Overview
This lecture covers the basics of Units and Measurements in physics, including physical quantities, systems of units, unit conversions, dimensional analysis, significant figures, error analysis, and relevant formulas.
Physical Quantities and Units
- Physical quantities are measurable properties (e.g., length, mass, time).
- Each physical quantity has a numerical value and a unit (e.g., 60 kg: 60 = value, kg = unit).
- A unit is an internationally accepted standard for measurement (e.g., meter, kilogram).
- Units ensure consistency, communication, and comparison across measurements.
Types of Units
- Fundamental units: Seven SI base units—length (meter), mass (kilogram), time (second), current (ampere), temperature (kelvin), amount of substance (mole), luminous intensity (candela).
- Derived units: Formed by combining fundamental units (e.g., velocity: m/s, force: kg·m/s²).
- SI (MKS) system uses meters, kilograms, and seconds.
- Other systems: FPS (foot, pound, second), CGS (centimeter, gram, second).
Supplementary Quantities
- Not classified as base or derived: plane angle (radian), solid angle (steradian).
- Plane angle formula: arc length/radius.
- Solid angle formula: surface area/(radius)².
Unit Conversions and Prefixes
- Conversion: n₁u₁ = n₂u₂; changing units changes numerical value inversely.
- SI prefixes: giga (10⁹), mega (10⁶), kilo (10³), centi (10⁻²), milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹).
Dimensional Analysis
- Dimension: powers to which fundamental units are raised in a quantity (e.g., force: [M¹L¹T⁻²]).
- Used to check equation validity (principle of homogeneity: both sides must have same dimensions).
- Can derive formulas by equating dimensions (e.g., time period of pendulum ∝ √(L/g)).
- Limitations: cannot find constants, apply to non-algebraic functions, or determine vector/scalar nature.
Significant Figures
- Indicate precision of a measured value.
- Rules: all non-zero digits significant; zeros between non-zeros are significant; leading zeros non-significant; trailing zeros significant if decimal is present.
- During addition/subtraction, result has minimum decimal places; in multiplication/division, result has minimum significant figures.
Error Analysis
- Absolute error: |true value − measured value|
- Relative error: absolute error/true value
- Percentage error: relative error × 100
- For multiple readings, mean value is used as true value.
- Error propagation: errors add in addition/subtraction; for multiplication/division/powers, relative errors add.
Key Terms & Definitions
- Physical quantity — measurable property like length, mass, time.
- Unit — standard used to quantify a physical quantity.
- Fundamental unit — basic SI unit not derived from others.
- Derived unit — unit formed from fundamental units.
- Dimensional formula — expression showing powers of base quantities.
- Absolute error — difference between true and measured value.
- Relative error — ratio of absolute error to true value.
- Significant figure — digits that indicate measurement precision.
Action Items / Next Steps
- Practice unit conversions, dimensional analysis, and error calculations.
- Memorize SI base units, prefixes, and key dimensional formulas.
- Complete assigned homework problems, especially on error analysis and significant figures.
- Review relevant NCERT textbook exercises for further practice.