# Physical measurements

Measurement is the process of comparing an unknown quantity with another quantity of its kind ( called the unit of measurement ) to find out how many times the first includes the second , Key elements of measurement process are the physical quantity , measuring tools and units of measurement .

Measurements translate our daily observations into quantities amounts that can be expressed in terms of numerals , for example , describing the temperature of a person as being high is scientifically inaccurate , better to measure it using a thermometer to know its value .

## Physical Quantities

Quantities such as mass , length , time ….etc. are called physical quantities and we need to measure them accurately in our daily life , Physical quantities can be classified into the fundamental physical quantities and the derived physical quantities .

The fundamental physical quantities are the physical quantities which can not be defined in terms of the other physical quantities such as length , time and mass , Length ( L ) is defined by itself , No other physical quantities is needed to define length , The length of a ruler = 20 cm .

The derived physical quantities are the physical quantities which can be defined in terms of the fundamental physical quantities such as volume , speed and acceleration , Volume is derived from length , Volume of a cuboid = length × Width × Height .

Physical Quantities is a shorthand formula to give a physical illustration of a particular indication , The relation among physical quantities can be expressed by mathematical equations which are shorthand illustration of a particular indication ( Physical Meaning ) .

For example : when a moving body covers a distance ( d ) in time ( t ) , then its velocity ( v ) can be expressed as , Velocity = displacement ÷ Time , V = d ÷ t , This relation is called physical mathematical equation .

Physical Quantities and measuring tools

## Measuring tools

Man in ancient eras used parts of his body as tools of measurement such as the arm , the hand span and the foot as the tools to measure length , Man used natural phenomena as tools of measurement such as the sunrise , the sunset and the Moon phases to measure time .

The measuring tools have been tremendously developed in the context of the great industrial evolution next to the Second World War , consequently , these tools were very helpful to man in describing phenomena accurately and exploring facts .

The used measuring tool depends on the physical quantity to be measured , some ancient and modern tools for measurement , To measure length , There are some tools such as Meter tape , Ruler , Vernier caliper & Micrometer .

To measure Mass , We use Roman scale , Beam balance , Analog scale , Digital balance , To measure Time , We use Hourglass , Clock , Stopwatch & Digital watch .

## Measuring length using the vernier caliper

### Measuring short lengths precisely

Calipers have two jaws ( each is attached to a scale ) which are a fixed scale ( One division = mm ) , and a sliding ( vernier ) scale that can slide along the fixed scale and graduated into a number of divisions , ( one division = 0.99 mm ) , The division on the vernier scale is smaller than the division on the fixed scale by 0.01 mm .

The object is placed between the two jaws of the caliper and gently pressed , the reading on the fixed scale is recorded just before the zero mark of the sliding scale lines up .

You have to find out the mark on the vernier scale which most closely lines up with one of the marks on the fixed scale , multiply the number of divisions taken from the vernier scale by 0.01 mm .

The vernier reading = No. of divisions × 0.01

## Measuring the surface area of a cylinder

Assume that the radius of the cylinder base is ( r ) and its height is ( h ) , Its base area = π r² , The lateral surface area = base circumference × Height = 2π r h

### Determination of the area of the cylinder base

Put the cylinder base on a graph sheet and mark its base , Remove the cylinder and measure the diameter of its base ( 2r ) by the ruler , Calculate the radius ( r ) and then find the base area which is circular in shape ( π r² ) .

### Determination of the lateral area of the cylinder

Measure the height of the cylinder ( h ) , Calculate the base circumference that equals = 2π r , The lateral area = 2π r × h

### Another method to determine the lateral area of the cylinder

Wrap a cardboard sheet  around the cylinder exactly one complete turn , Straighten the cardboard sheet to get a rectangle of length equal to the base circumference and width equal to the cylinder height , Measure the length of this circumference , Multiply the circumference length × height to obtain the lateral area of a cylinder .