# 1.6.1 Momentum

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### Momentum Defined

• Momentum is defined by the equation:
`momentum  =  mass × velocity`

`p  =  m × v`

(where p stands for momentum)

Momentum is defined as the product of mass and velocity

• The units of momentum are kg m/s (the units of mass multiplied by the units of velocity)
• Momentum is a vector quantity – it has direction as well as magnitude
• This means that momentum can be negative as well as positive:
• If an object travelling to the right has positive momentum, an object travelling in the opposite direction (to the left) will have negative momentum

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### The Conservation of Momentum

• In the absence of external forces (such as friction), the total momentum of a system remains the same
• This means that in a collision, the sum of the momentums before the collision will be the same as the sum of momentums after the collision

Diagram showing the total momentum of a system before and after a collision

• In the above diagram the total momentum before and the total momentum after must be equal:
`m × u   =   M × V -  m × v`
• Note that because the red ball is travelling to the left after the collision, its momentum will be negative – hence the minus sign in the above equation

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### Impulse

• When a resultant (unbalanced) force acts on a mass, the momentum of that mass will change
• The impulse of a force is equal to that force multiplied by the time for which it acts:

impulse  =  F × t

• The change in momentum of a mass is equal to the impulse provided by the force:
`impulse = change in momentum`

`F × t  =  mv - mu`

(Where u is the initial velocity of the mass and v is the final velocity of the mass)

### Author: Jenna

Jenna studied at Cardiff University before training to become a science teacher at the University of Bath specialising in Biology (although she loves teaching all three sciences at GCSE level!). Teaching is her passion, and with 10 years experience teaching across a wide range of specifications – from GCSE and A Level Biology in the UK to IGCSE and IB Biology internationally – she knows what is required to pass those Biology exams.
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