.
To know more about angular speed, visit,
https://brainly.com/question/6860269
#SPJ4