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9.0Momentum and Its Conservation

Overview: Momentum and Its Conservation: Impulse and Collisions — American System Physics Revision Notes & Topical Questions

5 min read 7 parts Lesson 2 of 5 Unit quiz

📚 American System Physics Hub / Topical Revision
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Lesson summary

Calculate momentum and impulse.Momentum is conserved in all collisions if the system is isolated.In 2D, conserve x and y components separately.Rockets work by conservation of momentum.Area under a force–time graph equals impulse.Recoil velocity is inversely proportional to mass.C…

  • Direction matters
  • A 2000 kg truck at 10 m/s hits a stationary 1000 kg car and they stick. Final speed?
  • A 0.15 kg ball goes from 20 m/s to −20 m/s. Impulse?
  • Momentum (p)
  • Impulse–momentum theorem
  • Closed, isolated system

Part 1 of 7Key ideas

1
Momentum is conserved in all collisions if the system is isolated.
2
In 2D, conserve x and y components separately.
3
Rockets work by conservation of momentum.
4
Area under a force–time graph equals impulse.
5
Recoil velocity is inversely proportional to mass.

Part 2 of 7Learning objectives

Learning objectives
Calculate momentum and impulse.
Apply conservation of momentum.
Distinguish collision types.

Part 3 of 7Essential knowledge

9.1 Momentum and Its Conservation: Impuls… concept map: Units, Direction matters, A 2000 kg truck at 10 m/s hit, A 0.15 kg ball goes from 20 m, Momentum (p)
Visual guide to the key ideas explained in this lesson.
A heavier object at the same speed has more momentum.
Two ice skaters pushing apart gain equal and opposite momenta.
In perfectly inelastic collisions, vf = (m1v1 + m2v2)/(m1 + m2).
Units
Units kg·m/s = N·s.
Direction matters
Direction matters use signs.

Part 4 of 7Process & sequence

1
Define the system and positive direction.
2
Write total momentum before the event.
3
Write total momentum after in terms of unknowns.
4
Set pbefore = pafter.
5
Solve and check kinetic energy if needed.

Conservation of momentumwrite these steps in this order; each step is a marking point.

  1. Define system
  2. p before
  3. p after
  4. Equate
  5. Solve v

Part 5 of 7Worked examples

1

A 2000 kg truck at 10 m/s hits a stationary 1000 kg car and they stick. Final speed?

  • 20 000 = 3000v, v = 6.7 m/s.
2A 0.15 kg ball goes from 20 m/s to −20 m/s. Impulse?
  • Δp = 0.15 × (−40) = −6.0 N·s.

Part 6 of 7Summary

What the symbols mean:
p = mv.
What the symbols mean: p = momentum (kg m s−1) · m = mass (kg) · v = velocity (m s−1)
What the symbols mean:
Impulse = FΔt = Δp.
What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)
Momentum is conserved in isolated systems.

Part 7 of 7Compare: Compare

Types of collisions
TypeMomentumKinetic energyExample
ElasticConservedConservedBilliard balls (approx.)
InelasticConservedLostCar crash
Perfectly inelasticConservedMaximum lossObjects stick together
ExplosionConserved (total 0 if from rest)IncreasesRecoil of gun
Safety and impulse
DeviceHow it works
Air bagIncreases Δt, reduces F
Crumple zoneIncreases stopping time
Bent knees landingLonger impact time
Follow-through in sportLonger Δt, larger Δp

Key terms

Command terms

Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Exam technique

Keywords the mark scheme looks for in this lesson

Keywords the mark scheme looks for in this lesson
Momentum (p) · Impulse · Impulse–momentum theorem · Closed, isolated system · Conservation of momentum · Elastic collision · Inelastic collision · Angular momentum
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary (e.g. “active site”, “concentration gradient”, “allele”), never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.

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