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:

Copyright S-cool

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:

Copyright S-cool

(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 = Copyright S-cool

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.