Question

A computer hard disk starts from rest, then speeds up with an angular acceleration of 190 rad/s2rad/s2 until it reaches its final angular speed of 7200 rpmrpm. mastering physics

Answer 1

962 rpm.

Step-by-step explanation:

given,

angular acceleration = 190 rad/s²

initial angular speed = 0 rad/s

final angular speed = 7200 rpm

=
`7200*(2\pi)/(60)`

=
`754\ rad/s`

we need to calculate the revolution of disk after 10 s.

time taken to reach the final angular velocity

using equation of angular motion

`\omega_f - \omega_i = \alpha t`

`754 - 0 =190* t`

t = 4 s

rotation of wheel in 4 s

`\theta =\omega_i t+  (1)/(2)\alpha t`

`\theta = (1)/(2)\alpha t^2`

`\theta = (1)/(2)* 190 * 4^2`

θ = 1520 rad

`\theta = (1520)/(2\pi)`

`\theta =242\ rev`

now, revolution of the disk in next 6 s

angular velocity is constant

`\omega_f = (\theta_f-\theta_i)/(t_f-t_i)`

`754 = (\theta_f-1520)/(10-4)`

θ_f = 6044 rad

θ_f =
`(6044)/(2\pi)`

revolution of the computer hard disk

θ_f = 962 rpm.

total revolution of the computer disk after 10 s is equal to 962 rpm.