Momentum is a property of moving objects — AQA GCSE Combined Science
Test yourself on Momentum is a property of moving objects with AQA GCSE practice questions.
7 days Premium · Then free forever · No card, no charge
Momentum is a property of moving objects explained
Momentum is a vector property of a moving object, defined by the equation p = mv, where p is momentum in kilogram metres per second (kg m/s), m is mass in kilograms (kg) and v is velocity in metres per second (m/s).
Read the full explanation
Because velocity has direction, momentum also has direction. For example, a 1500 kg car travelling at 20 m/s east has a momentum of 30,000 kg m/s east. A stationary object has zero momentum. The equation shows that momentum increases with both mass and velocity. Note: Although the tier field states foundation and higher, all momentum content is strictly Higher Tier only (HT only) in the Combined Science specification.
momentum = mass × velocity
Momentum is a property of every moving object, calculated as momentum = mass × velocity. Mass is measured in kilograms (kg) and velocity in metres per second (m/s), so momentum has units kg m/s. Velocity is a vector, so momentum has direction as well as size. A 2 kg ball moving at 3 m/s has momentum 6 kg m/s in the direction of motion. If the ball moves in the opposite direction, its momentum is −6 kg m/s. A stationary object has zero momentum because its velocity is zero. Doubling the mass doubles the momentum if velocity is unchanged; doubling the velocity doubles the momentum if mass is unchanged. Momentum explains why a heavy lorry is harder to stop than a small car at the same speed, and why a fast-moving object is harder to stop than a slow one of the same mass.
p = m v
The equation p = mv defines momentum p as the product of mass m and velocity v. In this symbol equation, p is momentum in kilogram metres per second (kg m/s), m is mass in kilograms (kg) and v is velocity in metres per second (m/s). For example, a 1500 kg car travelling at 20 m/s has p = 1500 × 20 = 30,000 kg m/s. Because velocity is a vector, p is also a vector: reversing direction reverses the sign of p. A stationary object has v = 0, so p = 0. Note: Despite the tier field stating foundation and higher, this entire topic is assessed at Higher Tier only (HT only) in Combined Science.
momentum, p, in kilograms metre per second, kg m/s
Momentum is a property of moving objects, assessed at Higher Tier only. It is calculated using the equation p = m × v, where p is momentum, m is mass in kilograms, and v is velocity in metres per second. Because mass is measured in kg and velocity in m/s, the unit of momentum is the kilogram metre per second, kg m/s. For example, a 2 kg trolley moving at 3 m/s has a momentum of p = 2 × 3 = 6 kg m/s. Momentum is a vector quantity, meaning both its magnitude and direction are important. Consequently, an object moving in the opposite direction will have a negative momentum if the initial direction is defined as positive. Understanding this vector nature is crucial when analysing the motion of objects.
mass, m, in kilograms, kg
In momentum calculations (assessed at Higher Tier only), mass m must be measured in kilograms, kg. The kilogram is the SI base unit of mass, so it is the unit used in p = m × v. If a mass is given in grams, convert it by dividing by 1000; for example, 2500 g = 2.5 kg. If a mass is given in tonnes, multiply by 1000; for example, 0.4 tonnes = 400 kg. Using the wrong unit changes the numerical value of momentum and its unit, so unit consistency is essential. Mass is a scalar quantity, so it has magnitude but no direction, unlike velocity. Therefore, the direction of an object's momentum is determined entirely by its velocity, while the mass simply scales the magnitude of that momentum.
velocity, v, in metres per second, m/s
Velocity, v, is the speed of an object in a stated direction, measured in metres per second (m/s). It is a vector quantity, meaning a change of direction alters the velocity even if the speed remains constant. In the context of momentum (which is assessed at Higher Tier only), v represents the velocity of the moving object, and the equation p = m × v relies on this value. For example, a cyclist travelling at 6 m/s due north has a velocity of 6 m/s north. If she turns and rides at 6 m/s due south, her speed is unchanged but her velocity has reversed. When substituting into p = m × v, use the velocity value with its direction. A negative sign indicates motion in the opposite direction.
Your focus
- State and use the equation p = mv to calculate the momentum of a moving object (HT only).
- Explain why momentum is a vector and how direction affects its value (HT only).
- Compare the momentum of different objects based on their mass and velocity (HT only).
Show all 18 objectives
- Recall and use the equation momentum = mass × velocity to calculate momentum in kg m/s.
- Convert mass to kilograms and velocity to metres per second before substituting into p = m v.
- Describe momentum as a vector quantity and interpret positive and negative values in one-dimensional motion.
- Use the equation p = mv to calculate momentum, mass or velocity when the other two quantities are known (HT only).
- Apply correct units kg, m/s and kg m/s consistently in calculations (HT only).
- Interpret momentum as a vector and use signs to represent direction in one-dimensional problems (HT only).
- Identify p as the symbol for momentum.
- State kilograms metre per second (kg m/s) as the unit of momentum.
- Calculate momentum and report the result with the correct kg m/s unit.
- Identify m as the mass term in the momentum relationship.
- Convert a stated mass to kilograms before calculating momentum.
- Substitute mass in kilograms into p = mv with the correct unit.
- Identify v as the velocity term in the momentum relationship.
- Use metres per second (m/s) as the unit of velocity.
- Apply a signed velocity consistently when calculating momentum in one dimension.
Momentum is a property of moving objects exam tips
Marking Points
- State the defining equation p = mv and identify each symbol correctly (HT only).
