Conservation of momentum — AQA GCSE Physics
Test yourself on Conservation of momentum with AQA GCSE practice questions.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge
Conservation of momentum explained
A closed system is one on which no external resultant force acts, so nothing can add momentum to it or take momentum away.
Read the full explanation
In such a system the total momentum of everything before an event equals the total momentum afterwards. The event can be a collision, an explosion or two objects pushing apart. To use the idea, add the momenta before, remembering signs for opposite directions, then set that total equal to the momenta after. If a 2 kg trolley at 3 m/s strikes a stationary 1 kg trolley and they stick, the total before is 6 kg m/s, so the combined 3 kg mass must move at 2 m/s afterwards. Friction and other external forces stop a real system being truly closed, which is why trolley experiments use a level track and low-friction wheels.
This is called conservation of momentum.
The rule that total momentum before an event equals total momentum after it, in a closed system, is called conservation of momentum. It applies whether the objects bounce apart, stick together or blow apart. An explosion is the clearest test: a firework or a recoiling rifle starts at rest, so the total momentum before is zero, and the total afterwards must also be zero. That can only happen if the two parts move in opposite directions with momenta of equal size, which is why a light bullet leaving at high speed is matched by a heavy rifle recoiling slowly. Conservation of momentum holds even when kinetic energy is not conserved. In a collision where the objects stick together, kinetic energy is transferred to thermal and sound stores, but the total momentum is unchanged.
Students should be able to use the concept of momentum as a model to: describe and explain examples of momentum in an event, such as a collision (physics only) complete calculations involving an event, such as the collision of two objects.
Using momentum as a model means writing total momentum before = total momentum after and filling in each term as mass × velocity. Choose a positive direction first. In a collision where objects join, the after side uses the combined mass. Where they bounce apart, one velocity is likely to be negative. A worked example: a 0.5 kg ball travelling at 4 m/s to the right hits a stationary 1.5 kg ball and stops dead. The total before is 0.5 × 4 = 2 kg m/s, so the second ball must carry 2 kg m/s afterwards, giving 2 ÷ 1.5 = 1.3 m/s to the right. Always finish by stating the direction as well as the number. If an object starts at rest its momentum is zero, but its mass still counts on the other side of the equation once it has been set moving. Check your work by recalculating the total momentum from your final velocities.
Your focus
- Define a closed system in terms of external forces and total momentum.
- Calculate the common velocity of two trolleys that stick together after a collision.
- Determine an unknown velocity after a collision by equating total momentum before and after, using signs for direction.
Show all 9 objectives
- State the principle of conservation of momentum and the condition under which it applies.
- Calculate the recoil velocity of a rifle from the mass and velocity of the bullet it fires.
- Explain why the two parts of an object that explodes from rest must move in opposite directions.
- Calculate the velocity of an object after a collision using conservation of momentum in a closed system.
- Describe what happens to the momentum of each object in a collision, and to the total.
- Interpret a negative answer for a velocity as motion in the opposite direction to the one chosen as positive.
Conservation of momentum exam tips
Marking Points
- one mark for defining a closed system as one with no external forces, or zero resultant external force, acting
- one mark for stating that the total momentum before the event equals the total momentum after it
- one mark for calculating the total momentum before the event, with signs for direction
- one mark for equating it to the total momentum afterwards and solving for the unknown velocity or mass
- one mark for naming the principle as conservation of momentum
- one mark for stating that it applies in a closed system, where no external resultant force acts
- one mark for setting the total momentum before an explosion from rest equal to zero
- one mark for showing that the two parts must have equal and opposite momenta afterwards
- one mark for stating or using total momentum before = total momentum after
- one mark for calculating each momentum as mass × velocity with consistent directions
- one mark for a correct rearrangement to find the unknown mass or velocity
- one mark for the answer with its unit and its direction stated
Examiner Tips
- 💡Draw a before and after sketch with a velocity arrow and a value on each object.
- 💡State your positive direction, then write any leftward velocity as a negative number.
- 💡For objects that join together, use the combined mass on the after side of the equation.
- 💡Name the principle in words before you use it; the phrase itself is often a marking point.
- 💡For explosions, write 'total momentum before = 0' as your first line.
- 💡Keep kinetic energy out of the argument unless the question specifically asks about it.
- 💡Set out a before and after table with mass and velocity for every object.
- 💡Keep full accuracy in the working and round only the final answer.
- 💡If an answer comes out negative, say what that means: the object moves the opposite way.
Common Mistakes
- ignoring direction, so a momentum to the left is added rather than subtracted
- assuming kinetic energy is conserved as well in every collision
- using mass alone instead of mass × velocity when adding the two objects
- adding the two velocities together instead of the two momenta
- saying momentum is conserved because energy is conserved
- forgetting to use the combined mass when two objects move off together
- ignoring direction, so a rebounding object's momentum is added rather than subtracted
- claiming an explosion breaks conservation of momentum because nothing was moving at the start
- using the mass of only one object after two have joined together
- ignoring the sign of a velocity that points the opposite way
- rounding an intermediate momentum so the final velocity is outside the allowed range
- quoting a bare speed when the question asked for a velocity, which needs a direction