Momentum and Newton's Laws of Motion

2026 Syllabus Objectives

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

  1. Understand that mass is the property of an object that resists change in motion
  2. Recall F = ma and solve problems using it, understanding that acceleration and resultant force are always in the same direction
  3. Define and use linear momentum as the product of mass and velocity
  4. Define and use force as rate of change of momentum
  5. State and apply each of Newton's laws of motion
  6. Describe and use the concept of weight as the effect of a gravitational field on a mass and recall that the weight of an object is equal to the product of its mass and the acceleration of free fall

1. Mass and Inertia

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What is Mass?

Mass is a measure of how much matter is in an object. But more importantly for physics, mass tells us how much an object resists changes to its motion. This resistance to change is called inertia.

Think about it this way: if you try to push a shopping trolley and a car, which one is harder to get moving? The car, because it has more mass. Which one is harder to stop once it's moving? Again, the car. This is because the car has more inertia.

Key points about mass:

  • Mass is a scalar quantity (it only has size, no direction)
  • It is measured in kilograms (kg)
  • The more mass an object has, the more it resists changes in motion
  • Mass stays the same wherever you are in the universe

Inertia is the tendency of an object to keep doing what it's already doing. An object at rest wants to stay at rest. An object moving at constant speed wants to keep moving at that speed. The amount of inertia depends on the mass - more mass means more inertia.

2. Weight and Gravitational Fields

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What is Weight?

While mass stays the same everywhere, weight changes depending on where you are. Weight is the force that gravity exerts on a mass.

Weight is defined as: the effect of a gravitational field on a mass

The Relationship Between Weight and Mass

Weight is calculated using the equation:

W = mg

Where:

  • W = weight (measured in newtons, N)
  • m = mass (measured in kilograms, kg)
  • g = acceleration of free fall, also called gravitational field strength (measured in metres per second squared, m s⁻² or newtons per kilogram, N kg⁻¹)

On Earth, g = 9.81 m s⁻² (often rounded to 10 m s⁻² in calculations)

Understanding the Difference

Let's say you have a mass of 70 kg:

  • Your mass is 70 kg everywhere - on Earth, on the Moon, in space
  • Your weight on Earth = 70 × 9.81 = 687 N
  • Your weight on the Moon = 70 × 1.63 = 114 N (the Moon has weaker gravity)
  • Your weight in deep space = 0 N (no gravity acting on you)

Important distinctions:

  • Mass is measured with an electronic balance; weight is measured with a spring balance
  • Mass is a scalar; weight is a vector (it always acts downwards towards the center of the planet)
  • Mass tells us about inertia; weight tells us about gravitational force

Gravitational Field

A gravitational field is a region of space around a mass where another mass will experience a gravitational force. The Earth creates a gravitational field around it, which is why objects fall downwards and why we have weight.

Free Fall

An object is in free fall when it is falling under gravity alone, with no other forces acting on it (ignoring air resistance). All objects near Earth fall with the same acceleration of 9.81 m s⁻² regardless of their mass, as long as air resistance is negligible.

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