Absolute angular momentum

From Glossary of Meteorology

absolute angular momentum

The angular momentum as measured in an absolute coordinate system; hence, the vector product of the position vector of a particle into the absolute momentum of the particle.

In the atmosphere the absolute angular momentum M per unit mass of air is equal to the sum of the angular momentum relative to the earth and the angular momentum due to the rotation of the earth:
where r is the distance from the center of the earth to the particle, u the relative eastward component of velocity, φ the latitude, and Ω the angular rotation rate of the earth. Since the earth's atmosphere is shallow, the variable r is often replaced by the constant a, defined as the radius of the earth. The absolute angular momentum per unit mass is then approximated by

See angular-momentum balance, conservation of angular momentum.