GCSE Physics revision

Momentum is a property of moving objects

Momentum (HT only)

AQA 4.5.7.1

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AQA student objectives

Learning pathway

All · Most · Some

ALL 🎯

Define and calculate momentum using p = mv, measured in kilogram metres per second (kg m/s).

MOST 🎯🎯

Apply the specified scientific knowledge of momentum is a property of moving objects to a relevant example.

SOME 🎯🎯🎯

Analyse an unfamiliar example of momentum is a property of moving objects using the specified scientific ideas.

Revision summary

Key knowledge

Read on screen, then print for Cornell-style active revision.

Positive and Negative Momentum

If two identical cars travel in opposite directions at the same speed, they have equal magnitudes of momentum but opposite signs.
A positive momentum indicates motion in one chosen direction, whilst a negative momentum indicates motion in the opposite direction.
When calculating total momentum, it is essential to account for the signs, meaning a negative momentum must be subtracted from a positive one.

1. Positive and Negative MomentumAQA

Notes

If two identical cars travel in opposite directions at the same speed, they have equal magnitudes of momentum but opposite signs.
A positive momentum indicates motion in one chosen direction, whilst a negative momentum indicates motion in the opposite direction.
When calculating total momentum, it is essential to account for the signs, meaning a negative momentum must be subtracted from a positive one.

The Law of Conservation of Momentum

The law of conservation of momentum states that the total momentum of all objects in a system before an event equals the total momentum after that event.
This law applies to both collisions and explosions, provided no external forces act on the system.
Always state the law of conservation of momentum at the start of any momentum problem, as this guarantees marks even if the final answer is incorrect.

2. The Law of Conservation of MomentumAQA

Notes

The law of conservation of momentum states that the total momentum of all objects in a system before an event equals the total momentum after that event.
This law applies to both collisions and explosions, provided no external forces act on the system.
Always state the law of conservation of momentum at the start of any momentum problem, as this guarantees marks even if the final answer is incorrect.

Strategy for Solving Momentum Problems

Step 1: Always state the law of conservation of momentum at the beginning of your solution.
Step 2: Calculate the total momentum of the system either before or after the event, using whichever side you have enough information for.
Step 3: Use the total momentum and any known individual momenta to find the momentum of the unknown object.
Step 4: Use p = mv to calculate the missing mass or velocity of that object.

3. Strategy for Solving Momentum ProblemsAQA

Notes

Step 1: Always state the law of conservation of momentum at the beginning of your solution.
Step 2: Calculate the total momentum of the system either before or after the event, using whichever side you have enough information for.
Step 3: Use the total momentum and any known individual momenta to find the momentum of the unknown object.
Step 4: Use p = mv to calculate the missing mass or velocity of that object.

Explosion Problems

In an explosion, both objects are stationary before the event, so all velocities are zero and the total momentum before is always zero.
Because momentum is conserved, the total momentum after the explosion must also equal zero, meaning the two objects' momenta are equal in size but opposite in sign.
To find the velocity of one object after the explosion, calculate the momentum of the other using p = mv, then use the fact that the two momenta must sum to zero.
A negative velocity in the answer simply confirms that the object moves in the opposite direction to the other object.

4. Explosion ProblemsAQA

Notes

In an explosion, both objects are stationary before the event, so all velocities are zero and the total momentum before is always zero.
Because momentum is conserved, the total momentum after the explosion must also equal zero, meaning the two objects' momenta are equal in size but opposite in sign.
To find the velocity of one object after the explosion, calculate the momentum of the other using p = mv, then use the fact that the two momenta must sum to zero.
A negative velocity in the answer simply confirms that the object moves in the opposite direction to the other object.

Collision Problems: Objects That Stick Together

When two objects collide and stick together, their combined mass after the collision is the sum of their individual masses.
Calculate the momentum of each object separately using p = mv before adding them, as you must never add masses or velocities directly — only momenta.
The total momentum before the collision equals the total momentum after, so divide the total momentum by the combined mass to find the final velocity.
The sign of the final velocity tells you the direction of motion after the collision — a positive value means it moves in the same direction as the object with positive momentum.

5. Collision Problems: Objects That Stick TogetherAQA

Notes

When two objects collide and stick together, their combined mass after the collision is the sum of their individual masses.
Calculate the momentum of each object separately using p = mv before adding them, as you must never add masses or velocities directly — only momenta.
The total momentum before the collision equals the total momentum after, so divide the total momentum by the combined mass to find the final velocity.
The sign of the final velocity tells you the direction of motion after the collision — a positive value means it moves in the same direction as the object with positive momentum.

Collision Problems: Objects That Separate

When objects do not stick together after a collision, you need information about the velocity of one object after the collision to find the velocity of the other.
Calculate the total momentum before the collision, then calculate the known object's momentum after the collision using p = mv.
Subtract the known object's post-collision momentum from the total momentum to find the momentum of the unknown object.
Finally, rearrange p = mv to find the unknown object's velocity: v = p / m.

6. Collision Problems: Objects That SeparateAQA

Notes

When objects do not stick together after a collision, you need information about the velocity of one object after the collision to find the velocity of the other.
Calculate the total momentum before the collision, then calculate the known object's momentum after the collision using p = mv.
Subtract the known object's post-collision momentum from the total momentum to find the momentum of the unknown object.
Finally, rearrange p = mv to find the unknown object's velocity: v = p / m.

Worked Example: Explosion (Tennis Ball and Launcher)

Before the explosion, both objects are stationary, so total momentum = 0 kg m/s.
The momentum of the ball is calculated as p = 0.057 × 4 = 0.228 kg m/s, so the launcher's momentum must be -0.228 kg m/s.
Rearranging p = mv gives the launcher's velocity as v = -0.228 / 0.500 = -0.456 m/s, confirming it moves in the opposite direction to the ball.

7. Worked Example: Explosion (Tennis Ball and Launcher)AQA

Notes

Before the explosion, both objects are stationary, so total momentum = 0 kg m/s.
The momentum of the ball is calculated as p = 0.057 × 4 = 0.228 kg m/s, so the launcher's momentum must be -0.228 kg m/s.
Rearranging p = mv gives the launcher's velocity as v = -0.228 / 0.500 = -0.456 m/s, confirming it moves in the opposite direction to the ball.

Significant Figures in Momentum Answers

Always round your final answer to match the number of significant figures used for the velocities given in the question.
For example, if velocities in the question are given to two significant figures, your answer should also be given to two significant figures.
There is generally no need to give a momentum answer to more than three significant figures in GCSE problems.

8. Significant Figures in Momentum AnswersAQA

Notes

Always round your final answer to match the number of significant figures used for the velocities given in the question.
For example, if velocities in the question are given to two significant figures, your answer should also be given to two significant figures.
There is generally no need to give a momentum answer to more than three significant figures in GCSE problems.

Key Reminders for Momentum Problems

Never add masses or velocities together when finding total momentum — always calculate each object's momentum individually using p = mv first.
Always check the sign of your final velocity, as it tells you the direction of motion relative to your chosen positive direction.
The law of conservation of momentum applies to both collisions and explosions, making it a universal starting point for all momentum problems.

9. Key Reminders for Momentum ProblemsAQA

Notes

Never add masses or velocities together when finding total momentum — always calculate each object's momentum individually using p = mv first.
Always check the sign of your final velocity, as it tells you the direction of motion relative to your chosen positive direction.
The law of conservation of momentum applies to both collisions and explosions, making it a universal starting point for all momentum problems.