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Physics: Forces & motion 6.2 Conservation of momentum, elastic/inelastic collisions

GCSE level Physics exam revision notes on Forces & Motion Part 6

Forces and Newton's Laws of Motion Part 6.2

Explaining the Law of Conservation of Momentum & explaining the difference between elastic and inelastic collisions

[Author © Dr Phil Brown PhD: Doc Brown's physics exam revision notes suitable for students of UK IGCSE & GCSE level physics courses, ~ US grades 9-10 physics [forces-motion-6- updated Mar 28th 2026]

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INDEX physics notes: Conservation of momentum, elastic & non-elastic collisions, Newton's 2nd law calculations

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6.2 The Law of Conservation of Momentum

Here we will consider collisions between two objects in a closed system.

Here a closed system here means no other external forces affect the situation e.g. a collision between two objects - the event.

If an external force like friction is involved, total momentum cannot be conserved.

The total momentum of an event in a closed system is the same before and after the event (e.g. a collision between two objects).

This is called the 'Law of Conservation of Momentum' and you can use it do lots of calculations!

e.g. total momentum of two colliding objects = total moment of objects after collision

e.g. for two colliding objects, where p = momentum: p1 + p2 = p3 + p4

substituting m and v for the mass and velocity gives ...

m1v1 + m2v2 = m1v3 + m2v4

where v1 and v2 are the initial velocities and v3 and v4 the velocities after the collision,

(you are assuming there is no change in mass, i.e. no bits have flown off!)

and if two objects stick together' after the collision then: p1 + p2 = p3

substituting m and v for the mass and velocity gives ...

m1v1 + m2v2 = m3v3   (where m3 = m1 + m2)

where v1 and v2 are the initial velocities and v3 and m3 (m3 = m1 + m2) are the final velocity and mass after the collision.

In other words the large object formed by collision has the momentum equal to the two momentums of the colliding objects added together.

 

Momentum is conserved for both elastic and inelastic collisions

For a perfect elastic collision, no kinetic energy is lost - kinetic energy conserved.

In an elastic collision, the total energy in the kinetic energy stores of the colliding objects is the same as before and after the collision.

You will not have to solve problems for elastic collisions - the maths is too difficult for GCSE level physics, with two sets of equations, for momentum (mv) and kinetic energy (E = ½mv2), to solve e.g. for the resultant velocities!

 

For an inelastic collision, kinetic energy is not conserved - kinetic energy is lost in some form e.g. heat or sound energy to the surroundings.

In an inelastic collision, some of the moving objects kinetic energy stores are lost and transferred to other energy stores of the objects themselves or the environment.

This is because the atoms are bashed together increasing their potential energy store (compressed for a fraction of a second). They 'relax' to their normal state by losing the energy as heat  (thermal energy) or sound.

For inelastic collisions you can solve a variety of problems using the principle of 'conservation of momentum'.

 

See 6.4 for more complex momentum calculations

 Problem solving questions of more complex momentum calculations

 

INDEX physics notes: Conservation of momentum, elastic and non-elastic collisions, Newton's 2nd law calculations - problem solving

Key points force and motion: Law of Conservation of Momentum and elastic and inelastic collisions

Information sources for Doc Brown's key points: IGCSE-GCSE physics are based on textbooks & syllabus-specifications for students taking the UK AQA, Edexcel, OCR 21st Century Science, OCR Gateway science suite, WJEC, CCEA and CIE GCSE physics 9-1 level science examinations

A structured and exam-board-friendly set of GCSE/IGCSE Physics revision notes on the Law of Conservation of Momentum and the difference between elastic and inelastic collisions, tailored to AQA, Edexcel, OCR, WJEC, CCEA, and CIE specifications.

Law of Conservation of Momentum (p = mv)

Definition of the law of conservation of momentum

  • In a closed system (no external forces), the total momentum before an event equals the total momentum after.
  • Applies to collisions and explosions.

Momentum conservation equation

p1 + p2 = p3 + p4

substituting m and v for the mass and velocity gives ...

m1v1 + m2v2 = m1v3 + m2v4

if objects stick together: p1 + p2 = p3, therefore

m1v1 + m2v2 = m3v3   (where m3 = m1 + m2)

 

Key Points

  • Momentum is a vector: direction matters.
  • Conservation holds only if no external forces (e.g. friction, air resistance) act.
  • Used to calculate unknown velocities after collisions or explosions.

