Answer
The disk's angular velocity is 530 rpm.
Work Step by Step
We can find the moment of inertia of the disk.
$I = \frac{1}{2}MR^2$
$I = \frac{1}{2}(4.0~kg)(0.18~m)^2$
$I = 0.0648~kg~m^2$
We can find the torque exerted by the force.
$\tau = r\times F$
$\tau = (0.18~m)(5.0~N)$
$\tau = 0.90~N~m$
We can find the angular acceleration.
$\tau = I~\alpha$
$\alpha = \frac{\tau}{I}$
$\alpha = \frac{0.90~N~m}{0.0648~kg~m^2}$
$\alpha = 13.9~rad/s^2$
We can find the angular velocity after 4.0 seconds.
$\omega = \omega_0+\alpha ~t$
$\omega = 0+\alpha ~t$
$\omega = (13.9~rad/s^2)(4.0~s)$
$\omega = 55.6~rad/s$
We can convert the angular velocity to units of rpm.
$\omega = (55.6~rad/s)(\frac{1~rev}{2\pi~rad})(\frac{60~s}{1~min})$
$\omega = 530~rpm$
The disk's angular velocity is 530 rpm.
