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 …