Question

with the aid of a string, a gyroscope is accelerated from rest to 29 rad/s in 0.5 s.
a) what is its angular acceleration in rad/s^2
b) how many revolutions does it go though in the process

Answer 1

a) To find the angular acceleration, we can use the formula:

angular acceleration = (final angular velocity - initial angular velocity) / time

angular acceleration = (29 rad/s - 0 rad/s) / 0.5 s
angular acceleration = 58 rad/s^2

Therefore, the angular acceleration of the gyroscope is 58 rad/s^2.

b) To find how many revolutions the gyroscope goes through in the process, we can use the formula:

number of revolutions = final angular velocity / (2π)

number of revolutions = 29 rad/s / (2π)
number of revolutions ≈ 4.61 revolutions

Therefore, the gyroscope goes through approximately 4.61 revolutions in the process.