Final answer:
To find the magnitude of the average angular acceleration of the disk, subtract the final angular velocity from the initial angular velocity, and then divide by the time taken for the disk to come to rest. The magnitude of the average angular acceleration is approximately 1256.60 rad/s².
The correct option is not given.
Step-by-step explanation:
To find the average angular acceleration of the disk, we first need to calculate the initial angular velocity of the disk. We are given that the disk is spun at 4770 rpm while it is being read, which is the final angular velocity. We also know that the maximum angular velocity of the disk is 10,000 rpm. Therefore, the initial angular velocity is 10,000 rpm - 4770 rpm = 5230 rpm.
To convert the initial angular velocity to rad/s, we multiply it by 2π/60 to account for the conversion of minutes to seconds and radians to revolutions. So, the initial angular velocity is (5230 rpm)(2π/60) rad/s ≈ 546.77 rad/s.
Next, we use the equation of angular acceleration to calculate the average angular acceleration:
a = (ωf - ωi) / t,
where ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time taken for the disk to come to rest. Plugging in the values, we get:
a = (0 - 546.77 rad/s) / 0.435 s ≈ -1256.60 rad/s².
The magnitude of the average angular acceleration of the disk is approximately 1256.60 rad/s².
The correct option is not given.