Momentum and Collisions

Quantity of Motion and Impulse

Momentum is an object's quantity of motion, defined as $p = mv$ (mass times velocity). It is a vector pointing in the direction of motion.

Impulse links force and momentum via $J = F \Delta t = \Delta p$. A longer contact time softens an impact; airbags or bent knees increase $\Delta t$ to reduce peak $F$ for the same momentum change.

Conservation and Collision Types

Conservation of momentum states that in an isolated system, total momentum stays constant. Total momentum before equals total momentum after.

Collisions differ by energy conservation:

Pitfall: Assuming kinetic energy is conserved in every collision. Momentum is conserved in all isolated collisions, but kinetic energy is conserved only in elastic ones.