A merry$-$go$-$round $($approximated by a flat disc$)$ of mass $42\mathrm{.}87$ kg and radius $0\mathrm{.}53$ meters is initially spinning with an angular velocity of $3\mathrm{.}4$ rad$/$s$.$ If a child pushes the merry go round several times and causes it to now spin at $9\mathrm{.}11$ rad$/$s over the course of $6\mathrm{.}53$ seconds, what is the net torque of the child's push?