Conservation of Momentum (AQA GCSE Combined Science: Trilogy): Revision Note

Conservation of Momentum

• The principle of conservation of momentum states that:

  In a closed system, the total momentum before an event is equal to the total momentum after the event

• A closed system means the energy within the system is constant and the absence of external forces (e.g. friction)

• In other words:

  The total momentum before a collision = The total momentum after a collision

• A system is a certain number of objects under consideration

  • This can be just one object or multiple objects

• Since momentum is a vector quantity, a system of objects moving in opposite directions (e.g. towards each other) at the same speed will have an overall momentum of 0 since they will cancel out

  • Momentum is always conserved over time

• The diagram below shows two masses m with velocity u and M at rest (ie. zero velocity)

The momentum of a system before and after a collision

• Before the collision:

  • The momentum is only of mass m which is moving

  • If the right is taken as the positive direction, the total momentum of the system is m × u

• After the collision:

  • Mass M also now has momentum

  • The velocity of m is now -v (since it is now travelling to the left) and the velocity of M is V

  • The total momentum is now the momentum of M + momentum of m

  • This is (M × V) + (m × -v) or (M × V) – (m × v)