A $4\mathrm{.}0-$mm$-$diameter playground merry$-$go$-$round, with a moment of inertia of $300$ kg$$m$2$kg$$m$2,$ is freely rotating with an angular velocity of $2\mathrm{.}0$ rad$/$srad$/$s$.$ Raj, whose mass is $80$ kgkg$,$ runs on the ground around the outer edge of the merry$-$go$-$round in the opposite direction to its rotation. Still moving, he jumps directly onto the rim of the merry$-$go$-$round, bringing it $($and himself$)$ to a halt.