Systems of Units: MKS, CGS, and SI

Introduction

Measurement is fundamental to science. It allows us to describe the world quantitatively - how long, how heavy, how fast, and so on. But to communicate measurements clearly and accurately, scientists need standardized systems of units. Without standard units, a length measured in one place might mean something different elsewhere, leading to confusion and errors.

Over time, several systems of measurement units have been developed. Among these, the MKS (Meter-Kilogram-Second), CGS (Centimeter-Gram-Second), and SI (International System of Units) systems are the most important in physical science. Each system defines fundamental units for length, mass, and time, which form the basis for all other measurements.

In this section, we will explore these three systems, understand their fundamental and derived units, learn about the standards behind them, and practice converting between them.

MKS System

The MKS system is based on three fundamental units:

• Meter (m) for length
• Kilogram (kg) for mass
• Second (s) for time

This system was developed to provide a coherent set of units for scientific work, especially in physics and engineering. The MKS system is the foundation for the SI system, which extends it further.

The meter was originally defined as one ten-millionth of the distance from the equator to the North Pole along a meridian. The kilogram was once defined by a physical platinum-iridium cylinder kept in France, and the second was based on Earth's rotation.

Applications: The MKS system is widely used in engineering and physics, especially where larger units are convenient. For example, distances in meters and masses in kilograms suit everyday scales better than centimeters and grams.

CGS System

The CGS system uses smaller fundamental units:

• Centimeter (cm) for length
• Gram (g) for mass
• Second (s) for time

This system was popular in the 19th and early 20th centuries, especially in fields like electromagnetism and chemistry, where smaller units were more practical.

Note: 1 meter = 100 centimeters, and 1 kilogram = 1000 grams.

Applications: The CGS system is still used in some scientific fields, such as astrophysics and certain branches of physics, due to its convenience with small-scale measurements.

SI Units

The International System of Units (SI) is the modern, globally accepted system for measurement. It builds upon the MKS system and defines seven base units from which all other units are derived.

The seven SI base units are:

The SI units are defined today using fundamental physical constants, making them stable and universal. For example, the meter is defined by the distance light travels in vacuum in 1/299,792,458 seconds, and the kilogram is defined using the Planck constant.

Measurement Standards

Measurement standards ensure that units are consistent worldwide. Historically, units like the meter and kilogram were defined by physical objects:

• Meter: A platinum-iridium bar stored in France served as the standard meter.
• Kilogram: A platinum-iridium cylinder known as the "International Prototype Kilogram" was the mass standard.

However, physical objects can change over time, so modern definitions use universal constants:

graph TD    A[Physical Artifacts] --> B[Limitations: Wear, Damage]    B --> C[Need for Stable Standards]    C --> D[Fundamental Constants]    D --> E[Modern Definitions of Units]

The International Bureau of Weights and Measures (BIPM) in France oversees these standards, ensuring global uniformity.

Unit Conversion

Since different systems use different units, converting between them is essential. Conversion relies on known relationships between units.

Always use dimensional analysis - a method where units are treated algebraically - to ensure conversions are done correctly.

Worked Examples