Inertia, mass, weight and gravitational field strength

What you will learn

Define inertia, mass and weight; calculate W = mg with g = 9.81 N kg⁻¹.

Specification mapping: B2.2, B2.2.1, B2.2.2, B2.2.3

Prerequisites: B2.1

Physical principles

Inertia is resistance to a change in velocity. Mass is a measure of inertia and is measured in kilograms. A larger mass needs a larger resultant force for the same acceleration. Inertia is not a force opposing motion; it is a property of matter.

Weight is gravitational force on an object. W = mg, where g is gravitational field strength in N kg⁻¹. On Earth near the surface, the specification formula sheet gives g = 9.81 N kg⁻¹. The same value can be expressed as 9.81 m s⁻² for free-fall acceleration where other forces are negligible.

Mass remains the same when moving an object between gravitational fields, while weight changes with g. Weight acts towards the gravitating body. An apparent weighing reading can differ from true gravitational weight in an accelerating lift or while supported differently. On a horizontal stationary surface with no other vertical forces, normal reaction balances weight; the two are not a Newton’s-third-law pair because both act on the same object.

Scientific diagram and interpretation

Weight acts downward, normal reaction upward, drive right and resistance left. Horizontal arrows need not balance; N = mg only under the stated vertical conditions. Schematic lengths are not force values.

Equations and relationships

W = mg; g = 9.81 N kg⁻¹ (Pearson Appendix 5)

Worked examples and applications

Earth weight

m = 65.0 kg; W = mg = 65.0 × 9.81 = 637.65 N ≈ 638 N to three significant figures.

Mass from force

A weight of 196.2 N in a field of 9.81 N kg⁻¹ gives m = W/g = 196.2/9.81 = 20.0 kg.

Another field

A 10.0 kg object in a supplied field of 1.62 N kg⁻¹ weighs 16.2 N. Its mass is still 10.0 kg.

Common misconceptions

Weight is in newtons; mass is in kilograms. Inertia is not a separate arrow in a free-body diagram.

Examination technique

Use the supplied g value and identify which force is being called weight.

For an explanation, connect the physical cause to its effect. For a calculation, state the model, rearrange before substitution, retain intermediate digits, and finish with units. For a data question, refer to the actual readings and distinguish a trend from proof of a cause.

Check your understanding

Five questions. Choose an option, then Check Answer. Read the feedback and use Try Again to reset. Use Tab between controls, arrow keys within radio groups, and Enter or Space on buttons. These local practice answers are not saved.