Units and Measurement Fundamentals

Jul 30, 2024

Science and Fun - Lecture Notes: Units and Measurement

Introduction

  • Study based on combination and understanding
  • Chapter: Units and Measurement (2024-25 session)
  • Name: Ashu Gahi

Purpose of the Session

  • Connect the subject to daily life
  • Explain methods of units and measurement

Quantity

  • Quantity: Anything that can be measured
    • Example: Time, Mass, Force
    • Love, hate, or happiness cannot be measured

Units

  • Unit: A standard that helps in measuring any quantity
    • Example:
      • Mass: milligram, gram, kilogram
      • Time: second, minute, hour
  • Units are divided into two categories:
    • Fundamental Units: Accepted units (such as 7 fundamental units)
    • Derived Units: Derived from other units

Fundamental and Derived Units

  • Fundamental Units (7 in number)
    • Example:
      • Length: meter
      • Mass: kilogram
      • Time: second
  • Derived Units: Like Force (Newton) = kg * m/s²

Dimensions

  • Study of Dimensions:
    • Denotes the measure of any quantity
  • Example:
    • Mass = M
    • Length = L
    • Time = T
  • Dimension is an estimate but the Units depend on their form

Examples and Formulas

  • Force = Mass * Acceleration (F = m * a)
    • Dimensions of Force = ML T⁻²
  • Pressure = Force/Area
    • Dimensions = ML⁻¹T⁻²

Principle of Homogeneity

  • In any calculation, all terms should have the same dimensions
  • Equation:
    • If a term is on the LHS, it should be the same on the RHS

Applications of Dimensions

  1. Check if equation is dimensionally correct
    • If LHS = RHS in dimensions, the equation is dimensionally correct.
  2. Convert system of units
    • MKS (Meters, Kilograms, Seconds) to CGS (Centimeters, Grams, Seconds) etc.
  3. Derive formulas
    • Using dimensional analysis to derive relationships between quantities.

Significant Figures

  • Significant Figures: Indicates the accuracy of measurement
    • Non-zero digits are always significant
    • Leading zeros are not significant
    • Zeros between non-zeros are significant
  • Rules for Rounding Off
    • Add, Subtract: Final answer as per least decimal place
    • Multiply, Divide: Final answer as per the least number of significant figures

Conclusion

  • The materials learned in this chapter will definitely be used in the future. In our next class, we will work on more questions.