Angular Momentum and Angular Impulse Practice Test

A spacecraft with $I=80\ \text{kg·m}^2$ must reach $\omega=0.60\ \text{rad/s}$ from rest; during a short burn, external torques are negligible except for the thrusters, so $J=\Delta L=I\Delta\omega$. Assume the torque direction matches the desired rotation. Considering the described system, calculate the angular impulse applied to the spacecraft during the interval.

An ice skater rotates about a vertical axis with $I_i=3.0\ \text{kg·m}^2$ and $\omega_i=2.0\ \text{rad/s}$. The skater pulls in arms to $I_f=1.2\ \text{kg·m}^2$ with negligible external torque, so $L=I\omega$ is conserved. Considering the described system, what is the final angular velocity of the system after the skater pulls in arms?