CIE A Level Physics (9702) 2019-2021

Revision Notes

4.2.1 Conservation of Momentum

The Principle of Conservation of Momentum

  • The principle of conservation of momentum is:
    • The total momentum of a system remains constant provided no external force acts on it
  • For example if two objects collide:

the total momentum before the collision = the total momentum after the collision

  • Remember momentum is a vector quantity. This allows oppositely-directed vectors to cancel out so the momentum of the system as a whole is zero
  • Momentum is always conserved over time

External and Internal Forces

  • External forces are forces that act on a structure from outside e.g. friction and weight
  • Internal forces are forces exchanged by the particles in the system e.g. tension in a string
  • Which forces are internal or external will depend on the system itself, as shown in the diagram below:

External and internal forces on a mass on a spring, downloadable AS & A Level Physics revision notes

Internal and external forces on a mass on a spring

  • You may also come across a system with no external forces being described as a ‘closed’ or ‘isolated’ system
  • These all still refer to a system that is not affected by external forces
  • For example, a swimmer diving from a boat:
    • The diver will move forward, and, to conserve momentum, the boat will move backwards
  • This is because the momentum beforehand was zero and no external forces are present to affect the motion of the diver or the boat

Collisions in One & Two Dimensions

One-dimensional momentum problems

  • Momentum (p) is equal to: p = m × v
  • Using the conversation of linear momentum, it is possible to calculate missing velocities and masses of components in the system. This is shown in the example below

Worked example - 1D momentum conservation, downloadable AS & A Level Physics revision notes


  • To find out whether a collision is elastic or inelastic, compare the kinetic energy before and after the collision
    • If the kinetic energy is conserved, it is an elastic collision
    • If the kinetic energy is not conserved, it is an inelastic collision
  • Elastic collisions are commonly those where objects colliding do not stick together and then move in opposite directions
  • Inelastic collision are where objects collide and stick together after the collision

Two-dimensional momentum problems

  • Since momentum is a vector, in 2D it can be split up into its x and y components
  • Review revision notes 1.3 Scalars & Vectors on how to resolve vectors

Worked example - 2D momentum conservation, downloadable AS & A Level Physics revision notes


Exam Tip

If an object is stationary or at rest, it’s velocity equals 0, therefore, the momentum and kinetic energy are also equal to 0.

When a collision occurs in which two objects are stuck together, treat the final object as a single object with a mass equal to the sum of the two individual objects.

In 2D problems, make sure you’re confident resolving vectors. Here is a small trick to remember which component is cosine or sine of the angle for a vector R:


Vector components, downloadable AS & A Level Physics revision notes

Resolving vectors with sine and cosine

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