Notes on Measurements: Physical Quantities and Units

Introduction

Definition: Physical quantity is a measurable attribute of an object (e.g., mass).
Representation: A physical quantity is expressed as a magnitude and a unit (e.g., 10 kilograms).

Base Quantities
- Fundamental physical quantities, not defined by other quantities.
- Five base quantities to know:
  - Length (SI unit: meters)
  - Mass (SI unit: kilograms)
  - Time (SI unit: seconds)
  - Temperature (SI unit: kelvin)
  - Current (SI unit: ampere)
Derived Quantities
- Created by combining various base quantities.
- Examples:
  - Volume (Length × Breadth × Height)
  - Speed (Distance ÷ Time)

Example: Measuring small time fractions (e.g., 0.0001 seconds) can be expressed in standard form (e.g., 10^-6 seconds = microsecond).
Prefixes: Used to simplify naming of small or large quantities.
- Common prefixes:
  - nano (10^-9)
  - micro (10^-6)
  - milli (10^-3)
  - centi (10^-2)
  - deci (10^-1)
  - kilo (10^3)
  - mega (10^6)
  - giga (10^9)

Definition: Precision is the smallest unit an instrument can measure.
Examples of measuring instruments:
- Ruler: Measures up to millimeter precision.
- Vernier Caliper: Measures lengths with precision of 0.1 mm (best for 1 to 15 cm).
- Micrometer Screw Gauge: Measures small lengths with precision of 0.01 mm (best for lengths < 2.5 cm).
- Stopwatch: Typical precision up to three decimal places, but usually recorded to one decimal place to reduce errors.

To measure the period of a pendulum:
- Record time for multiple cycles (e.g., 20 cycles) to reduce error.
- Calculate average duration for more accurate results.

Parallax Error: Error due to eye positioning at an angle to measurement markings.
- Prevention: Align eye directly with the measurement marking when taking readings (e.g., measuring liquid levels).