Conservation of Angular Momentum

The $80-ky$ man is holding two dumbbells while standing on a turntable of nepligible mass, which turns freely about a vertical axis. When his arms are fully exiended, the furntabic is rotating with an angular velocity of $0\mathrm{.}5re\frac{v}{s}.$ Deternine the anyular velocity of the man when he retracts his arms to the position shown. When his arms are fully extended. approximate each arm as a uniform $6-kg$ rod having a length of $650mm.$ and his body as a $68kg$ solid cylinder of $400-mm$ diameter. With his arms in the retracted position, assume the man as an $801-kg$ solid eylinder of $450-mm$ diameter. Each dumbhell consists of two $5kg$ spheres of negligible size,