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# Is angular momentum is a relative term? I have many books in which there are many questions in my book which clearly shows that angular velocity is always relative to any point but my coaching sir told me that it is not relative to any point. PLEASE HELP

Aman Bansal
592 Points
8 years ago

Dear James,

Angular momentum L equates with the cross product of the position (vector) r of a particle (or fluid parcel) and its absolute linear momentum p, equal to mv, the product of mass and velocity. Mathematically,

$\mathbf{L} = \mathbf{r} \times m \mathbf{v}$

## Definition

Absolute angular momentum sums the angular momentum of a particle or fluid parcel in a relative coordinate system and the angular momentum of that relative coordinate system.

Meteorologists typically express the three vector components of velocity v = (uvw) (eastward, northward, and upward). The magnitude of the absolute angular momentum L per unit mass m

$\left|\frac{\mathbf{L}}{m}\right| = M = u r \cos (\phi) + \Omega r^2 \cos^2(\phi)$

where

• M represents absolute angular momentum per unit mass of the fluid parcel (in m2s),
• r represents distance from the center of the earth to the fluid parcel (in m),
• u represents earth-relative eastward component of velocity of the fluid parcel (in ms),
• φ represents latitude (in rad), and
• Ω represents angular rate of Earth''s rotation (in rads , usually 2 π rad1 sidereal day ≈ 72.921150 × 10-6 rads ).

The first term represents the angular momentum of the parcel with respect to the surface of the earth, which depends strongly on weather. The second term represents the angular momentum of the earth itself at a particular latitude (essentially constant at least on non-geological timescales).

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Thanks

Aman Bansal