MomentumOxford AQA IGCSE Physics: Revision notes

Momentum is a property of a moving object, calculated using:

p = m x v

where p is momentum (kg m/s), m is mass (kg), and v is velocity (m/s). Momentum is a vector quantity — it has both magnitude and direction, in the same direction as the object's velocity.

In a closed system (one with no external forces acting), momentum is conserved: the total momentum before an interaction equals the total momentum after it.

This applies to both:

• Collisions — e.g. two vehicles crashing into one another
• Explosions — e.g. two objects pushing apart, such as a gun firing a bullet

Because momentum is a vector, direction matters: momentum in opposite directions has opposite signs and can cancel.

Force is related to the rate of change of momentum:

F = delta p / t

where F is force (N), delta p is the change in momentum (kg m/s), and t is the time taken for that change (s). A larger change in momentum, or a shorter time for the change, produces a larger force.

In a collision, a vehicle's momentum changes very quickly (from its initial value to zero, or close to it). Safety features work by increasing the time over which this change in momentum happens, which reduces the force experienced by the people inside (since F = delta p / t):

• Air bags — increase the time over which the head/chest decelerates
• Seat belts — stretch slightly, increasing the time the body takes to stop, and spread the force over the chest/pelvis
• Side impact bars — absorb energy and increase the time of impact, protecting occupants from a side collision
• Crumple zones — the front/back of a car deforms in a crash, increasing the time taken for the car's momentum to reach zero
• Crash mats — increase the time taken for a person landing on them to stop, e.g. in gymnastics
• Cycle helmets — the crushable foam increases the time over which the head decelerates in an impact