In a playground there is a small merry$-$go$-$round of radius $1\mathrm{.}62$ m and mass $159$ kg$.$ The radius of gyration is $0\mathrm{.}987$ m$.$ A child of mass $46\mathrm{.}6$ kg runs at a speed of $3\mathrm{.}14$ m$/$s tangent to the rim of the merry$-$go$-$round while it is at rest, and then jumps on$.$ Find the angular velocity $($in radians$/$second$)$ of the merry$-$go$-$round and child together. Neglect friction.