An optical disk drive in your computer can spin a disk up to 10,000 rpm (about 1045 rad/s ). If a particular disk is spun at 411.5 rad/s while it is being read, and then is allowed to come to rest over 0.569 seconds , what is the magnitude of the average angular acceleration of the disk

Explanation:

The angular acceleration of an object in rotation is equal to the rate of change of its angular velocity.

Mathematically:

where

is the angular acceleration

is the initial angular velocity

is the final angular velocity

t is the time elapsed

For the optical disk in this problem, we have:

is the initial angular velocity

is the final angular velocity (because the disk comes to rest)

t = 0.569 s is the time elapsed

So, the angular acceleration is

And since we are only interested in the magnitude, then the magnitude is

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