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CGS, FPS, and MKS Systems of Units in Physics

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The CGS, FPS, and MKS systems are different sets of standards used to measure physical quantities like length, mass, and time. Long ago, people in different parts of the world used their own ways to measure things, which made it very difficult to trade goods or share scientific discoveries. To solve this, scientists created organized systems where everyone agreed on which units to use for basic measurements, ensuring that a "meter" or a "gram" meant the exact same thing to everyone, everywhere.

Understanding these systems is important because they form the foundation of all physics and engineering. While most of the world now uses a modern version called the SI system, you will still see these older systems in textbooks, historical documents, and even in daily life. Knowing how to switch between them allows you to understand how big an object is or how much it weighs, regardless of which country the information came from or which century it was written in.

Key Concepts

  • The CGS System: This stands for Centimeter, Gram, and Second. It was often used in labs for measuring small things. In this system, length is measured in centimeters (cm), mass is measured in grams (g), and time is measured in seconds (s).
  • The FPS System: This stands for Foot, Pound, and Second. It is also known as the British Imperial System. In this system, length is measured in feet (ft), mass is measured in pounds (lb), and time is measured in seconds (s).
  • The MKS System: This stands for Meter, Kilogram, and Second. It was designed for measuring larger, everyday objects. In this system, length is measured in meters (m), mass is measured in kilograms (kg), and time is measured in seconds (s). The MKS system eventually became the basis for the modern International System of Units (SI) that we use in schools today.
  • Base Quantities: All three systems focus on the same three fundamental "base" quantities: length (how long), mass (how much matter is inside), and time (how long it takes).

How It Works

Every system of units works by following a specific set of steps to ensure measurements are consistent across the world. First, a standard physical object or a natural constant is chosen as the "base" unit. For example, in the MKS system, a specific distance was originally defined as one meter. Once the base unit is set, scientists can derive other units for more complex things like speed or force.

To use these systems, you must follow these steps:

  1. Identify the System: Look at the problem to see if it uses centimeters (CGS), feet (FPS), or meters (MKS).
  2. Keep Units Consistent: Never mix units from different systems in the same calculation. If your length is in meters, your mass must be in kilograms.
  3. Use Conversion Factors: If you need to move from one system to another, you use a fixed number to multiply or divide. For example, 1 meter in MKS is exactly 100 centimeters in CGS.
  4. Calculate Derived Units: Once you have your base units, you combine them. In MKS, speed is meters divided by seconds (m/s). In CGS, speed is centimeters divided by seconds (cm/s).

Worked Example

Problem: A toy car travels a distance of 5 meters in 2 seconds. Calculate its speed in the MKS system, and then convert that speed into the CGS system.

Step 1: Calculate Speed in MKS In the MKS system, we use meters for length and seconds for time. Speed = Distance / Time Speed = 5 meters / 2 seconds Speed = 2.5 m/s (MKS System)

Step 2: Convert to CGS Units In the CGS system, length must be in centimeters. We know that 1 meter = 100 centimeters. Distance in CGS = 5 meters × 100 = 500 centimeters. Time remains the same because both systems use seconds. Time = 2 seconds.

Step 3: Calculate Speed in CGS Speed = Distance / Time Speed = 500 centimeters / 2 seconds Speed = 250 cm/s (CGS System)

Common Misconceptions

  • The "Time" Unit: Many students think that because length and mass change between systems, time must change too. However, the Second is the standard unit for time in CGS, FPS, and MKS. It never changes between these three systems.
  • Weight vs. Mass in FPS: In the FPS system, people often use "pound" to mean weight (force), but in basic physics, the pound is treated as a unit of mass. This can be confusing, so it is important to check if a problem refers to "pound-mass" or "pound-force."
  • MKS is the same as SI: While MKS is the foundation of the SI system, they are not exactly the same. The SI system includes four more base units (like Kelvin for temperature and Ampere for electricity) that the basic MKS system does not include.

Real-World Applications

The MKS system is the most common system used by engineers and architects to build houses, bridges, and cars because its units are a convenient size for human-made structures. The CGS system is frequently used by chemists and physicists when they are working with very small amounts of chemicals or tiny particles where meters and kilograms would be too large to manage easily. Meanwhile, the FPS system is still used today in construction and aviation in countries like the United States and the United Kingdom, where you might hear people measuring height in feet or weight in pounds.

To master physics, you must remember that CGS, FPS, and MKS are just different "languages" for the same physical reality. Whether you measure a desk in centimeters, feet, or meters, the desk stays the same size; only the numbers and labels we use to describe it change based on the system we choose.

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