Defining momentum
Momentum (p) is the product of mass and velocity. It is a vector, so direction matters, and its unit is kg m s⁻¹. A heavy, fast object has large momentum.
Key formula
p = mv
where p = momentum (kg m s⁻¹), m = mass (kg), v = velocity (m s⁻¹).
Principle of conservation of momentum: total momentum before = total momentum after, when no external force acts.
Conservation of momentum
In a closed system the total momentum stays constant. For a collision of two objects:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. In an elastic collision the objects bounce apart; in an inelastic collision they stick together and move with a common velocity.
Worked example
A 2 kg trolley moving at 3 m s⁻¹ collides and sticks to a stationary 1 kg trolley. Find their common velocity.
Momentum before = (2 × 3) + (1 × 0) = 6 kg m s⁻¹.
After: (2 + 1)v = 6, so v = 6 ÷ 3 = 2 m s⁻¹.
Explosions
In an explosion the total momentum before is zero, so the fragments move in opposite directions with equal and opposite momenta.
Remember
- Momentum p = mv is a vector.
- Total momentum is conserved with no external force.
- Take one direction as positive and be consistent.