Choosing correct units and Dimension of Physical quantity

Explain  the reason of using different smaller and larger units for measuring a particular quantity.

To measure a particular quantity we use both smaller and larger units as per  requirement. For example. To measure the length of a room , we use metre(m) to measure the distance between two cities we use kilomete(km). For the measurement of the distance of a star from the earth the commonly used unit is light year. Because kilometer is considered to be a very small unit in this case.

To measure the length of a very small quantity we consider smaller unit of lengths as centimetre, millimeter, micron etc. For example to measure the thickness (or diameter) of a wire, we use centimetre or millimeters. In this case unit taken as metre is absurd.    If the thickness of  a paper measured in millimeter(mm) is 1 mm, then expressed in metre is 0.001 m, which look odd.
Therefore we should carefully examine that what unit we have to take for the measurement of a thing . If we chose a thing to measure we should take its standard unit.

Dimension of a physical quantity
Having defined the units of physical quantities, we now briefly mention the concept of dimensions of other physical quantities.
The dimension of a physical quantity is represents the powers to which the fundamental units have raised in order to obtain the derived units of the physical quantity.
The dimensions of length, mass and time are expressed in L, M and T’ respectively. Dimensions generally represents the nature of the units only. It does not indicate the magnitude of the units.

Discussion : Speed has the derived units –cm/sec., km/hr., mi/hr. etc. The most  common feature in them is that they all are  derived by dividing a unit of length by a unit of time. So the dimension of speed will be L/T or  LT ^-1    where ‘L’ stands for length and ‘T’ stands for time. Similarly different units of acceleration e.g ., cm/sec², ft/sec², mi/hr² etc. represents a unit of length divided by square of unit of time. Hence its dimension will be L/T² or L/T ^-2.
Following the same reasoning ,force which is the product of mass(M) and
aceleration (LT ^-2), has the dimension MLT ^-2.

 Measuring Instruments

 As the measurement of length, volume, mass and time  was thoroughly taken into consideration in the previous article, we shall not go through it any more.

In this article we shall rather present a brief description of some appliances for measurement of length which enables greater accuracy to be obtained than is possible by mere eye-estimation.

 To measure the different physical quantities, the commonly used measuring devices are the following.
1.    Ordinary scale (metre scale) use to measure the length of an object.

                                                            
2.     Common balance - it is used to measure the mass of a body.

                                                                            
3.     Spring balance – it is used to measure the weight of a body.

                                                              
4.     Measuring cylinder – it is used to measure the volume of a body a liquid.
        It is also used to measure the volume of a solid by displacement method.

                                                                   
5.    Clock – it is used to measure the time.

                                                               
6.    Stop watch – it is used to measure a time interval between two events such as                  race, sports , football etc.

                                                                

System of Units

 System of Units

A complete sets of units, both fundamental and derived, for all physical quantities is called a system of units. There are now mainly three systems
in common use, each of which derives its name from the initial letters of the fundamental units upon which it is based. These are:

(1 C.G.S. system, having centimetre, gram and second a fundamental units .
(2) M.K.S system, in which fundamental units are metre, kilogram and second.
(3) F.P.S system, based on foot,pound and second as fundamental units.

A fourth system of unit, namely S.I., (systeme internationale) is introduced in 1960, is described in the appendix.

The first two namely C.G.S. and  M.K.S. systems are also called metric system
and obviously metric standards of length and mass are used in them.

The F.P.S on the other hand based on the British standards.

The metric system has a definite advantage over the F.P.S. system calculations
are made easier , since the various multiples and submultiples of unit are
related by simple power of 10 .

On the other hand the F.P.S system has however , no such advantage .The
relation between the various subdivisions of a unit are rather obscure and inconvenient , such as 1 foot =12 inches ,1 yard =3 feet, 1 mile=1760 yds.
Even an inch is divided into 8ths, 16ths, 64ths to measure very small lengths.
Units of volumes of liquids.

The unit of volume of liquids, through derived ones, should be mentioned
especially, since these have different names. Thus , in metric system unit of volume is litre which is defined as the volume of 1 kg of water, at normal atmospheric pressur and the temperature of its maximum density (at 4^°C).

