Momentum, explained with examples

By The STEM-Tutor team · Updated October 2026

Momentum is the quantity of motion an object has. It explains why a lorry is harder to stop than a bicycle, why guns recoil, and why airbags save lives. It is a Higher tier GCSE Physics topic.

What momentum is

momentum = mass × velocity, or p = mv

• p is momentum, in kilogram metres per second (kg m/s);
• m is mass, in kilograms (kg);
• v is velocity, in metres per second (m/s).

Momentum is a vector: it has a direction, the same as the velocity. When objects move in opposite directions, choose one direction as positive and give the other a negative velocity, and therefore negative momentum.

Example 1: calculating momentum

Find the momentum of a 1200 kg car travelling at 15 m/s.

• p = mv = 1200 × 15 = 18,000 kg m/s.

Example 2: comparing objects

Which has more momentum: a 70 kg runner at 8 m/s or a 0.15 kg cricket ball at 40 m/s?

• Runner: 70 × 8 = 560 kg m/s. Ball: 0.15 × 40 = 6 kg m/s.
• The runner has far more momentum, even though the ball is faster.

Conservation of momentum

In a closed system, where no external forces act, the total momentum before an event equals the total momentum after it:

total momentum before = total momentum after

This applies to collisions, where objects hit each other, and to explosions, where objects push apart. It is one of the most powerful laws in physics, because it holds however complicated the forces during the event are. You never need to know the forces during the collision itself, only the masses and velocities before and after.

Example 3: objects sticking together

A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley, and they stick together. Find their velocity afterwards.

• Momentum before: 2 × 3 + 1 × 0 = 6 kg m/s.
• After: (2 + 1)v = 6, so v = 2 m/s in the original direction.

Example 4: a moving target

A 1000 kg car at 20 m/s runs into the back of a 1500 kg car moving at 10 m/s in the same direction. They lock together. Find their speed.

• Before: 1000 × 20 + 1500 × 10 = 35,000 kg m/s.
• After: 2500v = 35,000, so v = 14 m/s.

Example 5: a head-on collision

A 3 kg ball moving at 4 m/s to the right hits a 1 kg ball moving at 6 m/s to the left. They stick together. Find their velocity.

• Take right as positive. Before: 3 × 4 + 1 × (−6) = 12 − 6 = 6 kg m/s.
• After: 4v = 6, so v = 1.5 m/s to the right.

Example 6: an explosion (recoil)

A 4 kg rifle fires a 0.01 kg bullet at 400 m/s. Find the recoil velocity of the rifle.

• Before firing, everything is at rest, so total momentum is 0.
• After: 0.01 × 400 + 4v = 0, so 4v = −4 and v = −1 m/s: 1 m/s backwards.

Momentum and kinetic energy

Momentum is always conserved in a closed system, but kinetic energy often is not. In Example 3, the kinetic energy before the collision is ½ × 2 × 3² = 9 J, and afterwards it is ½ × 3 × 2² = 6 J, as the diagram shows. The missing 3 J was transferred to the thermal energy store of the trolleys and to sound when they stuck together. Collisions where kinetic energy is also conserved are called elastic; they are rare in everyday life, though collisions between gas molecules come close. If a question asks about energy after a collision, use momentum to find the velocities first, then calculate the kinetic energy.

Force and the rate of change of momentum

Newton's second law can be written in terms of momentum:

F = Δp / Δt = mΔv / Δt

The force on an object equals the rate at which its momentum changes. For a given change in momentum, a longer time means a smaller force. This is the idea behind many safety features.

Example 7: stopping a ball

A 0.4 kg football moving at 15 m/s is stopped by a goalkeeper in 0.05 s. Find the average force.

• Δp = 0.4 × 15 = 6 kg m/s.
• F = 6/0.05 = 120 N. Pulling the hands back increases the stopping time and reduces the force on them.

Momentum and safety

In a crash, a passenger's momentum must drop to zero. Safety features cannot change that change in momentum, but they can make it happen over a longer time, which reduces the force:

• Crumple zones at the front and back of a car deform gradually, increasing the time of the collision.
• Seat belts stretch slightly, so the passenger stops over a longer time.
• Airbags inflate and then compress, slowing the head and chest gradually.
• Cycle helmets, gym mats and playground surfaces work in the same way.

Exam answers should use the full chain: the feature increases the time taken for the momentum to change, so the rate of change of momentum is smaller, so the force is smaller, so injuries are less severe.

Common mistakes

• Ignoring direction: momentum to the left must be negative if right is positive.
• Forgetting to add the masses when objects stick together.
• Using kinetic energy conservation instead of momentum in a sticky collision; kinetic energy is not conserved there.
• Saying safety features reduce the change in momentum; they increase the time.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Is momentum in Combined Science?

Momentum and its conservation are Higher tier in both Combined Science and separate Physics. Force as rate of change of momentum is separate Physics, Higher tier, on AQA.

Is p = mv on the equation sheet?

For GCSE exams in 2025, 2026 and 2027, an equations sheet is provided with the Physics and Combined Science papers, including the equations students previously had to recall. Check the arrangements for your exam year, and learn the equation anyway, because using it fluently saves time.

Key takeaways

• p = mv, a vector in kg m/s.
• In a closed system, total momentum before = total momentum after.
• Use negative velocities for the opposite direction.
• F = Δp/Δt: a longer time means a smaller force.
• Crumple zones, seat belts and airbags all increase the stopping time.

Related guides

• Newton's laws of motion
• Kinetic energy
• GCSE Physics forces