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An optical disk drive in your computer can spin a disk up to 10,000 rpm (about 1045 rad/s 1045 rad/s ). If a particular disk is spun at 440.9 rad/s 440.9 rad/s while it is being read, and then is allowed to come to rest over 0.569 seconds 0.569 seconds , what is the magnitude of the average angular acceleration of the disk?

Respuesta :

MechEngineer

Answer:

-775 rad/s^2

Explanation:

Knowing the initial and final angular speed is [tex]\omega_0 = 440.9 rad/s[/tex] and [tex]\omega = 0 rad/s[/tex], respectively. We can use the following formula for equation of motion to calculate the average angular acceleration in t = 0.569 seconds

[tex]\Delta \omega = \alpha t[/tex]

[tex]\omega - \omega_0 = \alpha t[/tex]

[tex]0 - 440.9 = \alpha 0.569[/tex]

[tex]\alpha = \frac{-440.9}{0.569} = -775 rad/s^2[/tex]

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