A.2.16—Linear momentum conservation

Momentum

Linear momentum is

$\vec p=m\vec v$

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.

How it is assessed

The evidence uses a collision and a rod–particle system to test vector momentum conservation and the motion of the combined system after interaction.

Command terms

Predict / Calculate

What earns marks

Choose the system and a positive direction, then set vector total momentum before equal to vector total momentum after when external impulse is negligible. In collisions, keep each mass–velocity product and sign explicit.

Watch for

Conserving speed rather than signed momentum, or ignoring a non-negligible external force on the chosen system.

Representative question

[Maximum number: 1]

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

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

$1 \mathrm{~m} \mathrm{~s}^{-1}$ to the right

$1 \mathrm{~m} \mathrm{~s}^{-1}$ to the left

$2 \mathrm{~m} \mathrm{~s}^{-1}$ to the right

$2 \mathrm{~m} \mathrm{~s}^{-1}$ to the left

A.2.16—Linear momentum conservation

Conserve Linear Momentum

A.2.16 Exam Analysis

Assessment in practice

Question 1