Areal velocity equal to the magnitude of the cross product of vectors "AB" and "AC". This area can also be viewed as a vector with this magnitude, pointing in a direction perpendicular to the parallelogram; this vector is the cross product itself: Hence The areal velocity is this vector area divided by Δ"t" in the limit that Δ"t" becomes vanishingly small: But, formula_4 is the velocity vector formula_5 of the moving particle, so that On the other hand, the angular momentum of the particle is and hence the angular momentum equals 2"m" times the areal velocity. Conservation of areal velocity is a
Moment (physics) of "n" corresponds to a different moment: the 1st moment corresponds to "n" = 1; the 2nd moment to "n" = 2, etc. The 0th moment ("n" = 0) is sometimes called the "monopole moment"; the 1st moment ("n" = 1) is sometimes called the "dipole moment", and the 2nd moment ("n" = 2) is sometimes called the "quadrupole moment", especially in the context of electric charge distributions. Moments of mass: Assuming a density function that is finite and localized to a particular region, outside that region a 1/"r" potential may be expressed as a series of spherical harmonics: The