In the last section, we showed that the momentum of a system of two particles is conserved when the system is isolated. For any collision of two particles, this result implies that the momentum in each of the directions x, y, and z is conserved.

An important subset of collisions takes place in a plane. The game of billiards is a familiar example involving multiple collisions of objects moving on a two-dimensional surface. For such two dimensional collisions, we obtain two component equations for conservation of momentum:

m₁v_1ix + m₂v_2ix = m₁v_1fx + m₂v_2fx             Eq. 3.13
m₁v_1iy + m₂v_2iy = m₁v_1fy + m₂v_2fy             Eq. 3.14

Let us consider a two-dimensional problem in which particle 1 of mass m₁ collides with particle 2 of mass m₂ , where particle 2 is initially at rest, as in Figure 23.