16. Angular Momentum

Suppose a diver spins at 8 rad/s while falling with a moment of inertia about an axis through himself of 3 kg•m². What moment of inertia would the diver need to have to spin at 4 rad/s? 

BONUS:How could he accomplish this?

Two astronauts, both 80 kg, are connected in space by a light cable. When they are 10 m apart, they spin about their center of mass with 6 rad/s. Calculate the new angular speed they'll have if they pull on the rope to reduce their distance to 5 m. You may treat them as point masses, and assume they continue to spin around their center of mass.

Under what condition is the angular momentum $L$ of an object conserved?

In the context of conservation of angular momentum, consider the system shown in Figure 2, part e. For which of the following diagrams is the $L$ (angular momentum) of the system constant?