What is linear momentum in the context of Cambridge International A Levels Physics?

In Cambridge International A Levels Physics, linear momentum is defined as the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction. Linear momentum is a fundamental concept in the study of dynamics, as it helps describe the motion of objects and how they interact with forces.

How is the principle of conservation of linear momentum applied in Physics?

The principle of conservation of linear momentum states that in a closed system with no external forces, the total linear momentum remains constant. This principle is crucial in solving problems involving collisions and explosions in Cambridge International A Levels Physics. For example, in a perfectly elastic collision, the total momentum before and after the collision is the same, allowing students to calculate unknown velocities or masses.

Why is linear momentum considered a vector quantity in dynamics?

Linear momentum is considered a vector quantity because it depends on both the magnitude and direction of an object's velocity. In dynamics, understanding the direction of momentum is essential for analyzing motion and predicting the outcomes of interactions, such as collisions. This vector nature is crucial for solving problems in Cambridge International A Levels Physics, where precise calculations are needed.

Can you explain the difference between elastic and inelastic collisions in terms of momentum conservation?

In Cambridge International A Levels Physics, elastic collisions are those in which both momentum and kinetic energy are conserved. In contrast, inelastic collisions conserve momentum but not kinetic energy, as some energy is transformed into other forms, such as heat or sound. Understanding these differences is key to analyzing collision problems and applying the conservation of momentum principle effectively.

How do external forces affect the conservation of linear momentum in a system?

External forces can alter the total linear momentum of a system. In Cambridge International A Levels Physics, the conservation of linear momentum only holds true in isolated systems where no external forces act. If external forces are present, they can change the momentum by accelerating or decelerating objects, thus affecting the system's total momentum. This concept is crucial for understanding real-world applications where external influences are often present.

Why is "Assuming KE always conserved" a common mistake in Linear momentum and its conservation?

Why it happens: Energy conservation lesson. How to avoid it: KE conserved ONLY in ELASTIC collisions. In inelastic, KE → heat/sound/deformation. Total energy (incl. heat) is always conserved, but KE alone is not. Source: 9702 Examiner Reports 2022-2024

Why is "Ignoring direction (signs) of momentum" a common mistake in Linear momentum and its conservation?

Why it happens: Treating as scalar. How to avoid it: Momentum is VECTOR. Use signs. Bullet forward → rifle backward gives net zero. Source: 9702 Examiner Reports 2022-2024

DynamicsCambridge International A Level Physics 9702

Linear momentum and its conservation

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Linear Momentum Conservation Study Notes — Cambridge International A Level Physics 9702 Dynamics (2025-2027 syllabus)

Conservation of momentum. Elastic vs inelastic collisions. Recoil and explosions.

What you’ll learn

Mapped to the Cambridge International A Level 9702 syllabus (2025-2027).

3.3.1 — State and apply conservation of momentum.
3.3.2 — Distinguish elastic and inelastic collisions.
3.3.3 — Solve 1D collision and recoil problems.

Conservation of momentum

Always true for closed system.

Statement. Total momentum of a system is constant if no external forces act.

Comes from Newton's 3rd law. Internal forces during collision are equal and opposite; they cancel out, leaving total momentum unchanged.

Always conserved in collisions (and explosions), provided no external impulse.

Method.

Choose positive direction.
Compute total momentum BEFORE.
Compute total momentum AFTER.
Set equal; solve.

Example. Trolley 1.5 kg at 4.0 m/s hits stationary 2.5 kg trolley; they stick.

Before: $1.5 \times 4.0 + 0 = 6.0$ kg·m/s.
After: $4.0 v$ .
$v = 1.5$ m/s.

Cambridge tip. State 'conservation of momentum' explicitly.

In an isolated collision total momentum is conserved; in a perfectly inelastic collision the bodies stick and some KE is lost.

Closed system.
$\sum p$ before = $\sum p$ after.
Always works (elastic + inelastic).

See the full worked example for linear momentum and its conservation →

Elastic vs inelastic

Whether KE conserved.

Elastic. BOTH momentum AND KE conserved.

Atomic-level collisions (gas molecules, billiard balls approximate).
Relative velocity REVERSES: $v_2 - v_1 = -(u_2 - u_1)$ .

Inelastic. Momentum conserved. KE NOT conserved (converted to heat, sound, deformation).

Most real-world collisions.

Perfectly inelastic. Bodies STICK together. Maximum KE loss.

Total energy IS conserved in all collisions (KE → other forms). But KE alone is conserved only in elastic.

1D elastic collision useful identity. $v_1 = \frac{m_1 - m_2}{m_1 + m_2}u_1 + \frac{2m_2}{m_1 + m_2}u_2$ $v_2 = \frac{2m_1}{m_1 + m_2}u_1 + \frac{m_2 - m_1}{m_1 + m_2}u_2$

Cambridge tip. Don't memorise above; derive via momentum + relative-velocity reversal.

Elastic: KE conserved.
Inelastic: KE lost.
Perfectly inelastic: stick together.

See the full worked example for linear momentum and its conservation →

Recoil and explosions

Initial $p$ = 0.

Recoil / explosion. Object initially at rest splits into parts moving in opposite directions.

