Collisions in Two Dimensions and Center of Mass

• A collision in two dimensions obeys the same rules as a collision in one dimension:
  • Total momentum in each direction is always the same before and after the collision
  • Total kinetic energy is the same before and after an elastic collision
• Note that the kinetic energy is not calculated for each direction separately, but depends on the magnitude of the total velocity of each object.
• The center of mass of a system is the average position of all the objects, weighted by their masses:

                                          m1*x1 + m2*x2 + ...
                  center of mass   X  =  ----------------------
                                               m1 + m2 + ...
  
                                          m1*y1 + m2*y2 + ...
                  center of mass   Y  =  ----------------------
                                               m1 + m2 + ...
  

• The center of mass of a system behaves like the position of a big single object with the mass of the system: it obeys Newton's Laws.

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