Mass Continuity Equation

            The Continuity Equation, applied to the atmosphere, is simply a rendition of the principle of Conservation of Mass, stating that matter can neither be created nor destroyed. Yet implying that, again, for the atmosphere, the [constant] mass may be redistributed. However, air parcels expand and contract as they respond to pressure changes that may alter their volume in one of two ways: those that are associated with sounds waves and those which occur in association with hydrostatic pressure changes; granted that hydrostatic volume changes are only taken into account when the equation is expressed in (x, y, p) coordinates.

Conservation of Angular Momentum (Derivation of the Coriolis Force)

Angular Momentum takes into account the rotation of the object. Whereas, the conservation of angular momentum is a law of physics that states the angular momentum of a rotating object (with no outside force) remains constant regardless of changes within the system (i.e. Earth’s rotation Ω). This conservation of angular momentum will always be maintained as long as there is no net external torque acting on the object or on the system itself.

Example: Derive the Coriolis Force.