Linear momentum ($\vec{p}$) is a measure of how much "oomph" an object has in its motion. It's the product of an object's mass ($m$) and its velocity ($\vec{v}$). $\vec{p} = m \vec{v}$

Impulse ($\vec{J}$) is the change in momentum of an object. It's also equal to the net force ($\vec{F}$) acting on an object multiplied by the time interval ($\Delta t$) over which the force acts. $\vec{J} = \vec{F} \Delta t$

A collision in which kinetic energy is conserved. Objects bounce off each other without losing energy to heat or deformation. Momentum is always conserved.

A collision in which kinetic energy is not conserved. Some kinetic energy is converted into other forms of energy, such as heat or sound. Objects may stick together after the collision.

A special type of inelastic collision where objects stick together after colliding. The final velocity of the combined mass can be calculated using conservation of momentum.

Elastic: Kinetic energy is conserved. Inelastic: Kinetic energy is not conserved, often converted to heat/sound.

Total momentum before a collision equals total momentum after a collision (conservation of momentum).

Total kinetic energy before an elastic collision equals total kinetic energy after the collision.

Total kinetic energy before an inelastic collision is greater than the total kinetic energy after the collision. Kinetic energy is lost to other forms of energy.

Positive momentum: motion to the right or upwards. Negative momentum: motion to the left or downwards.

1. Identify the system and ensure it's closed (no external forces). 2. Write down the initial momentum of all objects in the system. 3. Write down the final momentum of all objects in the system. 4. Set the total initial momentum equal to the total final momentum: $\vec{p}_{initial} = \vec{p}_{final}$. 5. Solve for the unknown quantities.