$)$ Conservation of angular momentum: A uniform disk has a mass of $3\mathrm{.}7$ kg and a radius of $0\mathrm{.}40$ m$.$ The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at $30$ rpm$.$ A thin$-$walled hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for $0\mathrm{.}20$ s until it acquires the same final angular velocity as the turntable. What is the final angular momentum of the system?