Competitive divers pull their limbs in and curl up their bodies when they do flips. Just before entering the water, they fully extend their limbs to enter straight down. Explain the effect of both actions on their angular velocities. Also explain the effect on their angular momenta.

The law of conservation of angular momentum states that there will be no change in the angular momentum unless an external torque acts on the object. Angular momentum of a system is conserved as long as there is no external torque acting on the system. Mathematically,

$L=I\omega$

Here, L is the angular momentum, I is the moment of inertia, and $\omega$ is the angular velocity.

When the diver pulls their limb in and curl up their bodies during the flip, they gain angular momentum along the center of the mass of the body. The gravitational force that acts on the center of the mass exerts torque on the body and increase the angular velocity. This increased angular velocity increases the rotational kinetic energy and hence it increases the angular momentum.

Just before entering the water, the diver fully stretches its body. By doing so, the angular velocity of the body decreases and the body enters easily into water. With decreased angular velocity, the angular momentum also decreases.