2.2 SI units and unit conversions

SI units form the backbone of measurement in science and engineering. They provide a universal language for expressing physical quantities, ensuring consistency and clarity in calculations and communication across disciplines.

Unit conversions are essential skills for working with SI units. By understanding prefixes and conversion factors, engineers can easily switch between different scales and units, making problem-solving more efficient and reducing errors in calculations.

SI Units and Base/Derived Units

International System of Units and Base Units

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• Internationally recognized system of units provides a standardized way to measure physical quantities
• Consists of seven base units that are considered fundamental and cannot be broken down further
• Base units include meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), and candela (luminous intensity)
• All other units in the SI system can be derived from these base units through multiplication or division

Derived Units and Scientific Notation

• Derived units are formed by combining base units to represent other physical quantities
• Examples include newton (force), joule (energy), watt (power), and volt (electric potential difference)
• Derived units often have special names and symbols to simplify expressions and calculations
• Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10
• Useful for representing very large or very small quantities in a concise manner
• Helps to avoid writing out long strings of zeros and makes calculations more manageable

Unit Prefixes and Conversions

Prefixes for Multiples and Submultiples

• SI prefixes are used to indicate multiples or submultiples of units, allowing for convenient expression of quantities at different scales
• Prefixes for multiples include kilo- (10^3), mega- (10^6), giga- (10^9), and tera- (10^12)
• Prefixes for submultiples include milli- (10^-3), micro- (10^-6), nano- (10^-9), and pico- (10^-12)
• Prefixes are attached to the unit symbol without a space (kilometer, milligram, microsecond)
• Using prefixes helps to keep numerical values within a manageable range and reduces the need for scientific notation in many cases

Unit Conversion Factors and Dimensional Analysis

• Unit conversion factors are ratios of equivalent quantities expressed in different units, allowing for the conversion between units
• Conversion factors are derived from the relationships between units within the SI system or from known physical constants
• Examples include 1 kilometer = 1000 meters, 1 hour = 3600 seconds, and 1 joule = 1 newton × meter
• Dimensional analysis is a problem-solving method that uses unit conversion factors to convert between different units while ensuring that the final result has the correct units
• Involves multiplying the initial quantity by a series of conversion factors, canceling out units until the desired unit is obtained
• Helps to organize calculations, check for errors, and maintain consistency in units throughout the problem-solving process