$(2$ pts$)$ A gymnast doing a front flip received an average torque of $523$ Nm during the $0\mathrm{.}31$ seconds during the takeoff phase $($i$.$e$.,$ the time during which the feet push on the ground$).$ If the gymnast started the flip from a stationary position, calculate $($a$)$ the angular impulse exerted on the gymnast during the takeoff phase, and $($b$)$ the gymnast's angular velocity immediately after the takeoff phase if her moment of inertia is $5k{g}^{**}{m}^2.$

$($a$)$ Angular impulse:

$($b$)$ Angular velocity: