Momentum

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Define momentum as mass × velocity; recall and use the equation p = mv
  2. Define impulse as force × time for which force acts; recall and use the equation impulse = FΔt = Δ(mv)
  3. Apply the principle of the conservation of momentum to solve simple problems in one dimension
  4. Define resultant force as the change in momentum per unit time; recall and use the equation F = Δp/Δt

What is Momentum?

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Momentum is a measure of how difficult it is to stop a moving object. It tells us about the "strength" of motion.

Think of it this way: A large truck moving slowly and a small car moving very fast could both be equally difficult to stop. This is because momentum depends on both how heavy something is (its mass) and how fast it's moving (its velocity).

The Momentum Equation

Momentum is calculated using this equation:

p = mv

Where:

  • p = momentum, measured in kilogram metres per second (kg m/s) or newton seconds (Ns)
  • m = mass, measured in kilograms (kg)
  • v = velocity, measured in metres per second (m/s)

Key points:

  • An object that is not moving (v = 0) has no momentum (p = 0)
  • The more massive an object is, the more momentum it has
  • The faster an object moves, the more momentum it has
  • Momentum keeps an object moving in the same direction

Momentum is a Vector Quantity

Because velocity is a vector (meaning it has both size and direction), momentum is also a vector. This means momentum has both magnitude and direction.

What does this mean in practice?

  • We need to choose a positive direction (usually right or up)
  • Movement in the opposite direction is negative
  • If a ball is moving to the right with momentum of +5 kg m/s, then a ball moving to the left at the same speed has momentum of -5 kg m/s

Example: A 60 g tennis ball approaches a wall at 2 m/s (moving right). After hitting the wall, it bounces back at 2 m/s (moving left).

Taking right as positive:

  • Before collision: p = mv = 0.06 × 2 = +0.12 kg m/s
  • After collision: p = mv = 0.06 × (-2) = -0.12 kg m/s

The negative sign shows the ball is now moving in the opposite direction.

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