Elastic versus Inelastic Collisions

Feature Elastic Collision Inelastic Collision
Momentum Conserved Conserved
Kinetic Energy Conserved Not conserved
Objects after collision Bounce off each other May stick together or deform
Energy transfers Minimal (ideal case) Converted to heat, sound, deformation
Real-world examples Gas molecules, steel balls on ice Car crashes, clay hitting a wall

Perfectly Inelastic Collision

  • Objects stick together after impact.
  • Maximum loss of kinetic energy.

Worked Example: Inelastic Collision

Two trolleys collide:

  • Trolley A: 2 kg at 3 m/s → ( p = 6 )
  • Trolley B: 3 kg at 0 m/s → ( p = 0 )
  • Calculate the final velocity if they stick together

Total momentum before: p = (2 x 3) + (3 x 0) = (6) + (0) = (6)
If they stick together: mv = 6, total m = 3 + 2 = 5 kg

final p = mv, so v = p / m = 6 / 5 = 1.2 m/s

Note that both objects can be moving prior to collision.

Typical Exam Board Highlights about momentum and elastic/inelastic collisions

Focus Areas
Conservation of momentum, elastic/inelastic collisions, safety applications
Momentum calculations, energy transfers, vector nature
Newton’s laws, momentum in collisions and explosions
Impulse, car safety, momentum and force
Momentum conservation, collision types, exam-style problems
Momentum, impulse, collision analysis, energy changes

Common Misconceptions about momentum and elastic/inelastic collisions

  • “Momentum is always conserved” → Only in closed systems.
  • “Elastic collisions happen in real life” → Rare; most are inelastic.
  • “Momentum is scalar” → False: it’s a vector.
  • “Kinetic energy is always conserved” → Only in elastic collisions.

Student Tips about momentum and elastic/inelastic collisions

  • Use signs (+/–) for direction in momentum calculations.
  • Always state conservation laws in written answers.
  • Check units: momentum in kg·m/s, energy in J.
  • In collision questions, draw diagrams to visualise before/after.
  • Practice multi-step problems combining momentum and energy.

Keywords, phrases and learning objectives for elastic/inelastic collisions and momentum

Be able to explain and use the Law of Conservation of Momentum.

Know that momentum is conserved in both elastic collisions and inelastic collisions.

Be able to describe and explain the difference between elastic collisions, where kinetic energy is conserved and inelastic collisions in which kinetic energy is not conserved.

Revision notes on explaining the difference between elastic & non-elastic collisions based on the syllabus-specifications for students taking IGCSE/GCSE level physics examinations, summary revision notes and key points on explaining the difference between elastic & non-elastic collisions for students taking the AQA igcse/gcse physics notes on explaining the difference between elastic & non-elastic collisions, Edexcel gcse physics notes on explaining the difference between elastic & non-elastic collisions,  OCR 21st century GCSE physics notes on explaining the difference between elastic & non-elastic collisions, OCR gateway GCSE physics notes on explaining the difference between elastic & non-elastic collisions, WJEC gcse physics notes on explaining the difference between elastic & non-elastic collisions, CCEA gcse physics notes on explaining the difference between elastic & non-elastic collisions for students taking CIE Cambridge igcse physics, exam revision notes on explaining the difference between elastic & non-elastic collisions, useful for US grade 9-10 physics courses, importance of explaining the law of conservation of momentum in GCSE level physics, What you need to know about explaining the law of conservation of momentum for GCSE level physics, Explaining the use of explaining the law of conservation of momentum knowledge in GCSE level physics, Examples of explaining the law of conservation of momentum explained when studying GCSE level physics, What is significant about explaining the law of conservation of momentum, describing the theory of explaining the law of conservation of momentum when studying GCSE level physics, revision notes for explaining the law of conservation of momentum in exams, online exam help for explaining the law of conservation of momentum, revision notes about explaining the law of conservation of momentum, what do I need to learn about explaining the law of conservation of momentum for by GCSE physics exam? help to understand the explaining the law of conservation of momentum topic in preparation for GCSE physics exam question, how to prepare for questions involving explaining the law of conservation of momentum in a GCSE physics examination?

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INDEX physics notes: Conservation of momentum, elastic and non-elastic collisions, Newton's 2nd law calculations - problem solving

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