Add up all the individual momenta, remembering that momentum is a vector (direction matters!).

Define your system to identify if external forces are present and if momentum is conserved.

Elastic Collision: Kinetic energy is conserved; objects bounce off each other. | Inelastic Collision: Kinetic energy is not conserved; some energy is converted to other forms (e.g., heat, sound); objects may stick together.

Zero Net External Force: Total momentum of the system remains constant; momentum is conserved within the system. | Nonzero Net External Force: Momentum can be transferred between the system and its surroundings; momentum is not conserved within the system alone.

Momentum: A vector quantity; conserved in a closed system regardless of elasticity of collision. | Kinetic Energy: A scalar quantity; conserved only in elastic collisions.

Impulse: The change in momentum of an object. It is a force acting over a period of time. | Momentum: The mass of an object multiplied by its velocity. It is a measure of how difficult it is to stop a moving object.

1D Collisions: Momentum conservation applied along a single axis; simpler algebraic solutions. | 2D Collisions: Momentum conservation applied along two axes (x and y); requires vector decomposition and potentially more complex algebraic solutions.

The velocity of the system's center of mass.

$$v_{cm} = \frac{\sum \vec{p}}{\sum m}$$ where $\sum \vec{p}$ is the sum of all individual object momenta and $\sum m$ is the total mass of the system.

Sum of all individual momenta in a system.

Impulse ($j$) is the change in momentum ($\Delta p$) of a system: $$j = \Delta p$$

Any change in momentum for one object is balanced by an equal and opposite change in momentum for another object (Newton's Third Law).

Impulse is equal to the change in momentum: $$j = \Delta p$$