Final answer:
To calculate the time it took for the computer disk drive to complete its first revolution, the disclosed kinematic equations for rotational motion are applied, along with the given constraint of constant angular acceleration. By deriving the angular acceleration from the known time for two revolutions, it is possible to solve for the time taken for the first revolution, which is approximately 0.480 seconds.
Step-by-step explanation:
If a disk drive's angular acceleration is constant and it takes 0.690 seconds to complete the second revolution from rest, we can employ kinematic equations to determine the time taken for the first revolution. The total time taken for two revolutions equals the time for the first revolution plus the time for the second. For constant angular acceleration, the angular displacement (θ) is given by θ = ω0t + 1/2αt2, where ω0 is the initial angular velocity and α is the angular acceleration. As the drive starts from rest, ω0 = 0, and so the equation simplifies to θ = 1/2αt2. For two complete revolutions, the angular displacement is 4π radians. Therefore, 4π = 1/2α(0.6902). To find the time for the first revolution, 2π = 1/2αt2, we can rearrange to get t2 = 4π/α, and using the previously found α, we can calculate the time for the first revolution. After solving the equation for α and substituting back to find t, we find the time taken for the first revolution is approximately 0.480 seconds. This demonstrates the fundamental principles of rotational motion and allows for an understanding of how uniformly accelerated angular motion behaves.