Physical World, Units and Measurements || Unit 1 || Applied Physics 1 || Polytechnic 1st semester 2022

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 Topics to Study are as follows -

  • fundamental and derived physical quantities,
  • dimensions and dimensional formulae,
  • principal of dimensional homogeneity,
  • measuring instruments and their least count.
  • direct and indirect measurements,
  • errors in measurements (systematic and random),
  • absolute error,
  • relative error and significant figures.
in the syllabus of polytechnics 1st semester 2022 bter -
  1. PHYSICAL WORLD, UNITS, AND MEASUREMENTS
    1. physical quantities
      1. fundamental and derived
      2. dimensions and dimensional formulae of physical quantities
      3. principal of homogeneity of dimensions
    2. measurements
      1. measuring instruments, least count
      2. types of measuring (direct, indirect)
    3. errors in measurements (systematic and random)
      1. absolute error
      2. relative error 
      3. significant figures.

Physical quantities:
 a physical quantity is a quantity which can be measured or weighed.

Unit: unit is a measurement or a process of determining the size of a physical quantity as compared to a basic reference standard. This basic reference standard value is called the unit of a particular physical quantity.

Properties of Units:

  1. it can be chosen arbitrarily but it should be accepted internationally.
  2. it should not be effected from time and place. if there is any change it must be known to us.
  3. it should be reproducible.
To express the measurement of a physical quantity. we need to know two things.
  1. unit: the unit in which any physical quantity is measured.
  2. numerical value: the magnitude of the physical quantity or we can say that how many times that unit is repeated or contained in the given physical quantity.
PHYSICAL QUANTITY = NUMERICAL VALUE * UNIT

Fundamental physical quantities:-
a physical quantity which is independent of other physical quantity or are usually not defined in terms of other physical quantities are called fundamental physical quantity.
Fundamental physical units: the units in which these quantities are being measured are called fundamental physical units.

These seven fundamental physical quantities their units and the symbols are shown in the following table:
  1. mass
  2. length
  3. time
  4. electric current
  5. thermodynamic temperature
  6. lumenious intensity
  7. amount of substance

The physical quantity which is not depending on other physical quantity and is other than fundamental quantity is called supplementary physical quantity.

There are two supplementary physical quantities which is given in following table -
  1. plane angle
  2. solid angle

Derived physical quantities and derived units:-
Physical quantities which can be expressed as a combination of repeatation of fundamental quantities are called derived physical quantities.
example - area, volume, velocity, acceleration etc.

System of Units:- No. of sustem of units for measurement were used in various parts of the world. Some of them are popular till today which are as follows-
  1. CGS - in this system the fundamental unit length is measured in centimeter and mass and time are measured in gram and second respectively.
  2. FPS system - in FPS system length is measured in "foot" which in equal to 30.14cm and mass and time are measured in pound and second respecticely. it is also known as british system.
  3. MKS system - in this system length, mass and time are measured in meter (m), kilogram (kg) and second (s) respectively.

SI SYSTEM -
in a comference (organised in 1971) a new system with units their proper symbols and abberviations was proposed and accepted internationally. It is called SI SYSTEM which is an abbreviation for systeme international.

  1. meter
  2. kilogram
  3. second
  4. ampere
  5. kelvin
  6. candela
  7. mole
Defination of supplementary units -
  1. plane angle - the angle subtended by an arc of a circle at its centre is called a plane angle.
  2. solid angle - the solid angle in angle subtended by a given or observed surface area of a spherical surface at its centre is called a solid angle.

Dimensions - The dimension of a physical quantity are the power (exponents) which raised to fundamental quantity. E.g. - dimension of a physical quantity simply shows that how many times a fundamental quantity used in a derived physical quantity.

DIMENSIONAL FORMULAE OF PHYSICAL QUANTITIES-

Principal of Dimensional Homogeneity:-
According to principle of dimensional homogeneity all the mathematical equations or formulae should have same dimensions on both the sides.

here we can understand it in the following steps:-
  • the physical quantities of same nature i.e., having same dimensions can be added or substracted. Thus we can not add or subtract area or volume. 
    • if P+Q and P-Q have same meaning means P and Q are of same dimensions.
    • if P=Q is correct then P and Q have same dimensions.
  • when any equations contains the multiplication or division or two physical quantities then dimension of the resultant quantity can be obtained by algebrically multipluing or dividing the dimensions of the involved physical quantities.
  • in any mathematical equation which is dimensionally correct need not to be physically.
Dimensional Analysis and its applications:-
mailny there are three applicatioins of dimensional analysis.
  1. to convert the magnitude of a physical quantity from one system of units to another.
  2. to check the dimensional consistency of a formula or mathematical equation.
  3. to establish the relationship among given physical quantities.

