Conservation of Linear Momentum for a System of Particles

In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.

The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When considering a system of particles in motion, the sum of external impulses is of great importance. If this sum equals to zero, the principle of linear impulse and momentum comes into play, elegantly illustrating the conservation of linear momentum. This principle finds widespread application in scenarios involving particle collisions or interactions.

Within impulse-momentum analysis, forces can be categorized as impulsive or non-impulsive. Impulsive forces, despite their brief duration, instigate significant momentum changes. A prime example is the forceful collision between a moving ball and a stationary one in billiards, triggering an instantaneous shift in momentum for both spheres.

Conversely, non-impulsive forces operate over extended periods, surpassing the collision timeframe. These forces, exemplified by friction between balls and the table, subtly influence momentum but pale in comparison to the transformative impact of collision forces.