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
Tensor product of modules "R" of "N". Then the tensor product of "M" and "N" over "R" can be defined as the coequalizer: together with the requirements If "S" is a subring of a ring "R", then formula_1 is the quotient group of formula_155 by the subgroup generated by formula_156, where formula_157 is the image of formula_158 under formula_159 In particular, any tensor product of "R"-modules can be constructed, if so desired, as a quotient of a tensor product of abelian groups by imposing the "R"-balanced product property. In the construction of the tensor product over a commutative ring "R", the "R"-module structure can