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
Angular velocity its dual to get a 3 dimensional pseudovector that is precisely the previous angular velocity vector formula_107: Substituting "ω" for "W" into the above velocity expression, and replacing matrix multiplication by an equivalent cross product: It can be seen that the velocity of a point in a rigid body can be divided into two terms – the velocity of a reference point fixed in the rigid body plus the cross product term involving the angular velocity of the particle with respect to the reference point. This angular velocity is the "spin" angular velocity of the rigid body as opposed to