Unit 4 · 4.3 — Conservation of Linear Momentum

10 learning items · ~3% exam weight (unit share)

Everything to learn here

Concept: In a closed and isolated system where the net external force and impulse are zero, the total vector momentum of the system remains perfectly constant regardless of the nature of internal interactions.
Concept: During internal collisions and explosions, internal force pairs sum to zero by Newton's Third Law, leaving the total system momentum unchanged.
Concept: The velocity of the center of mass of an isolated system remains absolutely constant before, during, and after any internal collisions, explosions, or reorganizations.
Equation: $\sum p_{i} ni t ia l = \sum p_{f} ina l (Conservation of Linear Momentum)$
Equation: $m_{1} \cdot v 1 i + m_{2} \cdot v 2 i = m_{1} \cdot v 1 f + m_{2} \cdot v 2 f (Expanded momentum conservation)$
Vocabulary: Isolated System — A predefined system boundary where the net external force (and thus external impulse) is exactly zero, meaning no external impulse is delivered.
Skill: Argumentation — Justifying the choice of an isolated system boundary to validate the use of momentum conservation equations on the FRQ section.
Skill: Paragraph-Length Argument (FRQ Q4) — Formulating a logical argument using momentum conservation to predict the final trajectory of a two-body system after an off-center 2D collision, explicitly justifying the conservation in both the x and y axes.
Equation: $v f = \frac{m _{1} \cdot v 0}{m _{1} + m _{2}} c a l c u l a t es t h e f ina l v e l oc i t y w h e nam o v in g o bj ec t hi t s an d s t i c k s t o a s t a t i o na r y o bj ec t .$
Skill: Apply conservation of momentum to determine system velocities immediately before and after one-dimensional or two-dimensional collisions and explosions.

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