- Use the correct unit, kg m/s, and recognise that momentum is a vector quantity (HT only).
- Calculate momentum by multiplying mass in kilograms by velocity in metres per second (HT only).
- Explain that a stationary object has zero momentum because its velocity is zero (HT only).
- State the equation momentum = mass × velocity and identify momentum, mass and velocity with their units kg m/s, kg and m/s.
- Substitute values correctly into p = m v, including converting grams to kilograms and km/h to m/s where needed.
- Recognise that velocity is a vector, so momentum has direction; use positive and negative values for opposite directions.
- Explain that a stationary object has zero momentum and that changing mass or velocity changes momentum proportionally.
- Calculate momentum for a moving object and interpret the result in terms of how difficult it is to stop.
- Identify each symbol in p = mv: p is momentum, m is mass and v is velocity, with units kg m/s, kg and m/s (HT only).
- Rearrange p = mv to find mass (m = p / v) or velocity (v = p / m) when momentum is known (HT only).
- Substitute numerical values into p = mv and evaluate correctly, including standard form (HT only).
- Interpret the vector nature of p, using signs to represent opposite directions in one-dimensional problems (HT only).
- States that momentum is calculated using p = m × v, with p as momentum, m as mass and v as velocity.
- Uses the correct unit, kg m/s, and recognises that it comes from multiplying kg by m/s.
- Substitutes mass in kilograms and velocity in metres per second into the equation without mixing units.
- Recognises that momentum is a vector quantity, so direction must be considered when assigning positive or negative values.
- Rearranges p = m × v correctly to find mass or velocity when momentum is known.
- States that mass is measured in kilograms, kg, in momentum calculations.
- Converts grams to kilograms by dividing by 1000, and tonnes to kilograms by multiplying by 1000.
- Recognises that mass is a scalar quantity and does not require a direction.
- Substitutes mass in kg into p = m × v to obtain momentum in kg m/s.
- States that velocity is speed in a stated direction, making it a vector quantity.
- Identifies the standard unit of velocity as metres per second (m/s).
- Applies velocity, v, correctly in the Higher Tier momentum equation p = m × v.
- Recognises that changing direction changes velocity, even at a constant speed.
- Interprets a negative velocity value as motion in the opposite direction to the chosen positive axis.
Examiner Tips
- 💡Write the equation p = mv, substitute values with units, then state the unit kg m/s in your answer (HT only).
- 💡Include the direction of momentum whenever the question gives velocities along a specific line (HT only).
- 💡Write the equation, substitute the numbers with units, then give the unit kg m/s in your answer.
- 💡Check that mass is in kg and velocity is in m/s before calculating; convert first if necessary.
- 💡For direction questions, choose a positive direction and give momentum a sign, explaining what the sign means.
- 💡Write the equation p = mv, then rearrange before substituting numbers to reduce errors (HT only).
- 💡Include units throughout your working and check that the final unit is kg m/s (HT only).
- 💡Always write the equation p = m × v before substituting values, then show the substitution with units.
- 💡When a question involves opposite directions, state which direction is positive and give momentum values with signs.
- 💡Underline the mass value and its unit in the question, then convert to kg if it is not already in kg.
- 💡Write the conversion explicitly, for example 2500 g ÷ 1000 = 2.5 kg, so the examiner can see your method.
- 💡Always check if a direction is specified in the question before using a velocity value in a momentum calculation.
- 💡If a calculation results in a negative velocity, explain that the negative sign indicates motion in the opposite direction.
Common Mistakes
- Using speed instead of velocity. Correction: Treat momentum as a vector and include its direction when required (HT only).
- Mixing units, such as using mass in grams. Correction: Always convert mass to kilograms before calculating momentum (HT only).
- Omitting the units of momentum. Correction: Memorise and append kg m/s to all final answers, as it is often required for a mark (HT only).
- Using grams instead of kilograms: convert mass to kg by dividing by 1000 before multiplying.
- Treating velocity as a scalar and ignoring direction: state the direction or use a sign for momentum in one-dimensional problems.
- Confusing momentum with kinetic energy: momentum is m v, while kinetic energy is ½ m v², so the values and units differ.
- Rearranging incorrectly, for example writing m = pv. Correction: Use inverse operations carefully to get m = p / v (HT only).
- Mixing units, such as using mass in grams with velocity in m/s. Correction: Convert all quantities to kg and m/s first (HT only).
- Forgetting that p is a vector. Correction: Include direction or a negative sign when velocities are in opposite directions (HT only).
- Using grams instead of kilograms for mass; the correction is to divide grams by 1000 before calculating momentum.
- Writing the unit as kg/m/s or kg m s; the correction is to write kg m/s, which is kilogram metre per second.
- Treating momentum as a scalar and ignoring direction; the correction is to assign positive and negative signs to opposite directions.
- Forgetting to convert grams to kilograms; the correction is to divide the mass in grams by 1000 before using p = m × v.
- Mixing kilograms and grams in the same calculation; the correction is to convert all masses to kilograms first.
- Treating mass as a vector and giving it a direction; the correction is to treat mass as a scalar and only give velocity or momentum a direction.
- Treating velocity and speed as identical: correct this by stating that velocity includes a specific direction, whereas speed is a scalar.
- Writing the unit as m/s²: correct this by using m/s for velocity, as m/s² is the unit for acceleration.
- Ignoring direction when comparing velocities: correct this by checking whether the direction of travel has changed before concluding the velocity is identical.