| 1.6: MOMENTUM |
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Key Definition Momentum is a vector quantity defined as the product of mass and velocity (p = mv), measured in kg m s⁻¹.
Because velocity has direction, momentum also has direction, so a sign convention must be established before any calculation.
- Impulse links the force acting on an object and the time for which it acts to the resulting change in momentum
- The impulse experienced by an object equals FΔt, which in turn equals the change in momentum Δ(mv)
- Impulse is a vector measured in newton seconds (N s, equivalent to kg m s⁻¹) and equals the area under a force–time graph
- A longer contact time for the same momentum change results in a smaller force, which is the physical basis of safety features such as crumple zones and airbags
FΔt = Δ(mv)
Principle of the Conservation of Momentum
Key Definition The principle of the conservation of momentum states that the total momentum of a system remains constant provided no resultant external force acts.
This principle applies to:
- Collisions (where objects meet)
- Explosions (where objects separate)
- Recoil situations
In every case, total momentum before equals total momentum after — with careful attention to vector signs.
Elastic and Inelastic Collisions
- In an elastic collision, both total momentum and total kinetic energy are conserved
- In an inelastic collision, momentum is still conserved but total kinetic energy is not — some is transferred to other forms such as internal (thermal) energy, sound and deformation
- In an explosion or recoil, the total momentum is zero before and after, so the fragments move apart with equal and opposite momenta
Resultant Force and Rate of Change of Momentum
The resultant force on an object equals the rate of change of its momentum.
F = Δp / Δt
This is the general form of Newton's second law. When mass is constant the equation reduces to
F = ma
but the momentum form is needed whenever mass changes or when momentum data is given directly. In all problems, the direction of the resultant force matches the direction of the momentum change.