Unit 5: Momentum

Executive Summary

Momentum is conserved in every isolated system, which makes collisions and explosions solvable even when forces are unknown.

Momentum and impulse

$p = mv$; impulse $J = F\Delta t = \Delta p$. A force-time graph's area is the impulse. Airbags and crumple zones reduce injury by stretching the same Δp over a longer time, lowering the force.

Conservation

In an isolated system (no external net force), total momentum is constant: $m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$. Elastic collisions also conserve kinetic energy; perfectly inelastic collisions stick together (maximum energy loss). Explosions are "reverse collisions" — momentum conserved while objects fly apart.

Center of mass

The center of mass of an isolated system moves at constant velocity, even while parts collide.

Exam traps

Momentum is a VECTOR — direction matters, and 2-D collisions split into components. Kinetic energy is only conserved in elastic collisions; momentum is conserved in all isolated collisions. Impulse uses average force × contact time.