Angular momentum $H$ per elemental fluid mass $dm$ around some point is equal to the cross product $r_{x}u,$ where

$r$ is a position vector from that point to the elemental mass of fluid and $u$ is the velocity of that fluid element. Use

Reynolds Transport Theorem to write an integral form of the angular momentum balance:

a$)$ Write the integrals representing the partial derivative of the angular momentum in a control volume w$.$r$.$t

time and the flux of the angular momentum through the control surface.

b$)$ The total time derivative of the angular momentum obtained in part $($a$)$ is equal to the sum of the moments

of all forces about the same point, $(rxF).$