section_path: Rigid-body motion and rotation/Center of mass
section_name: Center of mass
paragraph_text: Center of mass
  
  Significant aspects of the motion of an extended body can be understood by imagining the mass of that body concentrated to a single point, known as the center of mass. The location of a body's center of mass depends upon how that body's material is distributed. For a collection of pointlike objects with masses m 1, …, m N {\displaystyle m_{1},\ldots,m_{N}} at positions r 1, …, r N {\displaystyle \mathbf {r} _{1},\ldots,\mathbf {r} _{N}}, the center of mass is located at R = ∑ i = 1 N m i r i M, {\displaystyle \mathbf {R} =\sum _{i=1}^{N}{\frac {m_{i}\mathbf {r} _{i}}{M}},} where M {\displaystyle M} is the total mass of the collection. In the absence of a net external force, the center of mass moves at a constant speed in a straight line. This applies, for example, to a collision between two bodies. If the total external force is not zero, then the center of mass changes velocity as though it were a point body of mass M {\displaystyle M}. This follows from the fact that the internal forces within the collection, the forces that the objects exert upon each other, occur in balanced pairs by Newton's third law. In a system of two bodies with one much more massive than the other, the center of mass will approximately coincide with the location of the more massive body.