Momentum (Edexcel IGCSE Physics)

• Momentum is a property that all moving objects have
• An object with mass, , moving at a velocity, , will have a momentum, 

The momentum equation

• Momentum is the product of an objects mass and velocity

• Where:
  • p = momentum in kilogram metre 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 with a large momentum

• Velocity is a vector with both magnitude and direction
• Therefore, the momentum of an object depends on its direction of travel
  • This means momentum can be either positive or negative

• If an object travelling to the right has positive momentum, then an object travelling in the opposite direction (to the left) will have negative momentum
  • This isn't a solid rule, but in questions, usually the positive direction is to the right and negative to the left

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

• The momentum of an object will change if:
  • it's velocity increases or decreases (acceleration)
  • it's direction changes (acceleration)
  • it's mass changes

The principle of conservation of momentum

• The principle of conservation of momentum states that:

The total momentum before an interaction is equal to the total momentum after an interaction, if no external forces are acting on the objects

• In this context, an interaction can be either:
  • A collision i.e. where two objects collide with each other
  • An explosion i.e. where a stationary object explodes into two (or more) parts

Collisions

• For a collision between two objects:

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

• In the example below:
• Before the collision:
  • The momentum is only generated by mass m  because it is the only moving object
  • 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 + the momentum of m
  • This is (M  × V) + (m  × -v) or (M  × V) – (m × v) written more simply

Conservation of momentum before and after a collision

The momentum of a system before and after a collision is always conserved

• 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