# 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. 