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# Principle of the Conservation of Momentum

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## Principle of the Conservation 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**.

**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:**

Momentum_{before} = Momentum_{after}

So, (P_{1} + P_{2}) before= (P_{1} + P_{2}) after

Or, m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}

But notice that in this example, **v _{1} = 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**.

**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.