 Standard.

A question still remains weather there is a unique standard  for a particular  fundamental quantity . Unfortunately, the answer is ‘no’. World  is still divided into two major portions using two different standards for each of length and mass.
     In metric  system the standard of length is taken as the distance between two fine lines engraved on a platinum-irridium bar kept at International Bureau of Weight and Measures in Paris maintained at  0^°C and called International Proto-type Metre.

Defination of Metre: A metre is defined as 1,553,164.1 times the waves length of the red line in the spectrum of cadmium.

Defination of Kilogram : International Proto-type Kilogram is the standard of mass in the metric system and  is defined as the mass of a platinum-irridium cylinder kept together with Proto-type metre  at Serves near Paris ,and the copies being distributed all over the world .It was also intended to be the mass of 1000 cc. of water at its maximum density.

 Defination of second : The standard of time called mean solar second (second) is the same in both systems and is defined as 1/86400 of the average length of a solar day (mean solar day) throughout the year. This definition of a second , although 
Satisfactory for our daily routine, fails to satisfy modern scientist since the mean solar day varies from year to year and century to century.
Hence, in 1946, International Bureau of Weights and Measures defined the second as the time in which a cesium atom(which has only one isotope) undergoes  9,192,631,770 internal vibrations.

There are also some bigger units of length they are  namely

1. Kilometer(km)             2. Light year             3. Astronomical unit(AU)

1 kilomatre is equal to 1000 metre
i.e 1 kg = 1000 m or(10³m)

2. 1 Light year is the distance traveled by light in Vaccum in one year.
     1 Light year = Speed of light x 1 year
                           = 3x10³m/s x 1 year
                           = 3x10³m/s x (365x24x60x60)s
                           =9.46x10¹² km
3. Astronomical unit(AU) : It is defined as the distance of the earth from the
     sun.
        1 A.U =1.499x 10 metre.

Smaller units of length . There are some smaller units of length they are
                                             namely, (SI unit of length is metre)

     1 metre = 100 cm =1/100m
     1 metre = 1000mm=1/1000m
     1 metre = 1000000 micron  or 1 micron =10^-6 m
    1 Nanometre =10^-9m

Classification of physical quantity

How a physical quantity can be classified?


A physical quantity can be classified into two broad categories:

(i)Scalar quantity                     (ii) Vector quantity


Scalar quantity: The physical quantities which have only magnitude but no direction are called scalar quantity.


Description: The rod is 2 metres long’, the vessel contains 200 gms. Of water’ and we  waited there for five hours’. In these expressions , 2 metre long , five hours , 200 gms , we have some ideas of magnitude  of a length , mass , and a time . But length mass and time has nothing  to do with any direction. Such quantities which gives the idea of some magnitude but are not associated with any direction are called scalar quantities.

Example : Volume, density, energy, , speed , mass, distance, work, time, power, electric current , mechanical advantage , pressure, etc are the examples of  scalar quantities.



Vector quantity : The physical quantities which have magnitude as well as direction is called vector quantity.


Description: The car is moving is moving with a velocity of 40 km/hr ‘east’ 

here east is representing the direction of the car and 40 represents the magnitude of the car .So in this example both magnitude and direction are coming so definitely it is a vector quantity, because it fulfils the condition to be a vector . A very important thing with regard to vector is that it is represented by an arrow sign (→ ). If in a problem vector word is not mentioned but the arrow sign (→ ) is there  it is a vector quantity.


Example : Displacement, velocity, acceleration, momentum, force, weight, temperature, electric field , magnetic field, retardation ,moment of force etc.


What observation should be taken for the choice of unit ?


The selection of unit to measure   a  physical quantity should have the following properties.

1.The unit should be convenient size.

2.The unit should be well defined .

3.The unit should not be changed with space , time and temperature.

4. It should be reproducible.



Fundamental quantities and derived quantities

Each of the various physical quantities is expected to have its own unit and a standard. But is found that nearly all physical quantities(except temperature,

Electric current and luminous intensity)can be derived from the units of three

physical quantities , namely, length, mass , time.



