Momentum
Momentum as mass × velocity, impulse, and conservation of momentum in collisions.
Review these first
Learning objectives
What you need to be able to do
Teacher-mapped phrasing — check against the official Cambridge syllabus for exact wording.
- 1.6.1Define momentum as p = mv and impulse as Ft = Δ(mv).Supplement
- 1.6.2Apply the principle of conservation of momentum to one-dimensional collisions.Supplement
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Momentum and conservation of momentum
Momentum is the product of mass and velocity: p = mv, measured in kg m/s. Because velocity is a vector, momentum is a vector too, and direction matters.
Conservation of momentum
In a closed system, with no external resultant force, total momentum before an event equals total momentum after it. This applies to collisions and explosions alike.
The method for every momentum question is the same: work out the total momentum before (adding with signs, since direction matters), set it equal to the total momentum after, and solve for the unknown.
Momentum and Newton's laws
Momentum conservation is really a consequence of Newton's third law. In a collision, each object exerts an equal and opposite force on the other for the same time, so the change in momentum of one object is equal and opposite to the change in momentum of the other — the total stays the same.
Explosions
The same principle applies to an explosion, such as a gun firing a bullet or two skaters pushing apart. Before the explosion the total momentum is zero (nothing is moving); afterwards, the two momenta must still sum to zero, so the objects move apart with momenta equal in size but opposite in direction.
Think of it like this
Think of momentum like a shared "moving budget" between colliding objects. They can hand it to each other during the collision, but the total in the system never changes — nobody can create or destroy momentum, only pass it around.
Worked examples
Method, step by step
A 2.0 kg trolley moving at 3.0 m/s collides head-on with a stationary 1.0 kg trolley. After the collision they move off together. Calculate their common velocity.
- 1Momentum before = 2.0 × 3.0 + 1.0 × 0 = 6.0 kg m/s
- 2Momentum after = (2.0 + 1.0) × v
- 3Set equal: 6.0 = 3.0v
v = 2.0 m/s, in the same direction as the first trolley.
Common misconceptions
- Adding momenta without considering direction. Momentum moving in one direction should be treated as negative if the other object moves the opposite way.
- Confusing conservation of momentum with conservation of kinetic energy — momentum is always conserved in a collision, but kinetic energy is only conserved in a perfectly elastic collision, which is rare.
- Thinking a stationary object has no role in the momentum equation. A stationary object still has zero momentum, and that zero must be included in the total.
In the exam
- Define a positive direction at the start of the question and stick to it — this is where most sign errors happen.
- When two objects stick together after a collision, use their combined mass in the "after" side of the equation.