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School-college Physics Notes: Forces & motion 6.1 What is momentum?

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

Forces and Newton's Laws of Motion Part 6.1

What is the momentum of a moving object and how do we calculate it? (brief mention of impulse)

[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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This page contains some online questions for you to do.

Jot down your answers and check them against the worked out answers at the end of the page

6.1 What is the momentum of an object and how do we calculate it?

All moving objects have what we call momentum.  (sometimes denoted by a lower case p)

The faster an object moves, the bigger its momentum.

The bigger the mass of a moving object, the bigger its moment.

The momentum of an object is directly proportional to its velocity AND its mass.

Momentum (p) is a vector quantity, it has both size and direction

Therefore the equation for momentum is ...

momentum (kilogram metre per second) = mass (kilogram) × velocity (metre per second)

momentum p (kg m/s) = mass m (kg) x velocity v (m/s)

p = m × v  and, as ever in physics, watch the units!

 

You may also need to know about impulse

In physics, impulse is a concept that describes the effect of a force acting over a period of time on the motion of an object.

Impulse is defined as the change in momentum of an object and equals the product of the average force applied to an object and the time interval over which it acts.

Impulse = mΔv = Δmv = F x Δt

(units are Newton seconds  N·s  or kilogram metres per second kg·m/s)

Force = rate of change of momentum = F = Δmv / Δt

Example of simple calculations using the formula for momentum

Q1  A 120 kg sprinter is travelling at 9.0 m/s, what is the momentum of the runner?

Worked out ANSWERS to momentum calculations

 

Q2 If a 20 g bullet has a momentum of 8 kg m/s, calculate its velocity.

p = m × v,  v = p/m     (don't forget to change the g to kg!)

Worked out ANSWERS to momentum calculations

 

Q3 What mass must an object have if it has a momentum of 1.5 x 106 kg m/s and a velocity of 30 m/s?

p = m × v,  m = p/v

Worked out ANSWERS to momentum calculations

 

Q4 What is the velocity of a 1500 kg car travelling north with 30 000 kg m/s of momentum?

Worked out ANSWERS to 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: momentum defined, equation and calculations

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 comprehensive set of GCSE/IGCSE Physics revision notes on momentum, tailored to the major UK exam boards: AQA, Edexcel, OCR, WJEC, CCEA, and CIE. It includes definitions, equations, worked examples, common misconceptions, and exam tips.

Momentum: Core Concepts

Definition of momentum

  • Momentum is the quantity of motion an object has.
  • It depends on mass and velocity.
  • It is a vector quantity (has direction and magnitude).

Equation of momentum

momentum = mass x velocity

p = m x v Where:

  • ( p ) = momentum (kg·m/s)
  • ( m ) = mass (kg)
  • ( v ) = velocity (m/s)

Momentum Calculations and Examples

Example: Basic Momentum

A 2 kg ball rolls at 5 m/s.
p = 2 x 5 = 10 kg·m/s

Changes in Momentum and Force

Impulse Equation

Impulse = F x Δt = mΔv = (units are  N·s  or  kg·m/s)

  • Force = rate of change of momentum
  • Longer time = smaller force (used in safety features)
  • F = impulse / Δp

Example: Car Crash

A 1000 kg car slows from 20 m/s to 0 in 4 s.
Change in momentum: Δp = (1000 x 20) - 0 = 20,000
Force:
F = 20,000/4 = 5000 N

Typical Exam Board Syllabus content about momentum

Key Focus Areas
Conservation of momentum, changes in momentum, safety features
Momentum in collisions, impulse, vector nature
Momentum calculations, Newton’s laws, real-world applications
Momentum and force, impulse, car safety features
Conservation of momentum, impulse, exam-style calculations
Momentum, impulse, conservation, applications in collisions and explosions

Common Misconceptions about momentum

  • “Momentum is always positive” → False: direction matters!
  • “Momentum is lost in collisions” → Only if external forces act.
  • “Heavier objects always have more momentum” → Depends on velocity too.
  • “Impulse is force” → Impulse = force × time, not just force.

Student Tips on momentum questions

  • Always include units: kg·m/s.
  • Watch for direction: use signs (+/–) for vector calculations.
  • Use conservation of momentum in collision questions.
  • In impulse questions, identify time and change in velocity.
  • Practice multi-step problems: combine momentum with force and acceleration.

Keywords, phrases and learning objectives for momentum, definition, equation and calculations

Know the formula for momentum is p = mv (momentum = mass x velocity)

Know how to calculate the momentum of a moving object.

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INDEX physics notes: Conservation of momentum, elastic and non-elastic collisions, Newton's 2nd law calculations - problem solving
Worked out ANSWERS to the simple momentum calculation questions

Example of how to work out simple calculations using the formula for momentum

Q1  A 120 kg sprinter is travelling at 9.0 m/s, what is the momentum of the runner?

momentum p = m × v

p = 120 x 9 = 360 kg m/s

 

Q2 If a 20 g bullet has a momentum of 8 kg m/s, calculate its velocity.

p = m × v,  v = p/m     (don't forget to change the g to kg!)

velocity = 8/(20/1000) = 400 m/s

 

Q3 What mass must an object have if it has a momentum of 1.5 x 106 kg m/s and a velocity of 30 m/s?

p = m × v,  m = p/v

mass = 1.5 x 106/30 = 5.0 x 104 kg

 

Q4 What is the velocity of a 1500 kg car travelling north with 30 000 kg m/s of momentum?

p = m x v, v = p / m

v = 30 000 / 1500 = 20 m/s in a northerly direction

 

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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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