4.3 Momentum

2026 Syllabus Objectives

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

  1. Use the definition of linear momentum and show understanding of its vector nature (for motion in one dimension only)

  2. Use conservation of linear momentum to solve problems involving the direct impact of two bodies (including cases where the bodies join together after impact)

What is Momentum?

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Momentum is a measure of how much "motion" an object has. It depends on two things: how heavy the object is (its mass) and how fast it's moving (its velocity).

The formula for momentum is:

p = m × v

Where:

  • p = momentum (measured in kg·m/s or kg m/s)
  • m = mass of the object (measured in kg)
  • v = velocity of the object (measured in m/s)

Understanding the Formula

  • If you double the mass of an object but keep the velocity the same, you double the momentum
  • If you double the velocity but keep the mass the same, you also double the momentum
  • A heavy object moving slowly can have the same momentum as a light object moving quickly

Example: A car with mass 1000 kg moving at 5 m/s has momentum: p = 1000 × 5 = 5000 kg·m/s

Momentum is a Vector Quantity

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This is one of the most important things to understand about momentum. A vector quantity is something that has both a size (magnitude) and a direction.

Because velocity is a vector (it has direction), and momentum = mass × velocity, this means momentum also has direction.

How to Handle Direction in Calculations

When solving problems, you must:

  1. Choose a positive direction at the start (for example, "right is positive" or "up is positive")
  2. Stick with this choice throughout the whole problem
  3. Use positive values for velocities in your chosen positive direction
  4. Use negative values for velocities in the opposite direction

Example:

Imagine you're standing on a road, and you decide "right is positive."

  • A 3 kg ball moving to the right at 4 m/s has velocity = +4 m/s

    • Its momentum = 3 × (+4) = +12 kg·m/s

  • A 2 kg ball moving to the left at 5 m/s has velocity = −5 m/s (because left is the negative direction)

    • Its momentum = 2 × (−5) = −10 kg·m/s

The negative sign tells you the momentum is in the negative direction (to the left).

Important Notes About Direction

  • Always write down which direction you're calling positive before you start calculating
  • If your answer comes out negative, it means the object is moving in the negative direction
  • Never just ignore the negative signs—they contain important information about direction!

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