📏 Units and Measurements

1. Introduction to Physical Quantities

A physical quantity is a property of a material or system that can be quantified by measurement. To measure any quantity, we need a standard reference called a Unit.

📏 Fundamental and Derived Quantities

Fundamental Quantities: Quantities that are independent of other quantities (e.g., Mass, Length, Time).

Derived Quantities: Quantities that are derived from fundamental quantities (e.g., Velocity = Length/Time, Force = Mass × Acceleration).

2. The SI System (Systeme International)

The internationally accepted system of units. It has 7 base units:

  • 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)

3. Errors in Measurement

No measurement is perfectly accurate. The difference between the true value and the measured value is called an error.

Types of Errors

1. Systematic Errors: Errors that tend to be in one direction (either positive or negative). E.g., zero error in an instrument.

2. Random Errors: Errors occurring irregularly due to random and unpredictable fluctuations.

Percentage Error = (Δa / a_mean) × 100% Where Δa is the absolute error and a_mean is the true/mean value.

4. Dimensional Analysis

Dimensions represent the nature of a physical quantity. We use square brackets [ ] to denote dimensions.

Key Dimensions

Velocity: [M⁰ L¹ T⁻¹]
Acceleration: [M⁰ L¹ T⁻²]
Force: [M¹ L¹ T⁻²]
Work/Energy: [M¹ L² T⁻²]