Conservation of Momentum

In physics and engineering we use a law called the conservation of momentum to predict the motion of objects which are in a collision. We can also use it to design rocket propulsion systems.

Momentum of an object is influenced by its mass and its velocity. It has to have both to have momentum.

Mathematically we express momentum as the mass of the object times its velocity. The momentum of a stationary object is zero as a result of its velocity being zero. From the definition you can see that the momentum of an object increases as its mass or velocity increases.

Definition of momentum is shown on a canvas with pictures of cars in a collision and a rocket taking off
Definition of Momentum

The law of Conservation of Momentum

A powerful concept is the law of conservation of momentum. This says that the total momentum before a collision equals the total momentum after the collision. This allows us to do some amazing calculations to predict the motion of objects after a collision.

For example, let us look at the situation where we have two train freight wagons in a collision.

Two green freight wagons are on a rail track with one moving towards the other
A rail freight wagon on the bottom right is moving towards a stationary wagon on the top left.

We can use the conservation of momentum to calculate the velocity of the two wagons after the collision. In this case we have only one of the wagons moving before the collision. We will also assume the wagons become locked together after the collision.

Two green freight wagons are on a rail track with them connected together following a collision
The two freight wagons are connected together by the grey coupler after a collision

Calculating velocity after a collision

The way you would use the conservation of momentum to calculate the velocity after the collision is:

  1. Identify the objects to be considered. In this case it is the two freight wagons. We refer to this as the system under consideration.
  2. Calculate the momentum of each freight wagon before the collision. The total of this is the total momentum before the collision.
  3. Calculate the total momentum of the system after the collision. The freight wagons are joined together and moving as one. The momentum is therefore the combined mass of the two wagons times their velocity. Note that since they are joined together, both wagons have the same velocity.
  4. Use the conservation of momentum to equate the momentum after the collision to the momentum before the collision. This is the key step as it enables us to calculate the velocity of the two wagons after the collision. Full details of the calculation are shown in the video at the top of this article.

External forces acting on the system

There is an important point to remember when using the conservation of momentum. It only works when there are no external forces acting on the system under consideration. If there are external forces acting on the system then the momentum of the system will change and you cannot use the conservation of momentum to do the calculation.

An example of external forces acting on the freight wagons would be where they collided with a fixed barrier on the track. You can see this in the video above.

Before you go

Why don’t you have a look at my video on Energy and Work. In it you will learn how to calculate the velocity of a dropped object just before it hits the ground.

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Mac

I teach physics and engineering through animation.

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2 Responses

  1. Clive Sutton says:

    Another great tutorial Iain. I wondered if you could tag onto the end of this one another way of looking at this problem i.e. that of the energy conservation case – to explain the loss of energy (in the barrier damped buffers) by the bump-stop? And if you could explain a rocket launch i could really use that to reinforce what i’m teaching in the STEM/.Space syllabus, to my Cadets . . .

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