$[0/1$ Points$]$

SERPSE$1033\mathrm{.}5\mathrm{.}0$P$\mathrm{.}017.$TX$.$

You are performing research on the development of optomechanical systems. In one of your experiments, a uniform circular disk of mass $m=21\mathrm{.}6g$ and radius $r=39\mathrm{.}0cm$ hangs vertically from a fixed, frictionless, horizontal hinge at a point on its circumference as shown below.

J

You aim a beam of electromagnetic radiation with intensity $9\mathrm{.}5M\frac{W}{m^2}$ so that it is incident on the disk in a direction perpendicular to its surface. The intensity of the radiation is uniform over the entire face of the disk. The disk is perfectly absorbing$,$ and the resulting radiation pressure makes the disk rotate about the hinge, as shown below.

$($i$)$

In order for the rotation of the disk to activate a switch in a circuit, the disk must rotate through $4\mathrm{.}00.$ Determine the angle $($in degrees$)$ through which the disk rotates.