Units and Measurements

• Introduction

  • Need for Measurement
  • Role of Physics in understanding nature

• The International System of Units (SI)

  • Fundamental Units (Base Quantities)
    • Length -> Meter ($\text{m}$)
    • Mass -> Kilogram ($\text{kg}$)
    • Time -> Second ($\text{s}$)
    • Electric Current -> Ampere ($\text{A}$)
    • Thermodynamic Temperature -> Kelvin ($\text{K}$)
    • Amount of Substance -> Mole ($\text{mol}$)
    • Luminous Intensity -> Candela ($\text{cd}$)
  • Supplementary Units
    • Plane Angle -> Radian ($\text{rad}$)
    • Solid Angle -> Steradian ($\text{sr}$)

• Measurement of Length, Mass, and Time

  • Length
    • Direct methods (Meter scale, Vernier callipers, Screw gauge)
    • Indirect methods (Parallax Method for large distances)
  • Mass
    • Ordinary balances
    • Unified atomic mass unit ($\text{u}$) for atoms
  • Time
    • Cesium atomic clock (Standard time)

• Significant Figures

  • Definition and rules for determination
  • Rules for arithmetic operations
    • Addition and Subtraction
    • Multiplication and Division
  • Rounding off uncertain digits

• Accuracy, Precision, and Errors in Measurement

  • Accuracy vs Precision
    • Accuracy: Closeness to true value
    • Precision: Resolution or limit of measurement
  • Types of Errors
    • Systematic Errors (Instrumental, environmental, observational)
    • Random Errors (Unpredictable fluctuations)
    • Least Count Error
  • Expressing Errors
    • Absolute Error ($\Delta a$)
    • Relative Error ($\frac{\Delta a}{a}$)
    • Percentage Error ($\frac{\Delta a}{a} \times 100%$)
  • Combination of Errors
    • Sum or Difference
    • Product or Division
    • Powers/Exponents

• Dimensions of Physical Quantities

  • Dimensional Formula and Equation
  • Dimensional Analysis
    • Checking the correctness of equations (Homogeneity principle)
    • Deriving relations among physical quantities
  • Limitations of Dimensional Analysis