 # Principle of the Conservation of Momentum

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## Principle of the Conservation of Momentum

#### Definition of momentum

Linear momentum, P, is defined as the mass, m, of an object multiplied by its velocity, v, so:

P = mv

Units: kgms-1 or Ns

(Sometimes momentum is given the symbol M). Momentum is a vector.

#### Principle of the conservation of momentum

The Principle of the Conservation of Momentum states that: if objects collide, the total momentum before the collision is the same as the total momentum after the collision (provided that no external forces - for example, friction - act on the system).

That's amazingly useful because it means that you can tell what is going to happen after a collision before it has taken place.

Principle of Conservation of Energy: Of course, energy is also conserved in any collision, but it isn't always conserved in the form of kinetic energy, so be careful.

Some simple examples:

To do any calculations for momentum, there are some simple rules to follow to make it easy:

Always decide which direction is positive and which is negative, then stick to it.

Always remember that the total momentum before the collision will be the same as the total momentum after the collision.

So, The conservation of momentum states:

Momentumbefore = Momentumafter

So, (P1 + P2) before= (P1 + P2) after

Or, m1u1 + m2u2 = m1v1 + m2v2

But notice that in this example, v1 = 0. So that term cancels and makes finding an answer much easier.

Common error number 1:

If the objects change direction in the collision or are going in different directions before the collision, make sure that you have got the signs for the velocities and therefore the momentums correct.

Example 1: Or

Example 2: Common error number 2:

When objects bounce back after a collision, be careful about the change in momentum. So change in momentum = final P - initial P

= -mu - (+ mu)

= - 2mu

Common error number 3:

Explosions are a special type of collision. Momentum is conserved in an explosion. This is made easier by the fact that usually, the momentum before an explosion is zero. The Principle of the Conservation of Momentum states that the momentum after the explosion must therefore be zero as well.

Here's an interesting example of this. What's the momentum of the universe? A tough question? Well, no! If the universe began with a Big Bang (for instance - an explosion), the momentum of the universe before the explosion was zero.

#### So what is its momentum afterwards?

Defining force

Force can be defined as the rate of change of momentum as: Question:

Hint: What is the total momentum before the collision? Remember that the cars are moving in opposite directions so you will need one to have negative momentum.

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