In inelastic collisions, momentum is conserved, meaning the total momentum before the collision equals the total momentum after the collision. The equation m_1\vec{v}_1 + m_2\vec{v}_2 = (m_1 + m_2)\vec{v}_f illustrates this principle, where m represents mass and v represents velocity. The vector nature of momentum indicates that both magnitude and direction must be considered in the calculations. Participants in the discussion referenced external resources to clarify concepts related to inelastic collisions. Understanding these principles is crucial for analyzing the behavior of colliding objects.