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Fundamental and derived quantities of measurements
From Activity 1.12, you should have discovered that any quantity of measurements are either a fundamental or derived quantity.
Fundamental quantities
A quantity may be defined as any observable property or process in nature with which a number may be associated. This number is obtained by the operation of measurements. The number may be obtained directly by a single measurement or indirectly, say for example, by multiplying together two numbers obtained in separate operations of measurement. Fundamental quantities are those quantities that are not defined in terms of other quantities. In physics there are 7 fundamental quantities of measurements namely length, mass, time, temperature, electric current, amount of substance and luminous intensity. In this book we will study the following 5 fundamental quantities: length, mass, time, temperature and electric current.
SI units and symbols
In order to measure any quantity, a standard unit (base unit) of reference is chosen. The standard unit chosen must be unchangeable, always reproducible and not subject to either the effect of aging and deterioration or possible destruction. Before 1960, there were several systems of measurements in use around the world. In 1960, an international system of units was established. This system is called the International System of Units (SI). Table 1.6 contains the 7 fundamental physical quantities, their SI units and symbols.
Derived quantities
Quantities which are defined in terms of the fundamental quantities via a system of quantity equations are called derived quantities. Examples of derived quantities include area, volume, velocity, acceleration, density, weight and force.
Note that some derived units have been given names. For example, force is measured in kg m/s2 and has been given a named unit called a newton (N). We shall encounter other derived quantities later in this course and other levels of physics.
Prefixes for SI units
Measurements involve comparing an unknown quantity with a known fixed unit quantity (standard unit). This measurement consists of two parts, the unit and the number indicating how many units are there in the quantity being measured. In order to obtain various measurements, early scientists had to develop measuring devices. A measuring device has a scale marked in the standard or multiple units of the quantity to be measured. The choice of the instrument to be used depends entirely on the quantity being measured and the level of accuracy needed. In this sub-unit, we shall learn how to use accurately the metre rule and tape measure for the measurement of length, beam balance for the measurement of mass, stop clock or stopwatch for the measurement of time and measuring cylinder, pipette, and burette for the measurement of volume.
Length is measured in metres. One metre is the distance between the two marks on a standard platinum-iridium bar kept at Paris (France).
Although the metre is the standard unit of length, it is sometimes too big to measure some distances and too small to measure others. We therefore need other larger and smaller units related to the metre to carry out some measurements.
Table 1.9 shows the SI units of length and its relationship with other larger and smaller units of length.
Let us now discuss some of the instruments used to measure length.
Meter stick
Metre rule
Straight distances which are less than one metre in length are generally measured using metre rules. Metre rules are graduated in millimetres (mm). Each division on the scale represents 1 mm unit (Fig. 1.10).
Note: It is not always necessary to start measuring at the zero mark of the metre rule as shown in Fig. 1.11. You may use any two points on the scale, make your readings and obtain the required length by subtraction.
Fig. 1.13 (b) shows the parts of a vernier calliper. The calliper consists of a steel rigid frame A, onto which a linear scale is engraved. This scale is called the main scale and it is calibrated in centimetres and millimetres. It has a fixed jaw E at one end and a sliding jaw B centrally aligned by a thin flat bar C. The spring-loaded button D is used to prevent the sliding jaw from moving unnecessarily. The sliding jaw carrying a vernier scale can move along the main scale and can be fixed in any position along the main scale by screw S. The outside jaws are used to take external length measurements of objects. The inside jaws are used to take internal length measurement of an object. The sliding f lat bar C is used to find the depth of blind holes.
Using a vernier scale
Least count of a vernier calliper
The vernier scale has a length of 9 mm. It is divided into ten equal divisions. Therefore, each division has a length of 0.9 mm. The difference between 1 division on the main scale and 1 division in the vernier scale is (1– 0.9) mm =0.1 mm. The smallest reading called the least count (LC) that can be read from vernier callipers is 1 mm – 0.9 mm = 0.1 mm or 0.01 cm . The second decimal value in a reading is obtained by identifying the mark on the vernier scale which coincides with a mark on the main scale called the vernier coincidence (VC) and multiplying it with the least count i.e 0.01 cm. Second decimal value = (VC × LC).
(a) beam balance
(b) traditional pan balance
(c) electronic balance
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