Conservation of momentum
Key ideas
In any collision or explosion with no outside forces, the total momentum before equals the total momentum after:
At Level 2 this is applied in one dimension — a straight line. The method never changes:
- Choose a positive direction and stick to it.
- Add up all momentum before (watch the signs).
- Set it equal to total momentum after, and solve.
A kg trolley moving at m s⁻¹ collides with a stationary kg trolley, and they stick together. Find their shared velocity.
Step 1 — Total momentum before
Step 2 — Set equal to momentum after
After the collision a combined kg mass moves at :
Two ice skaters, kg and kg, stand at rest and push apart. The kg skater moves off at m s⁻¹. Find the other skater's velocity.
Step 1 — Momentum before is zero
They start at rest, so .
Step 2 — Total momentum after must also be zero
Taking the kg skater's direction as positive:
Practice question
A kg bullet leaves a kg rifle at m s⁻¹. Find the rifle's recoil velocity.
Worked solution: , so m s⁻¹ — the rifle recoils backward at m s⁻¹.
Test yourself
Practice by grade
One question each at Achieved, Merit and Excellence. Have a go, then compare with the model answer.
A kg trolley moving at m s⁻¹ collides with a stationary kg trolley, and they stick together.
Calculate their common velocity immediately after the collision.
A kg bullet is fired at m s⁻¹ from a kg rifle that is initially at rest.
Calculate the recoil velocity of the rifle.
Two ice skaters, initially at rest, push off each other. The kg skater moves left at m s⁻¹.
Calculate the velocity of the kg skater, and explain, using physics principles, why the total momentum of the two skaters stays zero.