Initial momentum = 0 → final momentum = 0. $m_1 v_1 + m_2 v_2 = 0 \Rightarrow v_2 = -\frac{m_1 v_1}{m_2}$

Lighter object moves FASTER to balance momentum.

Example. Bullet 0.02 kg at 400 m/s from 3.0 kg rifle.

$v_{\text{rifle}} = -\frac{0.02 \times 400}{3.0} \approx -2.7$ m/s.
Rifle recoils backward at $\sim 2.7$ m/s.

Cambridge tip. Note that KE is NOT conserved in an explosion — energy comes from chemical/internal source.

Initial $p = 0$ → final $p = 0$ .
Lighter object moves faster.
Explosions inelastic (KE comes from chemical energy).

See the full worked example for linear momentum and its conservation →

How it’s examined

Momentum conservation heavily tested. Most-tested: 1D collision (6-8 marks), elastic vs inelastic identification (5 marks), recoil (5-7 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/22 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

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Step-by-step worked examples — Linear momentum and its conservation

Step-by-step solutions to past-paper-style questions on linear momentum and its conservation, written exactly the way a tutor would explain them at the board.

1Inelastic collision (6 marks)
Extended• Adapted from 9702/22 May/Jun 2024• collision
Question
A trolley of mass 1.5 kg moving at 4.0 m/s collides with a stationary trolley of mass 2.5 kg. They stick. Find their common velocity. (6 marks)
Step-by-step solution
1. Step 1
  Conservation of momentum. $m_1 u_1 + m_2 u_2 = (m_1 + m_2) v$ .
2. Step 2
  Substitute.
  $1.5 \times 4.0 + 2.5 \times 0 = (1.5 + 2.5) v$
3. Step 3
  Solve.
  $6.0 = 4.0 v \Rightarrow v = 1.5 \text{ m/s}$
Answer
$v = 1.5$ m/s in original direction.
21D elastic collision (8 marks)
Extended• elastic
Question
Ball A (mass 0.5 kg, velocity 3.0 m/s) collides elastically with stationary ball B (mass 1.0 kg). Find velocities after collision. (8 marks)
Step-by-step solution
1. Step 1
  Conservation of momentum. $0.5 \times 3.0 = 0.5 v_A + 1.0 v_B$ .
2. Step 2
  Elastic: relative velocity of separation = relative velocity of approach. $v_B - v_A = 3.0 - 0 = 3.0$ .
3. Step 3
  Solve system. From (2): $v_B = v_A + 3.0$ . Sub into (1):
  $1.5 = 0.5 v_A + 1.0(v_A + 3.0) = 1.5 v_A + 3.0$
4. Step 4
  $v_A = -1.0$ m/s; $v_B = 2.0$ m/s.
Answer
$v_A = -1.0$ m/s (bounces back); $v_B = 2.0$ m/s (forward).
3Gun recoil (5 marks)
Extended• recoil
Question
A bullet of mass 0.020 kg leaves a 3.0 kg rifle at 400 m/s. Find the recoil velocity of the rifle. (5 marks)
Step-by-step solution
1. Step 1
  Initial momentum = 0. Both at rest before firing.
2. Step 2
  Conservation.
  $0 = m_b v_b + m_r v_r$
3. Step 3
  Solve.
  $v_r = -\dfrac{m_b v_b}{m_r} = -\dfrac{0.020 \times 400}{3.0} \approx -2.67 \text{ m/s}$
Answer
Rifle recoils at $\approx 2.7$ m/s in opposite direction.

Key Formulae — Linear momentum and its conservation

The formulae you need to memorise for linear momentum and its conservation on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Conservation of momentum
$\sum p_{\text{before}} = \sum p_{\text{after}}$
When to use
Closed system (no external impulse). Always works — true for elastic AND inelastic.
Elastic collision condition
$v_2 - v_1 = u_1 - u_2 \quad (\text{relative velocity reverses})$
When to use
For elastic collision in 1D — combined with momentum conservation gives two equations.

Key Definitions and Keywords — Linear momentum and its conservation

Definitions to memorise and the exact keywords mark schemes credit for linear momentum and its conservation answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Conservation of momentum
Examiner keyword
Total momentum of a CLOSED system (no external forces) is constant.
Elastic collision
Examiner keyword
Both momentum AND kinetic energy conserved. Bodies separate.
Inelastic collision
Examiner keyword
Momentum conserved; kinetic energy NOT conserved (some converted to heat, sound, deformation).
Perfectly inelastic collision
Maximum KE loss. Bodies STICK TOGETHER after collision.

Common Mistakes and Misconceptions — Linear momentum and its conservation

The traps other students keep falling into on linear momentum and its conservation questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Assuming KE always conserved
9702 Examiner Reports 2022-2024
Why it happens
Energy conservation lesson.
How to avoid it
KE conserved ONLY in ELASTIC collisions. In inelastic, KE → heat/sound/deformation. Total energy (incl. heat) is always conserved, but KE alone is not.
✕Ignoring direction (signs) of momentum
9702 Examiner Reports 2022-2024
Why it happens
Treating as scalar.
How to avoid it
Momentum is VECTOR. Use signs. Bullet forward → rifle backward gives net zero.

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