Momentum (Years 10–11) — Science

Momentum p = mv, its conservation in collisions, impulse as Ft, and how these ideas make cars safer.

A tennis ball and a lorry can travel at the same speed, yet you would happily catch the ball and never step in front of the lorry. The difference is momentum — a measure of how much motion an object carries, combining both its mass and its velocity. Momentum explains why heavy, fast things are so hard to stop, and it is one of physics' great conservation laws.

Why this matters Conservation of momentum lets us predict the outcome of any collision or explosion without knowing the messy forces during the impact. It underpins rocket propulsion, snooker, car-crash safety design and particle physics. In the exam it delivers reliable calculation marks.

Calculating momentum

Momentum is defined by a simple product:

p = m v — momentum (kg m/s) = mass (kg) × velocity (m/s)
Momentum is a vector: it has direction. Moving right is positive, moving left is negative, which matters when objects collide head-on.

Quantity	Symbol	Unit
Momentum	p	kg m/s
Mass	m	kg
Velocity	v	m/s

They stick together: total momentum is the same before and after (6 kg m/s).

Conservation of momentum

The law of conservation of momentum states that, provided no external force acts, the total momentum before a collision equals the total momentum after:

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
In the figure, a 2 kg trolley at 3 m/s hits a stationary 1 kg trolley and they stick. Total momentum before = (2 × 3) + (1 × 0) = 6 kg m/s. After, the combined 3 kg mass moves at v, so 3v = 6 giving v = 2 m/s.

Impulse and safety

Newton's second law can be written in terms of momentum: a force acting for a time causes a change of momentum. This product Ft is called the impulse:

Ft = Δp = mv − mu — force × time = change in momentum
Rearranging, F = Δp ÷ t. For a given change in momentum, making the time longer makes the force smaller.
This is why cars have crumple zones, and why we use airbags and seatbelts: they extend the stopping time, so the force on the passenger is reduced.

A crumple zone lengthens the collision time, cutting the force on the occupants.

Worked example (3 marks). A 1000 kg car moving at 20 m/s is brought to rest in 4 s. Calculate the average braking force. Change in momentum Δp = mv − mu = (1000 × 0) − (1000 × 20) = −20 000 kg m/s [1]. F = Δp ÷ t = −20 000 ÷ 4 [1] = −5000 N (5000 N opposing motion) [1].

Common exam mistake: ignoring direction. Momentum is a vector, so give leftward velocities a negative sign in head-on collisions, or the totals will not balance.

Memory hook: "momentum = mass in motion" (p = mv). Longer impact time means smaller force — the whole point of a crumple zone. Exam technique: for Explain questions about safety, always link back to F = Δp ÷ t.