Momentum (Cambridge (CIE) IGCSE Physics): Revision Note

Momentum

Extended tier only

• An object with mass that is in motion has momentum 

The momentum equation

• Momentum is defined by the equation:

$\mathrm{momentum}=\mathrm{mass}\times \mathrm{velocity}$

$p=mv$

• Where:

  • $p$ = momentum, measured in kilogram metres per second (kg m/s)

  • $m$ = mass in kilograms (kg)

  • $v$ = velocity in metres per second (m/s)

• This means that an object at rest (i.e. v = 0) has no momentum

• Momentum keeps an object moving in the same direction

  • It is difficult to change the direction of an object that has a large momentum

• Velocity is a vector with both magnitude and direction

  • This means that the momentum of an object also depends on its direction of travel

  • Therefore, momentum can be either positive or negative

• If an object has positive momentum, then an object travelling in the opposite direction will have negative momentum 

How does the momentum of a ball change after a collision?

The momentum of the tennis ball is positive as it approaches the wall and negative after the collision, as it moves in the opposite direction

Conservation of momentum

Extended tier only

• 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 system, in physics, is an object or group of objects

• A closed system means that no energy is transferred into or out of the system and there are no external forces acting

• The principle of conservation of momentum can also be written as:

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

• 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)

Principle of conservation of momentum for a collision

The momentum of a system before and after a collision is constant

• 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)