Question

With the aid of a string, a gyroscope is accelerated from rest to 32 rad/s in 0.40 s.

(a) What is its angular acceleration in rad/s₂ ?
(b) How many revolutions does it go through in the process?

Answer 1

The angular acceleration is 80 rad/s² and the gyroscope goes through approximately 5.093 revolutions.

Step-by-step explanation:

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

angular acceleration = final angular velocity / time

Given that the gyroscope is accelerated from rest to 32 rad/s in 0.40 s, we can substitute the values:

angular acceleration = 32 rad/s / 0.40 s = 80 rad/s²

To find the number of revolutions, we can use the formula:

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

Converting 32 rad/s into revolutions, we get:

number of revolutions = 32 rad/s / (2π) = 16 / π revolutions ≈ 5.093 revolutions