# Measurement

## Meaning and definition of measurement

“Whatever exists at all, exists in some amount. To know it thoroughly involves knowing its quantity as well as its quality”.
Edward Thorndike (1918, p. 16)

Measurement is the process of attaching a numeric value (datum) to an aspect of a natural phenomenon, such as the volume of the milk produced by a cow, in order to be able to describe that phenomenon accurately and make comparisons to other similar phenomena, like "the crop production of the farm have had a 120% growth over the last 5 years."

To begin the process of measurement, we need to recognize the type of phenomenon, called the physical dimension, that we would like to measure. For example the diameter of the front wheel of a bicycle is of type Length, how fast the bicycle is moving is described by Speed and the amount of air crammed inside the wheel is determined by Pressure. The next thing we are going to need for doing a measurement is a Standard Unit for that type of aspect of natural phenomenon. For example, we can select a special person, like a king, and announce the length of his foot as the standard unit of length. From now on, when we are talking about the height of a sapling, we are talking of how many feet, each as long as the king's foot, do we need to cover the sapling. The number of the feet needed, which might turn out to be 7.75 and there is nothing wrong with that, is now considered the length of that thing. Congratulations! we have managed to correctly attach a numeric value (7.75) to the length of the sapling.

Now, for a more formal definition of measurement, we can refer to wikipedia, which says: "Measurement is the process of estimating the ratio of a magnitude of a quantity to a unit of the same type. A measurement is the result of such a process, expressed as the multiple of a real number and a unit, where the real number is the ratio. An example is 9 metres, which is an estimate of an object's length relative to a unit of length, one metre."

## Importance of measurement

Unless we are able to measure some phenomena, we cannot say we scientifically know anything about that thing.

Measurement gives a base to understand the universe. All around us we are surrounded by various things. We might not note it but unconciously we are actually "measuring" things and understanding them one way or the other. Just imagine how a world would be without being able to measure anything. We are surrounded by Measurement.

## Base Units

In Physics, we have now moved from Imperial units (pounds, yards etc), to the Metric System (metres, grams etc). However, we also use a variety of base units, and from these base units, we are able to derive some of the familiar units we know, e.g. the Newton. This range of units compile into a group known as the Le Système International d'Unités (SI). Most of the units you should recognize from your previous studies; these units are the base units in the SI system measurement:

 Dimension Unit of Measure Description Symbol Base Unit Symbol Length x, y, z, d, l, r, or s meter m Time t second s Mass M or m kilogram kg Current I or i Ampere Amp Temperature T or θ kelvin K Amount of Substance n mole mol Luminous intensity I candela cd

## Derived Units

With these base units, we can combine them to form derived units, such as the Newton, acceleration or speed; as an example, let us look at speed. Speed is described by the following equation:

$Speed={\frac {Distance}{Time}}$

As you know, Distance is in Metres, and Time is in Seconds, so m divided by s obviously gives us m/s. Since this is higher physics, it needs to be put into index notation, which means that the derived unit now becomes $ms^{-1}$  If we write this as a non-negative power, then we get:

$ms^{-1}={\frac {m}{s^{1}}}$

Now, let us use this derived unit to find another unit commonly met, Acceleration.

Acceleration is the rate of change of Velocity, described by the equation:

$Acceleration={\frac {Final~Velocity-Initial~Velocity}{Time~Taken}}$  or in symbols: $a={\frac {v-u}{\Delta \ t}}$

Thus, if we divide $ms^{-1}$  by the Time Taken (in seconds) we get $ms^{-2}$

Again, if we write this as a non-negative power, we get:

$ms^{-2}={\frac {m}{s^{2}}}$

## Homogeneity

This has shown how base units are used to form the derived units we know, the use of base units can also tell us whether an equation is Homogenous or not. Homogeneity can be used to see whether an equation is correct or not, but be warned, this does not necessarily mean that an equation is correct overall, it only says whether the base units are the same on both sides! The Speed equation is Homogenous because the product of the equation is $ms^{-1}$ , and we divided the distance (m) by the time (s), so the base units used on one side of the equation are the same as the base units used on the other side of the equation.

## Methods of Measurement

The base quantities are measured in different ways. The Kilogram is measured on scales, length is measured with a ruler, a Micrometre, Vernier Callipers, a Laser, etc. Current is measured with an Ammeter, Temperature with a thermometer, Time with a watch.
The amount of substance is deduced by equations, as is Luminous Intensity.

## Uncertainty

All measurements have a degree of uncertainty. This can be shown as an absolute uncertainty, or percentage uncertainty. (Percentage uncertainty) = 100 $\times$  (absolute uncertainty)/(measured value). The last figure in a number that is measured is called the doubtful figure.