Momentum

This guide covers subtopic 1.6 Momentum, from Topic 1, Motion, forces and energy, for Cambridge O Level Physics 5054, 2026–2028 series.

Where this fits in 5054

Momentum combines two ideas already covered — mass and velocity — into a single quantity, and gives a second, equivalent way to state Newton’s second law from Forces and Motion. It’s a compact topic (four outcomes), but a common source of collision and explosion questions, since conservation of momentum applies even in situations F = ma alone doesn’t easily handle.

Syllabus coverage

CAMBRIDGE O LEVEL PHYSICS 5054

• Define momentum as mass × velocity; recall and use p = mv (1.6)
• Define impulse as force × time for which the force acts; recall and use impulse = FΔt = Δ(mv) (1.6)
• Apply the principle of the conservation of momentum to solve simple problems in one dimension (1.6)
• Define resultant force as the change in momentum per unit time; recall and use resultant force = change in momentum ÷ time taken (1.6)

5054 is not tiered — every candidate covers all of the above.

Momentum

Momentum is defined as mass times velocity:

momentum = mass × velocity        p = mv

Momentum is a vector — it has the same direction as the velocity. This matters directly in the conservation calculations below, where a direction convention (positive one way, negative the other) is essential.

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

p = mv = 1200 × 15 = 18 000 kg·m/s

Impulse

Impulse is force multiplied by the time for which it acts, and is equal to the resulting change in momentum:

impulse = force × time = change in momentum        FΔt = Δ(mv)

This equation is the link between a force acting briefly and the momentum change it produces — the same momentum change can come from a large force acting briefly, or a smaller force acting for longer, which is the physics behind why airbags and crumple zones reduce injury: they extend the time over which a momentum change happens, reducing the force needed to produce it.

Conservation of momentum

The principle of conservation of momentum: in a closed system (no external forces), the total momentum before an event equals the total momentum after it. This applies to collisions and explosions alike, and 5054 requires only one-dimensional problems (all motion along a single line).

Worked example. A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley, and they stick together. Find their common velocity after the collision.

momentum before = momentum after
(2 × 3) + (1 × 0) = (2 + 1) × v
6 = 3v
v = 2 m/s

Worked example. A 5 kg object at rest explodes into two parts. A 2 kg piece moves off at 6 m/s in one direction. Find the velocity of the remaining 3 kg piece.

momentum before = 0 (object at rest)
momentum after = (2 × 6) + (3 × v) = 0
12 + 3v = 0
v = −4 m/s (i.e. 4 m/s in the opposite direction to the 2 kg piece)

The negative sign in the second example is doing real work: with momentum as a vector, the two pieces must move in opposite directions for the total to remain zero, and the sign convention is what shows that directly.

Resultant force as rate of change of momentum

Newton’s second law can also be written in terms of momentum rather than acceleration:

resultant force = change in momentum / time taken        F = Δp / Δt

This is equivalent to F = ma (from Forces and Motion) when mass is constant, since Δp = Δ(mv) = mΔv for constant m, giving F = mΔv/Δt = ma — the same law, written to also cover situations where mass itself changes (which 5054 does not require you to calculate, but is worth recognising as the reason two “different” force equations exist).

Common mistakes

• Forgetting momentum is a vector. In a collision or explosion problem, motion in each direction needs a consistent sign — this is exactly where the explosion worked example above goes wrong if the sign is dropped.
• Adding masses without adding momenta correctly when objects move in opposite directions before a collision. Assign a positive direction first, then treat momentum in the opposite direction as negative.
• Using impulse and momentum interchangeably. Impulse (FΔt) is a change in momentum, produced by a force acting over a time — it isn’t the momentum itself.
• Trying to apply conservation of momentum to a system with an external force acting on it (e.g. friction bringing a trolley to rest over a long time) — the principle assumes a closed system with no significant external force during the event.

Quick revision checklist

• p = mv, and that momentum is a vector
• Impulse: FΔt = Δ(mv), and why a longer collision time reduces the force for the same momentum change
• Conservation of momentum in one dimension, for both collisions and explosions, with a consistent sign convention
• F = Δp/Δt as an alternative statement of Newton’s second law

Related resources

• Forces and Motion — Newton’s second law in its F = ma form
• Kinematics and Motion Graphs — the velocity that momentum is built from
• Cambridge O Level Physics subject hub

Written against Cambridge O Level Physics 5054, 2026–2028 series. Always check the current syllabus for your examination year.