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

Answer:

962 rpm.

Explanation:

given,

angular acceleration = 190 rad/s²

initial angular speed = 0 rad/s

final angular speed = 7200 rpm

                                 =$7200\times\dfrac{2\pi}{60}$

                                 =$754\ rad/s$

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

time taken to reach the final angular velocity

    using equation of angular motion

 $\omega_f - \omega_i = \alpha t$

 $754 - 0 =190\times t$

    t = 4 s

rotation of wheel in 4 s

$\theta =\omega_i t+ \dfrac{1}{2}\alpha t$

$\theta = \dfrac{1}{2}\alpha t^2$

$\theta = \dfrac{1}{2}\times 190 \times 4^2$

 θ = 1520 rad

 $\theta = \dfrac{1520}{2\pi}$

 $\theta =242\ rev$

now, revolution of the disk in next 6 s

angular velocity is constant

$\omega_f = \dfrac{\theta_f-\theta_i}{t_f-t_i}$

$754 = \dfrac{\theta_f-1520}{10-4}$

θ_f = 6044 rad

θ_f = $\dfrac{6044}{2\pi}$

revolution of the computer hard disk

θ_f =  962 rpm.

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