Units and Measurements Lecture notes

Jul 16, 2024

Units and Measurements Lecture

Introduction

Story to Illustrate Concept: Chawal (Rice) Story

  • Confusion about quantity of rice needed from the store.
  • Highlight the importance of numbers (quantity) and units (kilograms).
  • Conclusion: Understanding numbers and units is essential for measurement.

Key Concepts

  • Number (Quantity): Specifies how much of something is there.
  • Unit: Specifies the scale or standard of measurement (e.g., kg, meters).

Units and Measurements Overview

  • Class 11th Physics topic
  • Worldwide standardization of units to avoid confusion.

Identifying Units

Basic Units and Derived Units

  1. Basic (Fundamental) Units
  • Quantities that are independently defined, not derived from other units.
  • Example: mass (kg), length (meter), time (second).
  1. Derived Units
  • Derived from a combination of basic units.
  • Example: speed (meters/second), area (meters²), volume (meters³).

SI Units (Système International d'Unités)

  • Globally accepted standard system for measurements.
  • Total of seven basic units in SI system:
    • Length: meter (m)
    • Mass: kilogram (kg)
    • Time: second (s)
    • Electric current: ampere (A)
    • Thermodynamic temperature: kelvin (K)
    • Amount of substance: mole (mol)
    • Luminous intensity: candela (cd)

Physical Quantities and Units

Physical Quantities: Quantities that can be measured (e.g., weight, length, volume, temperature).

Non-Physical Quantities: Quantities that cannot be measured (e.g., happiness, excitement).

Significant Figures

  • Used to represent the precision of a measurement.
  • Only the digits that carry meaning contributing to its precision.

Rules for Counting Significant Figures

  1. All non-zero digits are significant.
  2. Zeros between non-zero digits are significant.
  3. Leading zeros in decimal numbers are not significant.
  4. Trailing zeros in decimal numbers are significant.
  5. Trailing zeros in a whole number without decimal are not significant.

Arithmetic Operations with Significant Figures

  1. Multiplication/Division: Result should have the same number of significant figures as the least number in any of the data.
  2. Addition/Subtraction: Result should be rounded to the least number of decimal places in any of the data.

Rounding Off Significant Figures

  • Rounding Up: Increase the last digit by one if the first non-significant digit is greater than 5.
  • Rounding Down: Do not change the last digit if the first non-significant digit is less than 5.
  • If equal to 5:
    • Increase if the preceding number is odd (rounds up).
    • Do not increase if the preceding number is even (rounds down).

Dimensional Analysis

  • Dimensional Formula: Expresses physical quantities in terms of the basic quantities (like mass M, length L, time T).
    • Example: Acceleration (L T⁻²), Work (M L² T⁻²)

Applications: Verification of Physical Equations

  • Checking the dimensional consistency of equations.
  • Not all dimensionally correct equations are physically correct, but dimensionally incorrect equations are always wrong.

Dimensional Constants and Dimensional-less Constants

  • Dimensional Constants: Constants which have dimensions, e.g., gravitational constant.
  • Dimensionless Constants: Constants which have no dimensions, e.g., π (Pi).

Conclusion

  • Units and measurements are crucial for precise and standardized scientific communication.
  • Mastery over units, measurements, significant figures, and dimensional analysis ensures clarity and accuracy in physical computations.

Homework: Calculate the dimensional formula for pressure using the formula Pressure = Force/Area.

  • Hint: Force = mass × acceleration, Area = length²