Final answer:
In two-dimensional collisions, objects can scatter in different directions, necessitating the analysis of the collision as separate one-dimensional problems along perpendicular axes. Momentum is conserved overall, but individual objects might gain or lose momentum, and rotational effects are typically excluded from initial analyses by considering point masses.
Step-by-step explanation:
Crashes can be considered two separate collisions due to the different components involved in two-dimensional impacts. Unlike one-dimensional collisions where objects move along the same line, two-dimensional collisions involve objects scattering in various directions. This requires analyzing the collision as a pair of one-dimensional problems along perpendicular axes. For example, when billiard balls collide, they don't simply move back and forth along a line; they scatter to the sides, potentially causing the balls to rotate and transfer momentum in more than one direction.
To further understand this, consider two cars bumping into each other with negligible frictional forces. The total momentum of this system remains constant, where one car loses momentum as it slows down and the other gains momentum as it speeds up.
These dynamics are complicated by potential rotational effects which are typically excluded from the analysis by considering only point masses - structureless particles that cannot rotate or spin. This simplification allows for the focus on the translational components of the collision.