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Momentum and its conservation Cambridge International AS & A Level Physics revision

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In plain words

Momentum is mass times velocity: a measure of how hard something is to stop. Its great use is that the total never changes in a collision or an explosion, as long as nothing outside pushes on the objects. That lets you work out what happens next without knowing anything about the forces involved.

Three things to know

  1. Momentum p = mv. It is a vector, with units kg m/s (the same as N s).
  2. Conservation of momentum: the total momentum of a system stays the same, provided no resultant external force acts on it.
  3. This follows from Newton's third law. During a collision the two objects push on each other with equal and opposite forces for the same time, so one gains exactly the momentum the other loses.

Worked example

A 2.0 kg trolley moving at 3.0 m/s hits a stationary 1.0 kg trolley and they stick together. Find their speed afterwards.

  1. Momentum before = 2.0 × 3.0 + 0 = 6.0 kg m/s.
  2. Afterwards they move as one mass of 3.0 kg: 3.0 × v = 6.0.
  3. v = 2.0 m/s.

Tips and tricks

  • Choose a positive direction before you start. Anything moving the other way has negative momentum.
  • In an explosion from rest the total momentum is zero before, so it is zero after: the pieces fly apart with equal and opposite momentum.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Momentum and its conservation: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What is the momentum of a 3.0 kg mass moving at 4.0 m/s?
    • 0.75 kg m/s
    • 1.3 kg m/s
    • 7.0 kg m/s
    • 12 kg m/s (the answer)

    p = mv.

  2. What is needed for the total momentum of a system to be conserved?
    • The collision must be elastic.
    • No resultant external force acts on the system. (the answer)
    • The objects must stick together.
    • The objects must have equal masses.

    Internal forces come in equal and opposite pairs, so they can't change the total.

  3. A stationary object explodes into two pieces. What is their total momentum afterwards?
    • zero (the answer)
    • the momentum of the larger piece
    • twice the momentum of one piece
    • it depends on the energy released

    It was zero before, and momentum is conserved.

  4. Two trolleys of equal mass move towards each other at the same speed and stick together. What happens?
    • They stop. (the answer)
    • They move off at half the speed.
    • They bounce apart.
    • They move off at double the speed.

    Their momenta are equal and opposite, so the total is zero.

  5. Which is a unit of momentum?
    • N/s
    • N s (the answer)
    • kg m/s²
    • J s

    kg m/s is the same as N s.

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