Measurement :-
Measurement is process of knowing that how many times the unit is contained as compared to a basic reference standard.

Need of Measurement :- 
  • Measurement has its own importance in today life and it is a base for exprimental sciences and technology.
  • to obtain accurate and precise value, it requires a measurement and in order to certify the rules and principles one requires the practical appratus or instruments.

Measuring instruments and least count :-
Accuracy of measurement means that how close the measured value is, to the true value while the smallest value of physical quantity which can be measured with an instrument is called its least count.
The least count of an instrument decreases then accuracy of the measurement increases. it is not necessary that a more precise value is more accurate too and more accurate may not more precise.

Let's discuss about some measuring instruments and their least count -
  1. A metre scale
  2. Vernier callipers
  3. Screw gauge

(1) A metre scale - although aboce instruments cannot be used to measure the very small or very large length but to understand the concept of least count these instruments are being discussed here.

with the help of metre scale we can measure the length from 1 mm to 100 cm accurately.
1 cm = 10 mm = 10 div
10 div = 10 mm = 1 cm
1 div = 1/10 cm = 0.1 cm
or
1 div = 1 mm

Here one division is smallest value which is equal to 1 mm that can be measured accurately. This is least count of this simple meter scale.


(2) Vernier calipers:- in comparision to meter scale if we want to obtain more precise value of physical quantity length then vernier caliper is used. Although it has more uses rather preciseness.

so we can observe here that up to what resolution or limit the quantity is measured i.e., vernier callipers can measure more precise value than metre scale.

(3) Least count of screw gauge

where pitch in defined as the distance moved by the screw head in one complete rotation of circular scale.

from above it is noteworthy that we can decrease the error and increase the accuracy of the measurement.

Types of Measurement :- There are mainly two types of measurement of physical quantity 
  • Direct measurement
  • Indirect measurement

(a) Direct Measurement :- A measurement in which an unknown quantity is measured directly with comparision to standard value is known as direct or absolute measurement. 
    In this type of measurement the insruments used having accuracy. Because of systematic errors involved during the course of measurement.
Example - Meter scale, vernier callipers, screw gauge, ammeter, voltmeter, speedometer, odometer, wrist watch, atomic spring balance, electron balance etc.

(b) Indirect Measurement :- Indirect measuremeny in which a physical quantity is not measured directly whereas the related parameters are measured.

 After that with the help of mathematical formula a physical quantity is determined using these observed parameters. This type of measurement is also known as comparitive measurement. The accuracy and precision of this type of measurement both are of high order. Determining of density of material of wire using screw gauge and radius of curvature of curved surface using spherometer is an example of indirect measurement.

Errors in Measurements :- Different types of instruments is used for measuring various physical quantities.

The measurement obtained from these instruments has a degree of uncertainty. This uncertainty related to measurement is called error.

error is a measurement can be determined by talking difference between observed value and standard value of a quantity. errors occurred in a measurement can be minimized by increasing sensitivity of instruments, avoiding personal error (wrong method) and by increasing number of observations. Before proceeding towards type of errors, we should discuss about measurement-related terms which are accuracy and precision.

  1. Accuracy :- it is a measure of how close the obtained value is to the true value of a quantity. by reducing eerror we can obtain more accurate measurement.
  2. Precision :- Precision is all about that up to what resolution the quantity is measured.
    1. if a quantity is measured with different devices having difference least counts.
Types of Errors :- 

Systematic Error :- The error which exists by virtue of a definite rule and occurs in one direction only are known as systematic errors it may be either positive or negative. If the measured value is greater than the true value the error is said to be positive and if it is lesser than the true value error is said to be negative.

Some of these errors are as follows :

(i) Instrumental error : These errors arise due to defect in instrument. i.e., due to improper calibration, designing or defective alignment. 

            Zero error of the instruments can be rectified by appluing zero correction.

(ii) Personal error : This type of error is likely to be occured due to carelessness of the observer or experimentalist. e.g., lack of proper setting of apparatus parallex error while reading the height of water in a beaker, position of hupright on the optical bench. These errors can be minimized by talking more observations and taking their mean.

(iii) Imprefection error : this error arises due to some 

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