Wiley Since the total energy and momentum of the system are conserved and their rest masses do not change, it is shown that the momentum of the colliding body is decided by the rest masses of the colliding bodies, total energy and the total momentum. Momentum is easy to deal with because there is only “one form” of momentum, (p=mv), but you do have to remember that momentum is a vector. The final x and y velocities components of the first ball can be calculated as:This equation is derived from the fact that the interaction between the two bodies is easily calculated along the contact angle, meaning the velocities of the objects can be calculated in one dimension by rotating the x and y axis to be parallel with the contact angle of the objects, and then rotated back to the original orientation to get the true x and y components of the velocitiesIn an angle-free representation, the changed velocities are computed using the centers Elastic collision of masses in a system with a moving frame of referenceCraver, William E. "Elastic Collisions." London. London. m_1 - Mass of object 1; \qquad m_2 - Mass of object 2; v_{1i} - velocity of object 1 before collision; v_{2i} - velocity of object 2 before collision; v_{1f} … Now the above formulas follow from solving a system of linear equations for With respect to the center of mass, both velocities are reversed by the collision: a heavy particle moves slowly toward the center of mass, and bounces back with the same low speed, and a light particle moves fast toward the center of mass, and bounces back with the same high speed. Since this is an isolated system, the total momentum of the two of mThere it is! Cambridge. Dividing each side of the top equation by each side of the bottom equation, and using That is, the relative velocity of one particle with respect to the other is reversed by the collision. p. 197. If kinetic energy is conserved in a collision, it is Figure 1 illustrates an elastic collision in which internal kinetic energy and momentum are conserved. Williamecraver.wix.com.

MacMillanLove, A. E. H. (1897) "Principles of Dynamics" p. 262. During the collision of small objects, kinetic energy is first converted to A useful special case of elastic collision is when the two bodies have equal mass, in which case they will simply exchange their momenta. Relativistic energy and momentum are expressed as follows:

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