Physical World and Measurement Physics Notes

→ We are living in the age of science. The cell phoney television, computer, e-mail, internet, audio-video system, e-mail, car, bus, train… all are the gifts of science to humans. Every field of human activity, is influenced by science.

The word science comes from the Latin verb ‘Scientia’ meaning ‘to know’. Science refers to a system of acquiring knowledge. This system uses observation and experimentation to describe and explain natural phenomena.

The term science also refers to the organised body of knowledge, people have gained using that system. Less formally, the word ‘science’ often describes any systematic field of study or the knowledge gained from it.

→ Fields of science are commonly classified along two major lines:

Natural Sciences, the study of the natural world.
Social Sciences, the systematic study of human behaviour and society.

→ The science that deals with non-living things is called Physical Science e.g., Physics, Geology, Chemistry, Astronomy, Oceanology, Astrology, Geography etc.

→ The science that deal with living things is called Biological Science. For example, Zoology, Botany, Anthropology, Entomology, Forensic Science etc.

→ Physics: It is the branch of science in which we study about nature and natural phenomena.

→ Unit: The chosen standard of the same kind taken as a reference to measure a physical quantity is called the unit of that quantity.

→ Fundamental unit: Those units, which can neither be derived from one another, nor can they be further resolved into other units, are called fundamental units.
The units of mass, length and time are called fundamental units.

→ Derived units: The units of all such physical quantities, which can be expressed in terms of fundamental units of mass length and time are called derived units.

→ Standard unit: A standard unit should be well defined, of suitable size, easily reproducible, easily accessible, should not change with time and also from place to place and with change in physical conditions, (temperature, pressure etc.)

→ Systems of units:

M.K.S. system
CGS system
FPS system
SI

→ SI: It consists of seven basic units namely metre, kilogram, second, kelvin, ampere, candela, mole and two supplementary units namely radian and steradian.

→ Dimension: Dimensions are powers raised on fundamental units to represent the physical quantity.

→ Dimensional formula: The relation of M, L and T with its dimensions to represennt the physical quantity is called dimensional formula.

→ Dimensional equation: The equation obtained, when a physical quantity is equated with its dimensional formula is known as dimensional equation.

→ Principle of homogeneity of dimensions:
It states that the dimensions of the fundamental quantities are same in-ear, a and every term one either side of physical relation.

→ Uses of the dimensional equation:
(A) To check the correctness of a physical relation. It is based on principle of homogeneity of units.

(B) To derive the relation between different physical quantities involved in a physical phenomenon.
It is also based on the principle of homogeneity of units.

(C) To convert on a system of unit to another.
Mathematically: n2 = n1\(\left(\frac{m_{1}}{m_{2}}\right)^{a}\left(\frac{L_{1}}{L_{2}}\right)^{b}\left(\frac{T_{1}}{T_{2}}\right)^{c}\)

→ The constant such as integers (1, 2, 3…., n and c do not have dimensions, (dimensional constant)

→ A physical constant may posess dimensions.

→ A physical variable may not possess dimensional (dimension less variable). For example angle (plane or solid) T-ratios, specific gravity, strain, refractive index, power factor, relative permittivity and relative permeability.

→ A dimensional physical quantity may possess units. For example angle is dimensionless but it has got units.

→ A physical quantity having dimensions must possess units.

→ Significant figures: The digits, whose values are accurately known in a particular measurement are called its significant figures.

→ Significant figures in calculations: Do not retain a greater number of decimal places in a
result computed from addition and/or subtraction or multiplication and/or division than in the observation which has the fewest decimal places.

→ Errors in measurement:

Constant error: When the result of a series of observation are in error by same amount the error is said to be a constant one. It is because of the inbuilt error in the measuring instrument.
Systematic error: A systematic error is one that produces an error of same sign. The zero error in instruments, error due to variation in physical condition or the personal error are the causes of systematic errors.
Random errors: The errors due to unknown causes are called random or chance errors. It is eliminated by taking the arithmetic mean of a large number of observations.
Gross error: The error due to sheer carelessness on the part of the experimenter are called gross error.
The neglect of sources of error, reading the instrument incorrectly or recording the observation carelessly are the causes of gross errors.
Absolute error: The magnitude of the difference between the true value and the measured value is called absolute error.
Absolute error = True value – measured value,
Relative error: The ratio of the mean absolute error to the true value is called relative error Absolute error
Relative error = \(\frac{\text { Absoluteerror }}{\text { true value }}\)
Also percentage error = \(\frac{\text { Absoluteerror }}{\text { true value }}\) ×100

→ Science: Science is the study of the nature and behaviour of natural things and the knowledge that we obtain about them.

→ Physics: Physics is the natural science that involves the study of matter and its motion and behaviour through space and time, along with related concepts such as energy and force.

→ Measurement: Measurement is the assignment of a number to characteristics of an object or event, which can be compared with other objects or events.

→ Mole: The mole is the unit of measurement for the amount of substance in the international system of units (SI.)

→ Parallax: Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines.

→ Least count: The smallest value that can be measured by the measuring instrument is called its least count.

→ Error: An ‘error’ is a deviation from accuracy or correctness.

→ Significant digit: Each of the digits of the number that are used to express it to the required degree of accuracy, starting from the first no-zero digit.