Question

With the aid of a string, a gyroscope is accelerated from rest to 39 rad/s in 0.48 s. what is its angular acceleration in rad/s²? How many revolutions does it go through in the process?

Answer 1

The gyroscope's angular acceleration is 81.25 rad/s², and it goes through approximately 1.51 revolutions in the process.

Step-by-step explanation:

To calculate the angular acceleration of the gyroscope, we use the formula α = δω/δt, where α is the angular acceleration, δω is the change in angular velocity, and δt is the change in time. Substituting the given values:

α = (39 rad/s - 0 rad/s) / 0.48 s = 81.25 rad/s².

To find the number of revolutions, we need to integrate the angular velocity over the time of acceleration. The equation θ = 0.5 * α * t² gives the angle in radians. We can convert this to revolutions:

θ = 0.5 * 81.25 rad/s² * (0.48 s)² = 9.48 radians.

To convert radians to revolutions, we use the conversion factor 1 revolution = 2π radians:

Revolutions = 9.48 rad / (2π rad/rev) ≈ 1.51 revolutions.