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A.2.16—Linear momentum conservation

Syllabus
First assessment 2025
Objective
—
Level
SL

Conserve Linear Momentum

Momentum

Linear momentum is

p⃗=mv⃗\vec p=m\vec v

It is a vector. For an isolated system, total momentum is conserved before and after an interaction.

Check the system

Momentum is conserved when the resultant external impulse on the chosen system is negligible. Internal forces can change individual momenta while leaving the vector total unchanged.

Use signs or components

Choose a positive direction and conserve momentum component-by-component. A negative final velocity means motion opposite to the chosen positive direction.

Common trap

Do not conserve kinetic energy automatically. Momentum conservation and kinetic-energy conservation are separate claims.

A.2.16 Exam Analysis

[ 1 ]

Cart X , of mass 2 kg , is moving at a speed of 3 m s−13 \mathrm{~m} \mathrm{~s}^{-1} to the right and collides on a horizontal track with cart Y of mass 1 kg.Y1 \mathrm{~kg} . Y is initially stationary.

The velocity of Y immediately after the collision is 4 m s−14 \mathrm{~m} \mathrm{~s}^{-1} to the right. What is the velocity of X immediately after the collision?

Retrieve the A.2 Forces and Momentum Model

Build the force model

Choose the system, draw a labelled free-body diagram, classify the interactions and resolve components. Apply Newton’s laws with the correct boundary: contact forces, field forces, friction, tension, buoyancy and restoring forces each have their own direction and conditions.

Track momentum

Use ec p=m ec v, ec J=\Delta ec p and momentum conservation only after checking external impulse. Distinguish elastic and inelastic collisions, explosions and energy transfer.

Track circular motion

The inward resultant provides ac=v2/r=ω2ra_c=v^2/r=\omega^2r. It may come from tension, gravity, normal, friction or a field force. Angular and linear descriptions are linked by v=ωr=2πr/Tv=\omega r=2\pi r/T.

Final checks

Ask: Which body is the system? Which forces are external? Is mass constant? Is acceleration uniform or radial? Is kinetic energy conserved, transferred or increased?