1. Collisions don’t just occur in one dimension, as we have been studying; they also occur in two or three dimensions.

2. In an isolated system momentum is conserved, Pf = P0
In an isolated system momentum is conserved, Pf = P0. Remember that momentum is a vector quantity; when a collision in two dimensions occurs the x and y components are conserved separately.

3. Ex A ball of mass m2 = kg is moving along the x-axis at a velocity of v02 = m/s and collides with a ball of mass m1 = kg and a velocity of v01 = m/s at an angle of 50.0° to the y-axis. After the collision this second ball moves with a velocity of vf2 = m/s at an angle of 35.0° to the x axis. Find the velocity of ball 1 after the collision.

4. A point that represents the average location for the total mass of a system is known as the center of mass. If two particles of mass m1 and m2 are located on the x-axis at the points x1 and x2, then the location of the center of mass xcm is found from this equation: xcm = m1 x1 + m2 x2 / m1 + m2

5. If the objects in the system are moving, the equation becomes: Δxcm = m1 Δx1 + m2 Δx2 / m1 + m2 If both sides of this equation are divided by Δt, the equation becomes: Δxcm/Δt = (m1 Δx1/Δt + m2 Δx2/Δt)/ m1 + m2

6. Δx/ Δ t is velocity, so the equation is now an equation for the velocity of the center of mass:   vcm = m1v1 + m2v2/m1 + m2

7. vcm = m1v1 + m2v2/m1 + m2 The right-side numerator is the total momentum of the system. We have seen that in an isolated system, the total linear momentum remains constant during a collision. Therefore, the above equation shows that the velocity of the center of mass remains constant during a collision also.