Center of mass rigid body, the gravity forces will not cause the body to rotate, which means the weight of the body can be considered to be concentrated at the center of mass. The linear and angular momentum of a collection of particles can be simplified by measuring the position and velocity of the particles relative to the center of mass. Let the system of particles "P", "i"=1...,"n" of masses "m" be located at the coordinates r with velocities v. Select a reference point R and compute the relative position and velocity vectors, The total linear and angular momentum vectors relative to the
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