# S-Cool Revision Summary

## S-Cool Revision Summary

#### 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.

#### So what is its momentum afterwards?

*Defining force*

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

#### Perfectly Elastic collisions

**(A special case)**

- All momentum is conserved (not surprisingly - it always is!)
- Kinetic energy is conserved (that's what makes this special).
- Relative speed of approach = relative speed of separation.

#### Perfectly Inelastic collisions

**(Another special one)**

- All momentum is conserved (as always).
- Kinetic energy is not conserved.
- The relative speed of separation is zero.

#### Inelastic collisions

**(The usual old case) **

- All momentum is conserved (again).
- Kinetic energy is not conserved (again).
- You can't say anything about the speed at which they leave each other without doing a calculation.

#### Changing momentum

**From Newton's Second Law and the definition of force:**

(**mv** = final momentum, **mu** = initial momentum)

To achieve any particular **change in momentum,** you can either have a **large force** multiplied by a small time or a **small force** multiplied by a large time.

Change in momentum is called impulse,

So, impulse = mv - mu and F =

hence impulse = Ft

#### Force-time graphs

We can plot graphs of the force during a collision against time.

We can find the impulse, or change in the momentum, by calculating the area under the force-time graph.