2.1 Defining Mass

At its most fundamental level, mass is defined as a measure of the quantity of matter within an object.¹

• Formal Definition: More formal definitions sometimes include the phrase "at rest relative to the observer," which serves to establish a consistent frame of reference and avoid the complexities of relativistic physics, a topic beyond the scope of the iGCSE curriculum.²
• Conceptual Understanding: For the purposes of this syllabus, mass can be understood as the amount of "stuff" an object is made of.

2.2 Mass as Inertia

Beyond being a simple measure of matter, mass has a deeper physical significance: it is the quantitative measure of an object's inertia.¹

• Inertia: The property of an object that resists any change in its state of motion.
• Implication: A more massive object possesses greater inertia, meaning it is more difficult to accelerate (speed up), decelerate (slow down), or alter its direction of travel.¹ This concept is intrinsically linked to Newton's Second Law of Motion (F=ma), which states that the force required to accelerate an object is directly proportional to its mass.⁴

2.3 The Invariant Nature of Mass

A critical characteristic of mass is that it is an intrinsic and constant property of an object. An object's mass remains the same regardless of its location in the universe.²

• Example: An astronaut with a mass of 75 kg on Earth will have the exact same mass of 75 kg on the Moon, on Mars, or in the near-perfect vacuum of deep space.⁹

2.4 Measuring Mass

The correct instruments for measuring mass are a beam balance or a modern digital/electronic balance.²

A beam balance operates on the principle of moments, comparing an unknown mass on one pan to a set of known masses on the other. The system is in equilibrium when the beam is perfectly horizontal, indicating that the masses on both sides are equal.⁷

The reason a balance measures mass, and not weight, is fundamental to its design. The operation of a beam balance cancels out the effect of the local gravitational field. For a balance with arms of equal length (d) from the central pivot, the system is in equilibrium when the turning effects (moments) on both sides are equal. The force on each pan is the weight of the object (W = m × g).

Therefore, the equilibrium condition is:

(mass₁ × g) × d = (mass₂ × g) × d

Because the gravitational field strength (g) and the arm length (d) are the same for both sides of the equation, they cancel out, leaving:

mass₁ = mass₂

This demonstrates precisely why a balance provides a true measure of mass, a value that remains constant even if the balance is moved to a location with different gravity, such as the Moon.⁷ The instrument is specifically designed to make the local gravitational pull irrelevant to the measurement.

3.1 The Concept of a Field

A gravitational field is a region of space surrounding an object with mass, within which another object with mass will experience an attractive gravitational force.⁸

• While every object that has mass generates a gravitational field, this field is only significant and easily detectable for objects of very large mass, such as planets, moons, and stars.⁸
• The field itself is invisible, but its effect—the force of gravity—is observable.³

3.2 Gravitational Field Strength (g)

The intensity of a gravitational field at any point is quantified by its gravitational field strength, denoted by the symbol g.

Definition: Gravitational field strength is formally defined as the gravitational force exerted per unit mass on an object placed at that point in the field.⁴

This definition is expressed by the equation:

g = W / m

Where:

• W is the weight (gravitational force)
• m is the mass

Consequently, the SI unit for gravitational field strength is Newtons per kilogram (N/kg).¹

A crucial point of understanding is the equivalence between gravitational field strength and the acceleration of free fall (also denoted by g). While their definitions are different, their numerical values are equivalent at any given location. For iGCSE purposes, the value of g on Earth is taken to be approximately 9.8 N/kg or 9.8 m/s².⁸ In some contexts, for simplicity, this value is rounded to 10 N/kg or 10 m/s².¹

This table illustrates that the gravitational field strength varies depending on the mass and radius of the celestial body.⁹

4.1 Defining Weight

Weight is defined as the force of gravity acting on an object.³ It is the pull exerted by a gravitational field on a mass. This definition directly leads to the core equation linking weight, mass, and gravitational field strength.

By rearranging the equation for gravitational field strength (g = W/m), we derive the formula for weight:

W = m × g

4.2 Weight as a Vector

Unlike mass, weight is a vector quantity. This means it has both magnitude (size) and direction.²

• Magnitude: The size of the force, calculated as m × g.
• Direction: The direction of the gravitational pull, which is always towards the center of the large mass creating the field (e.g., towards the center of the Earth).¹

Because weight is a force, its SI unit is the Newton (N).¹

4.3 The Variability of Weight

A direct consequence of the formula W = m × g is that an object's weight is not constant; it depends entirely on the local gravitational field strength (g).¹

Consider our 75 kg astronaut again:

• On Earth (`g` ≈ 9.8 N/kg):

W = 75 kg × 9.8 N/kg = 735 N

• On the Moon (`g` ≈ 1.6 N/kg):

W = 75 kg × 1.6 N/kg = 120 N

This calculation clearly shows that while the astronaut's mass (the amount of matter) remains 75 kg, their weight (the gravitational force on them) is more than six times smaller on the Moon than on Earth.

4.4 Measuring Weight

Weight is measured using an instrument called a newton meter, also known as a spring balance or force meter.²

A newton meter consists of a calibrated spring that stretches when a force is applied to it. According to Hooke's Law, the extension of the spring is directly proportional to the applied force (within the elastic limit). The scale on the newton meter is calibrated to read the force in Newtons. Since weight is a force, this instrument provides a direct measurement of it.²

It is crucial to distinguish this from a common bathroom scale. While a bathroom scale provides a reading in kilograms, it is fundamentally measuring weight. It measures the compressive force exerted on it and then internally divides this force by the assumed value of Earth's gravity (g ≈ 9.8) to display a value for mass. If you were to take such a scale to the Moon, it would give an incorrect (and much lower) reading for your mass because it is calibrated for Earth's gravity.⁹

Mastering the difference between mass and weight is non-negotiable for success in iGCSE Physics. The following table provides a consolidated summary of the key distinctions.

Conceptual Checklist:

• [ ] Do I understand that mass is a measure of inertia?
• [ ] Can I explain why a beam balance measures mass, not weight?
• [ ] Can I define gravitational field strength in terms of force per unit mass?
• [ ] Do I know that weight is a force and is measured in Newtons?
• [ ] Can I calculate the weight of an object on different planets if given its mass and the local g?
• [ ] Do I understand why a spring balance measures weight, while a beam balance measures mass?

Worked Example 1: Calculating Weight

A lunar rover has a mass of 215 kg. The gravitational field strength on the Moon is 1.6 N/kg.

(a) What is the mass of the rover on the Moon?

Mass is an intrinsic property and does not change with location.

Mass = 215 kg

(b) What is the weight of the rover on the Moon?

Use the formula W = m × g.

W = 215 kg × 1.6 N/kg = 344 N

(c) The rover is brought back to Earth, where g = 9.8 N/kg. What is its new weight?

The mass is still 215 kg.

W = 215 kg × 9.8 N/kg = 2107 N

Practice Problems

1. An object has a weight of 120 N on Earth (g = 10 N/kg). What is its mass?
2. A probe has a mass of 500 kg. What is its weight on Mars, where the gravitational field strength is 3.7 N/kg?
3. A student has a mass of 60 kg. They stand on a weighing scale on Jupiter (g = 25 N/kg). What is the student's weight on Jupiter? What reading, in kg, would a bathroom scale (calibrated for Earth, g=10 N/kg) show?

This guide was compiled with information from standard iGCSE Physics textbooks and examination board specifications. The numbered superscripts correspond to common knowledge points found across these resources.