Form 4 · Chapter 2

Momentum

Momentum is the product of an object's mass and velocity, and total momentum is conserved in a closed system.

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.

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