Question

Your computer hard drive rotates at a rate of 10,000rpm. If I turn off the computer and it takes 17s for it to come to a complete stop, what is the angular acceleration of this motion? Please show your work

Answer 1

Initial angular frequency is given as

`f = 10,000 rpm`

now convert it into rounds per seconds

`f = 10000* (1)/(60) = 166.67 Hz`

now initial angular speed is given as

`\omega = 2 \pi f`

`\omega = 2\pi (166.67)`

`\omega = 1047.2 rad/s`

now finally it comes to rest in t = 17 s

now we can use kinematics equation to find the angular acceleration

`\omega_f - \omega_i = \alpha t`

`0 - 1047.2 = \alpha (17)`

`\alpha = - 61.6 rad/s^2`

so angular acceleration will be 61.6 rad/s^2