1. Physical World and Measurement

🧠 Introduction

Physics is the science of measurement. To understand and describe physical phenomena accurately, one must be able to measure physical quantities and express them in terms of units. This chapter lays the foundation for the entire subject by explaining how physical quantities are measured, their units, types of errors in measurement, and the importance of dimensions.

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📏 Physical Quantities

Definition: Quantities that can be measured and expressed in numbers are called physical quantities. They are of two types:

Type	Description
Fundamental Quantity	Cannot be broken down into simpler quantities. (e.g., length, time, mass)
Derived Quantity	Obtained by combining fundamental quantities. (e.g., velocity = distance/time)

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📐 Units

Definition: A standard of measurement for a physical quantity.

Types of Units

1. Fundamental Units – Basic units for fundamental quantities.
2. Derived Units – Formed from fundamental units. (e.g., m/s, N, J)

SI Units (International System of Units)

Quantity	Unit	Symbol
Length	meter	m
Mass	kilogram	kg
Time	second	s
Temperature	kelvin	K
Electric Current	ampere	A
Amount of Substance	mole	mol
Luminous Intensity	candela	cd

Supplementary Units (Now Derived)

Quantity	Unit	Symbol
Plane Angle	radian	rad
Solid Angle	steradian	sr

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📊 Systems of Units

System	Length	Mass	Time
CGS	cm	g	s
MKS	m	kg	s
FPS	ft	lb	s

SI system is based on the MKS system and is universally accepted.

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🧪 Measurement

Definition: Comparing an unknown quantity with a known standard unit.

Important Terms

• Accuracy – Closeness to the true value.
• Precision – Closeness of repeated measurements.
• Error – Difference between the measured value and the true value.

Types of Errors

1. Systematic Errors – Arise from flaws in the instrument or observer.
   • Instrumental Error
   • Observational Error
   • Environmental Error
2. Random Errors – Irregular and unpredictable.
3. Gross Errors – Due to human mistakes.

Absolute, Relative, and Percentage Error

• Absolute Error = |Measured Value – True Value|
• Relative Error = Absolute Error / True Value
• Percentage Error = (Relative Error) x 100

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🔢 Significant Figures

These indicate the precision of a measurement.

Rules

1. All non-zero digits are significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros are NOT significant.
4. Trailing zeros are significant if there is a decimal point.

Operations

Operation	Rule
Addition/Subtraction	Final answer has decimal places equal to the least in the input data
Multiplication/Division	Final answer has significant figures equal to the least in the data

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📐 Dimensions and Dimensional Analysis

Dimensions express physical quantities in terms of basic quantities.

Fundamental Dimensions

Quantity	Dimension Symbol
Length	[L]
Mass	[M]
Time	[T]
Electric Current	[A]
Temperature	[K]
Amount of Substance	[mol]
Luminous Intensity	[cd]

Dimensional Formula

Representation of a physical quantity in terms of fundamental dimensions.

Examples:

• Velocity: [M^0L^1T^-1]
• Acceleration: [M^0L^1T^-2]
• Force: [MLT^-2]
• Work/Energy: [ML^2T^-2]

Applications

1. Check correctness of physical equations.
2. Convert units.
3. Derive relations among physical quantities.

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🧮 Unit Conversion

Use dimensional analysis:

Example: Convert speed from km/hr to m/s.

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🧠 Example Problems

1. If a measurement gives values 4.25 m, 4.26 m, 4.24 m, find the average and error.
   • Average = (4.25 + 4.26 + 4.24)/3 = 4.25 m
   • Absolute Error = Max deviation from average = 0.01 m
2. Using dimensional analysis, check if
   • LHS:
   • RHS: → Correct

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📚 Revision Tips

• Memorize SI units and their symbols.
• Understand difference between precision and accuracy.
• Learn how to derive dimensional formulas.
• Practice dimensional analysis to verify equations.
• Solve numericals on significant figures and errors.