Question

An optical disk drive in your computer can spin a disk up to 10,000 rpm (about 1045 rad/s1045 rad/s ). If a particular disk is spun at 734.1 rad/s 734.1 rad/s while it is being read, and then is allowed to come to rest over 0.569 seconds0.569 seconds , what is the magnitude of the average angular acceleration of the disk

Answer 1

`1290.16\ \text{rad/s}^2`

Step-by-step explanation:

`\omega_i` = Initial angular velocity = 734.1 rad/s

`\omega_f` = Final angular velocity = 0

t = Time = 0.569 seconds

`\alpha` = Angular acceleration

From the kinematic equations of rotational motion we have

`\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=(\omega_f-\omega_i)/(t)\\\Rightarrow \alpha=(0-734.1)/(0.569)\\\Rightarrow \alpha=-1290.16\ \text{rad/s}^2`

The magnitude of the average angular acceleration of the disk is
`1290.16\ \text{rad/s}^2`.