Momentum in two dimensions: add the arrows

5 minAS Level3.3.2

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can apply conservation of momentum when objects move in two dimensions, by adding momentum vectors, and find the speed and direction of the result.

Key to the symbols

The main symbols used in this lesson:

Symbol	Meaning
$p_A$	momentum of object A
$p_B$	momentum of object B
$\theta$	an angle

Why does the wreck go diagonally?

A car heading east and a car heading north collide at a junction and lock together. The wreck slides off north-east-ish.

Not east, not north: somewhere in between, closer to whichever car brought more momentum.

The rule hasn't changed: total momentum before = total momentum after. But momentum is a vector, so "total" now means vector sum: add the arrows tip to tail, exactly as you added forces in topic 1.

Worked example: The junction crash

Car A ( $1200\ \text{kg}$ ) travels east at $15\ \text{m s}^{-1}$ and car B ( $1600\ \text{kg}$ ) travels north at $10\ \text{m s}^{-1}$ . They collide and lock together. Find the velocity of the wreck just after the collision.

Have a go first?

Quick check

Multiple choiceQuestion 1 · Apply

CalculateQuestion 2 · Apply

Answer the 2 questions above to continue.