Measurement and Units

Physics is built on measurement. Every physical quantity has a numerical value and a unit, without the unit, a number is meaningless. The system used internationally is the SI (Système International d'Unités).

Physical Quantities

A physical quantity is anything that can be measured. Every quantity is either fundamental or derived.

Fundamental quantities cannot be defined in terms of other physical quantities. The SI defines seven, of which five appear throughout CSEC Physics:

Derived quantities are combinations of fundamental ones. They come with derived units:

SI Prefixes

When quantities are very large or very small, prefixes scale the base unit:

Precision and Accuracy

These two are easy to confuse.

Accuracy describes how close a measurement is to the true value. An accurate measurement is correct; an inaccurate one contains systematic error.

Precision describes how repeatable a measurement is. Precise measurements cluster together, even if they are all slightly wrong. A well-calibrated instrument gives high accuracy; a sensitive instrument gives high precision. Both qualities are desirable but independent.

Significant Figures

Significant figures (s.f.) express the precision of a measurement. The number of significant figures is the number of meaningful digits, starting from the first non-zero digit:

• 4.52 m has 3 s.f.
• 0.0063 kg has 2 s.f.
• 1500 could be 2, 3, or 4 s.f., use standard form to remove ambiguity (e.g. 1.5 × 10³)

When calculating, the answer should match the lowest number of significant figures in the data. Rounding further than your data warrants gives a false impression of precision.

Sources of Error

Random errors affect individual measurements unpredictably. Taking multiple readings and averaging reduces their effect.

Systematic errors shift all readings in the same direction by the same amount. Averaging does not remove them. A classic systematic error is a zero error, when an instrument reads a non-zero value before any measurement is taken. Check for zero errors before using any instrument and subtract the offset from all readings.

Parallax error occurs when you read a scale at an angle rather than directly in front of it. Always position your eye so it is level with the scale marking.

Measuring Instruments

Different instruments suit different ranges and required precision.

Metre rule: measures lengths to ±1 mm. Suitable for objects 1 cm to 1 m.

Vernier caliper: measures lengths to ±0.1 mm. The vernier scale gives the fractional millimetre by finding which vernier division lines up with a main scale division.

Micrometer screw gauge: measures diameters and small lengths to ±0.01 mm. One full rotation of the thimble moves the spindle 0.5 mm. Read the sleeve, then add the thimble reading.

Balance: measures mass to varying precision depending on type. An electronic balance gives a direct reading; a beam balance compares the unknown mass to known masses.

Stopwatch: measures time intervals. Human reaction time (~0.2 s) limits its precision. For short events, use a motion sensor or light gate.

Thermometer: measures temperature. A liquid-in-glass thermometer relies on thermal expansion; a thermocouple converts a temperature difference to a small voltage and suits rapidly changing or extreme temperatures.

Density

Density is mass per unit volume:

$\rho = \frac{m}{V}$

where $\rho$ is density in kg m⁻³, $m$ is mass in kg, and $V$ is volume in m³.

Density is an intrinsic property of a material; it does not change with the size of the sample. A 1 kg block of iron and a 10 kg block of iron have the same density.

To measure density:

1. Measure mass using a balance.
2. Measure volume. For regular objects, calculate from dimensions. For irregular solids, use a displacement method: fill a measuring cylinder with water, record the volume, fully submerge the object, and record the new volume. The difference is the object's volume.

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