Measurement of Length, Mass and Time

Measuring Length: From a Metre Scale to Parallax

Length is measured using different instruments depending on the scale involved:

• For everyday lengths (centimetres to metres), an ordinary metre scale is adequate, with a typical least count of $0.1$ cm.
• For small lengths that need finer precision (a rod's diameter, the thickness of a coin), a vernier caliper (least count typically $0.01$ cm) or a screw gauge / micrometer (least count typically $0.001$ cm) is used — see the worked screw-gauge calculation later in this unit.
• For very large distances that cannot be reached with a scale at all — the distance to the Moon, a nearby star, or a ship at sea — indirect optical/geometric methods such as parallax are used: the same distant object is viewed from two known, separated points, and simple trigonometry converts the observed angular shift into a distance.

Measuring Mass

Mass is measured by comparing an unknown mass against a set of standard (reference)

masses, typically using a physical (beam) balance for laboratory-scale masses. For very

small masses (atomic and sub-atomic scales), instruments such as a mass spectrograph,

which sorts charged particles by their mass-to-charge ratio using electric and magnetic

fields, are used instead.

Measuring Time

Time is measured by counting a periodic, repeatable event. Historically this meant the

rotation of the Earth (a day) or the swing of a pendulum (seconds, using a stopwatch with a

typical manual least count of about $0.1$ s). The modern SI second, however, is defined

using an atomic clock: it is the duration of a fixed, very large number of oscillations of

the radiation emitted during a specific transition of the caesium-133 atom. Because this

atomic oscillation is a property of nature rather than a mechanical process, atomic clocks are

accurate and reproducible to about 1 part in $10^{13}$ or better — far beyond what any …