Conservation of Angular Momentum

The $80-kg$ man is holding two dumbbells while standing on a

turntable of negligible mass, which turns freely about a

vertical axis. When his arms are fully extended, the turn$-$

table is rotating with an angular velocity of $0\mathrm{.}5re\frac{v}{s}.$

Determine the angular 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 $68-kg$ solid

cylinder of $400-mm$ diameter. With his arms in the retracted

position, assume the man as an $80-kg$ solid cylinder of $450-mm$

diameter. Each dumbbell consists of two $5-kg$ spheres of

negligible size.