Momentum measures how much “motion” an object carries — its mass × velocity. The powerful idea in this topic is that in any collision or interaction, the total momentum stays the same, as long as no external resultant force acts. That single rule cracks most collision problems.
📘 What you need to know
Momentum:p = mv, measured in kg m s⁻¹.
Momentum is a vector — it has direction, so it can be positive or negative.
Conservation of momentum: total momentum before = total momentum after, unless an external resultant force acts.
Take the initial direction of motion as positive; anything moving the other way is negative.
Momentum is always conserved in a collision (kinetic energy may not be).
What momentum is
Any moving object with mass has momentum. It’s simply the product of its mass and velocity:
Linear momentump = mv
Because velocity is a vector, momentum is too — direction matters. Choose one direction as positive (usually the way an object starts moving); anything heading the opposite way then has a negative momentum.
Momentum is a vector: a ball rebounding at the same speed has the same magnitude of momentum but the opposite sign.
The principle of conservation of momentum
For a system with no external resultant force acting on it:
Conservation of momentum
total momentum before = total momentum after
This holds in every collision and interaction. When two objects collide, you add up the momentum of both before, add up the momentum of both after, and the two totals are equal — keeping careful track of signs.
Add up the momentum of everything before the collision and after — the two totals are equal.
🛠 Solving a collision
Choose a positive direction (usually the way the first object is moving).
Write the total momentum before — add each mv with the right sign.
Write the total momentum after the same way.
Set before = after and solve for the unknown.
A negative answer means that object moves in the negative direction.
Quick reference:p = mv (kg m s⁻¹) • momentum is a vector → mind the signs • Σpbefore = Σpafter when no external force acts.
Worked examples
WE 1
Tennis ball vs brick
A 60 g tennis ball moves at 75 m s⁻¹. A 3.0 kg brick moves at 1.5 m s⁻¹. Which has the greater momentum?
Ball: p = mv = 0.060 × 75= 4.5 kg m s⁻¹Brick: p = mv = 3.0 × 1.5= 4.5 kg m s⁻¹equal — both 4.5 kg m s⁻¹
WE 2
Trolleys that stick together
Trolley A (0.80 kg) moves at 3.0 m s⁻¹ and hits a stationary trolley B head-on. B has twice the mass of A. They stick together. Find their common velocity afterwards.
B has twice A’s mass → m_B = 1.60 kgBefore: p = (0.80 × 3.0) + 0= 2.4 kg m s⁻¹After: stuck together, mass = 2.40 kg2.4 = 2.40 × vv = 1.0 m s⁻¹
WE 3
A car hits a stationary van
A 990 kg car travelling at 10 m s⁻¹ collides with a stationary 4200 kg van. After the collision the car continues forward at 2.0 m s⁻¹. Find the velocity of the van.
Before: p = 990 × 10 + 0= 9900 kg m s⁻¹After: 990 × 2.0 + 4200 × v = 99001980 + 4200v = 9900v = 7920 ÷ 4200v ≈ 1.9 m s⁻¹ (forwards)
💡 Top tips
Pick a positive direction first and stick with it — every velocity then has a clear sign.
A stationary object has zero momentum, which simplifies the “before” total.
Stuck-together objects become one mass equal to the sum, moving at one velocity.
Draw a quick before/after sketch and label every mass and velocity.
A negative result is meaningful — it tells you the object moves backwards, not that you made an error.
⚠ Common mistakes
Ignoring direction. Momentum is a vector — a rebound flips its sign.
Forgetting to convert grams to kilograms before using p = mv.
Assuming kinetic energy is conserved. Momentum always is, but kinetic energy may not be.
Treating a stuck-together pair as two separate masses after the collision.
Conservation of momentum is the workhorse of this whole topic — it’s the same rule whether things bounce apart, stick together, or explode. Up next: Impulse & Momentum, which links a force acting over a time to the change in momentum it produces.
Need help with SL Forces & Momentum?
Get 1-on-1 help from an IB examiner who knows exactly what Paper 1 & 2 are looking for.
