Momentum (O-Levels/IGCSE)

What these notes cover

These notes cover momentum for Cambridge O Level Physics (5054) and Cambridge IGCSE Physics (0625): momentum as the product of mass and velocity, impulse and change in momentum, resultant force as the rate of change of momentum, the principle of conservation of momentum in collisions and explosions, how rockets and jet engines work, and why increasing the collision time reduces the force. They include worked examples and past-paper questions.

Key formulas and definitions

• Momentum is the product of mass and velocity: p = mv. It is a vector quantity. Unit: kg m/s.
• Impulse = force × time = FΔt = change in momentum. Unit: N s (equivalent to kg m/s).
• Resultant force is the change in momentum per unit time: F = Δp / Δt. For a constant mass this becomes F = ma.
• Increasing the time taken for the momentum to change reduces the force. This is how crumple zones, seat belts and airbags protect people in a crash.
• Principle of conservation of momentum: when objects collide or explode, the total momentum before equals the total momentum after, provided no external resultant force acts: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
• If two objects stick together after a collision: m₁u₁ + m₂u₂ = (m₁ + m₂)v.
• Rockets and jet engines: hot gas is pushed out backwards with large momentum, so the rocket gains an equal momentum forwards.
• In most collisions, kinetic energy is not conserved (some is transferred to thermal energy and sound), but total momentum always is.