Momentum & Impulse (Cambridge (CIE) O Level Physics): Revision Note

Momentum

• An object with mass that is in motion has momentum which is defined by the equation:

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

$p=mv$

• 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, making it difficult to change the direction of an object with a large momentum

• Since velocity is a vector this means that the momentum of an object also depends on its direction of travel

• This means that momentum can be either positive or negative

  • If an object travelling to the right has positive momentum, an object travelling in the opposite direction (to the left) will have negative momentum

Momentum of a Tennis Ball

The tennis ball's momentum is negative when it moves in the opposite direction to which it initially was travelling in

• Therefore, the momentum of an object will change if:

  • The object accelerates (speeds up) or decelerates (slows down)

  • Changes direction

  • Its mass changes

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 there are no external forces (e.g. friction) acting on the system

• 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)

Momentum of Masses Before and After a Collision

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)