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 is formula_5, and the linear velocity is formula_6, so that formula_7. In the general case of a particle moving in the plane, the angular velocity is measured relative to a chosen center point, called the origin. The diagram shows the radius vector r from the origin "O" to the particle "P", with its polar coordinates formula_8. (All variables are functions of time "t".) The particle has linear velocity splitting as formula_9, with the radial component formula_10 parallel to the radius, and the cross-radial (or tangential or circular) component formula_11 perpendicular to the radius. When there is no radial component, the