# Mechanics

1.3.1 Momentum
Momentum is de ned as (by Newton and our syllabus): The product of a body’s mass and velocity
Momentum = Mass×Velocity
p = mv
(side note: momentum is de ned by quantum mechanics as an operator which acts on the wave function, this explains why photons have momentum) It is an object’s ability to keep going. An object with lots of momentum is di cult to stop. If you change the velocity of an object, it’s momentum changes.
Change in momentum = Final momentum−Initial momentum
4p = mv−mu
If we want to change an object’s momentum, we must make it accelerate, and this requires a force. The force must act for a certain period of time, this is called impulse:
Impulse = Force×Time
I = Ft
Impulse and change in momentum are equal (but not the same!):
Ft = mv−mu
Note that this only gives us an average force value. A contact force tends to vary with time and can be seen on a Force-time graph:

1.3.2 Elastic Collisions
Elastic collision A collision in which there is no change in total kinetic energy.
Inelastic collision A collision in which (some) kinetic energy is lost.
Perfectly inelastic collision A collision in which all kinetic energy is lost.
1.3.3 Conservation of Momentum
Momentum is always conserved when no external force a ects the interaction.
Total momentum before = Total momentum after