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
Distribution function (physics) Distribution function (physics) In molecular kinetic theory in physics, a particle's distribution function is a function of seven variables, formula_1, which gives the number of particles per unit volume in single-particle phase space. It is the number of particles per unit volume having approximately the velocity formula_2 near the position formula_3 and time formula_4. The usual normalization of the distribution function is where, "N" is the total number of particles, and "n" is the number density of particles – the number of particles per unit volume, or the density divided by the mass of individual particles. A distribution function may