A solid disk of mass $M=0\mathrm{.}700kg$ and radius $R=0\mathrm{.}450m$ is suspended vertically and is free to rotate about its center without friction. A point object that has the same mass as the disk is placed at an angle ${}_i=15\mathrm{.}0$ clockwise from the top along the rim, causing the disk to rotate.

The acceleration due to gravity is $g=9\mathrm{.}80\frac{m}{s^2}.$

What is the angular speed ${}_f$ of the disk when the object is directly below the center of the disk?

${}_f=$

$ra\frac{d}{s}$