# 4.5.2 Conservation of Momentum

### The Principle of Conservation of Momentum

• The principle of conservation of linear momentum states:

The total momentum before a collision = the total momentum after a collision provided no external force acts

• Linear momentum is the momentum of an object that only moves in one dimension
• Momentum is a vector quantity
• This means oppositely-directed vectors can cancel each other out resulting in a net momentum of zero
• If after a collision an object starts to move in the opposite direction to which it was initially travelling, its velocity will now be negative
• Momentum, just like energy, is always conserved The conservation of momentum for two objects A and B colliding then moving apart

#### 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
• Forces which are internal or external will depend on the system itself, as shown in the diagram below:
• Systems with no external forces may be described as ‘closed’ or ‘isolated
• These are keywords that refer to a system that is not affected by external forces
• For example, a swimmer diving from a boat:
• The diver will move forwards, and, to conserve momentum, the boat will move backwards
• This is because the momentum beforehand was zero and no external forces were present to affect the motion of the diver or the boat

#### Worked Example

Trolley A of mass 0.80 kg collides head-on with stationary trolley B whilst travelling at
3.0 m s–1. Trolley B has twice the mass of trolley A. On impact, the trolleys stick together.

Using the conversation of momentum, calculate the common velocity of both trolleys after the collision.  ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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