Center of mass reference point R are and If R is chosen as the center of mass these equations simplify to where "m" is the total mass of all the particles, p is the linear momentum, and L is the angular momentum The Law of Conservation of Momentum predicts that for any system not subjected to external forces the momentum of the system will remain constant, which means the center of mass will move with constant velocity. This applies for all systems with classical internal forces, including magnetic fields, electric fields, chemical reactions, and so on. More formally, this is true for any
Angular velocity arbitrary vector, from nondegeneracy of scalar product follows For angular velocity tensor maps positions to velocities, it is a vector field. In particular, this vector field is a Killing vector field belonging to an element of the Lie algebra so(3) of the 3-dimensional rotation group SO(3). This element of so(3) can also be regarded as the angular velocity vector. The same equations for the angular speed can be obtained reasoning over a rotating rigid body. Here is not assumed that the rigid body rotates around the origin. Instead, it can be supposed rotating around an arbitrary point that is moving