Fundamental quantity : The quantities which are independent of any other quantity  or which can neither be changed nor be related  to any other quantity

are called  fundamental quantities.


Example : Length, mass, time, temperature, current, luminous intensity atc are the examples of fundamental quantities.



Derived quantities : The quantities which depend upon the fundamental quantities  or which can be expressed in terms of the fundamental quantities i.e derived from the fundamental quantities are called derived quantities.


Example : velocity, acceleration, energy, force, momentum, etc are the exaples of derived quantities.

Discussion :The velocity of a moving body is obtained by dividing the distance traveled by the body with time taken to travel the distance . When distance is expressed in the unit of length as centimetres and time is expressed in seconds then,

,unit of velocity = unit of length / unit of time = cm/second=cm/sec.

MEASUREMENT AND THEIR DEVICES

SYSTEM OF MEASUREMENT AND MEASURING DEVICES

By saying measurement a question arise in the mind that what is measurement?. The answer is as simple is that measurement is the numerical value multiplied by its unit.


Lets begin our study.

Some basic knowledge you have to acquire.


What is physical Quantity?


The quantities which we can measure are called physical quantity.

It is the measurable property of a matter. As per example, length, mass, density, velocity are all physical quantity because they all can be measured .For the measurement of a physical quantity we must know two basic things.


(i)The unit in which the quantity is to be measure

Example: If we have 10 kg of mangoes and we are measuring in litre  it is not the right process we have to measure it in the unit of Kg not in liter. 


(ii) The numerical value which express how many times the unit used

       is contained the given quantity.


What is unit?


To measure any physical quantity, we must first have a unit of measurement. By unit of a physical quantity we mean a definite and convenient amount of that quantity. The magnitude of a physical quantity is obtained by comparing it with the unit.The factor by which a quantity is bigger or smaller than the corresponding unit is called the numerical measurement of that quantity. As  per example “a room is 5  metre  long clearly showing that the physical quantity being measured is length, and the unit chosen  for measuring the room is metre and the numerical value  is 5.


In the previous para we have seen that the unit of length is metre. But what is a metre? To define it we evidently require a standard length. Similarly we require a standard for every other unit. A standard is the physical embodiment of a unit. It fixes up and preserves the size of the corresponding unit. A unit may be of same size as that of the standard or may me a multiple or submultiple of it. The standard Proto-type of kilogram is the standard of  mass, the units of mass being kilogram(kg.), metric ton(10³kg.), gram(10^-3kg.) etc.



All physical quantities have units?


The answer or this question is as simple is that there are many physical quantities which does not have any units .The question arise in the mind that if a thing is in the category its first condition is that it would be measurable

And for measuring a unit is required so how a quantity is physical but not measurable . As in the field of physics there are some physical quantities that does not have any units there are the exceptions  like six fingers in one hand of a human ,The reason is that for a non-unit physical quantity that those physical quantities which are expressed as the ratio of the same physical quantity do not have units .

Example : atomic weight of elements, specific gravity, refractive index.

Introduction

What is Physics?

The word physics comes from the Greek scripted word  Physis which means Nature.

It is only based upon the natural phenomenon.So while you are going to study physics just keep in mind that you are studying about the nature .The things which are happening in the nature the thing which are happening around and you are associated with the facts.

Starting the study of physics we should know some small but knowledgeable things.

Are you readdy

be calm ,keep patient.

Defination of physics : The branch of science which deals about the study of natural phenomenon is known as physics.

Modern defination of physics-The branch of science which deals with the study of  Matter,Energy,Light,

  optics, Electromagnetic waves is known as physics.                                                  

Details- It is related to the study of matter and energy and how they interact each other.

Physics cannot exist without a physicists ther are the one who discovered the basic laws related  to physics.There are the names of some physicists who work for the benefits of physics and gave physics its real position.

                                                                

Albert Einstein

Brian Cox

Newton

Branch of physics – Before studying physics we should know how it is divided . As we know that there are many branches of science so there exist different branches of physics also.

I am listing you the different branches of physics.

		Mechanics
Heat	Magnetism	Current Electricity	Optics
Electrostatics	General properties of matter	Vibrations and Waves	Modern Physics