A playground merry$-$go$-$round has a radius of $3\mathrm{.}0$ m and a rotational inertia of $600kg{m}^2.$ It is initially spinning at $0\mathrm{.}80ra\frac{d}{s}$ when a $20-kg$ child crawls from the center to the rim. When the child reaches the rim the angular velocity of the merry$-$go$-$round is:

$1\mathrm{.}10ra\frac{d}{s}$

$0\mathrm{.}80ra\frac{d}{s}$

$0\mathrm{.}73ra\frac{d}{s}$

$0\mathrm{.}89ra\frac{d}{s}$

$0\mathrm{.}62ra\frac{d}{s}$