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
- Basic (Fundamental) Units
- Quantities that are independently defined, not derived from other units.
- Example: mass (kg), length (meter), time (second).
- 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
- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Leading zeros in decimal numbers are not significant.
- Trailing zeros in decimal numbers are significant.
- Trailing zeros in a whole number without decimal are not significant.
Arithmetic Operations with Significant Figures
- Multiplication/Division: Result should have the same number of significant figures as the least number in any of the data.
- 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