System of Units

System of Units

A system is a set of things working together as parts of a mechanism or an interconnecting network. In simple words a group of interrelated elements. So a system of units is a set of interlinked standards of measurement.

In physics as a branch of science, we are going to study the following systems of units:

1. Foot Pound Second System of Units (FPS)
2. Meter Kilogram Second System of Units (MKS)
3. International System of Units (SI)
4. Centimeter Gram Second System of Units (CGS)
5. Supplementary System of Units

Foot Pound Second System: In this system of units the three fundamental quantities of Length, Mass, and Time are measured in the standard units of Foot, Pound (lb), and Second (s).

Foot is the thousandth part of three hundred and four meters i.e., 0.3048 m. Compared to inches a foot is 12 times in magnitude where one inch is equal to the hundredth part of two hundred and fifty-four centimeters i.e., 1 foot =0.3048 m =12 inches = 12 x 0.254 cm = 30.48 cm.

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Length Converter – From Feet

Type a value in the Feet field to convert the value to Meters, Centimeters, and Inches:

Meters:

Centimeters:

Inches:

function convertLength() { var feet = document.getElementById(“feetInput”).value; var meters = feet * 0.3048; var centimeters = feet * 30.48; var inches = feet * 12; document.getElementById(“outputMeters”).innerText = meters.toFixed(2); document.getElementById(“outputCentimeters”).innerText = centimeters.toFixed(2); document.getElementById(“outputInches”).innerText = inches.toFixed(2); }

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Pound: Pound is a unit for measurement of mass mostly used in British imperial and United States customary system of units. One pound mass in FPS System is equal to 0.45359237 kg in SI System of Units

Converter from Pound to Kg and Grams

Converter from Pound to Kg and Grams

Type a value in the pound field to convert the value to kg and grams:

Pound:

Kg:

Grams:

function convertWeight() { var pounds = document.getElementById(“pound”).value; var kilograms = pounds * 0.45359237; var grams = pounds * 453.59237; document.getElementById(“outputKg”).innerText = kilograms.toFixed(2); document.getElementById(“outputGrams”).innerText = grams.toFixed(2); }

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Second: It is used to measure time and is the same in FPS, MKS, CGS, and SI as standard units of measurement.

Meter Kilogram Second System: This system of units is a physical system of measurement in which length is measured in the standard unit of meter, mass in kilograms, and time in seconds. It is mostly used in engineering as a coherent system of units. In this system, all the physical quantities have one unit satisfying the coherent relationships to these base units of length, mass, and time. This system of units is more practical.

International System (SI): A system of units is said to be coherent if all of its units are either base units, or are derived from the base units without using any numerical factors other than one. The International System of Units is coherent as it satisfies this condition.

Centimeter Gram Second System (CGS): This system of units is a variant of the metric system of units with a centimeter as a unit of measurement for length, a gram for mass, and a second for time as base. In many subfields of science, it is preferred over SI. This system is not a coherent system of units. It is also called the Gaussian System of Units and is the most common of electromagnetic unit systems.

Supplementary System:

This system of units includes the geometrical units. Plane Angle and Solid angle are the two units available in the supplementary System of Units.

Let’s explore the relationship between plane angles and solid angles.

1. Plane Angles: A plane angle is a measure of the rotation between two intersecting lines or planes. It is usually expressed in radian (rad) or degrees (°). The unit of plane angle is dimensionless.
2. Solid Angles: A solid angle measures the amount of field of view covered by an object from a specific point (the apex). It is expressed in steradians (sr) and it is also a dimensionless unit. One steradian corresponds to one unit of area on the unit sphere surrounding the apex.
3. Interconversion: The value of a solid angle can be derived from a plane angle. The unit of solid angle (steradian) represents a coherent derived unit equal to a square radian.

Converter from Degrees to Radians

Converter from Degrees to Radians

Type a value in the degree field to convert the value to radians:

Degree:

Radian:

function degToRad(deg) { // Formula: rad = deg * (π / 180) let rad = deg * (Math.PI / 180); return rad; } function convertToRad() { let deg = document.getElementById(“deg”).value; let rad = degToRad(deg); document.getElementById(“outputRad”).innerText = rad.toFixed(3); }

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Converter from Radians to Steradians

Converter from Radians to Steradians

Type a value in the radian field to convert the value to steradians:

Radian:

Steradian:

function radianToSteradian(radian) { // Formula: steradian = radian^2 let steradian = Math.pow(radian, 2); return steradian; } function steradianToRadian(steradian) { // Formula: radian = sqrt(steradian) let radian = Math.sqrt(steradian); return radian; } function convertToSteradian() { let radian = document.getElementById(“radian”).value; let steradian = radianToSteradian(radian); document.getElementById(“outputSteradian”).innerText = steradian.toFixed(2); }

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Converter from Steradians to Radians

Converter from Steradians to Radians

Type a value in the steradian field to convert the value to radians:

Steradian:

Radian:

function steradianToRadian(steradian) { // Formula: radian = sqrt(steradian) let radian = Math.sqrt(steradian); return radian; } function convertToRadian() { let steradian = document.getElementById(“steradian”).value; let radian = steradianToRadian(steradian); document.getElementById(“outputRadian”).innerText = radian.toFixed(3); }

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Common Inter-Conversion Factors for Physical Quantities

Here are some common interconversion factors for physical quantities between different unit systems like MKS (SI), CGS, and FPS:


Length
1. 1 meter (m) = 100 centimeters (cm) = 39.37 inches (in)
2. 1 centimeter (cm) = 0.01 meters (m) = 0.3937 inches (in)
3. 1 foot (ft) = 0.3048 meters (m) = 30.48 centimeters (cm)


Mass
1. 1 kilogram (kg) = 1000 grams (g) = 2.20462 pounds (lb)
2. 1 gram (g) = 0.001 kilograms (kg) = 0.00220462 pounds (lb)
3. 1 pound (lb) = 0.453592 kilograms (kg) = 453.592 grams (g)

Force
1. 1 newton (N) = \(10^5\) dynes (dyn) = 0.224809 pounds-force (lbf)
2. 1 dyne (dyn) = \(10^{-5}\) newtons (N) = \(2.24809 \times 10^{-6}\) pounds force (lbf)
3. 1 pound-force (lbf) = 4.44822 newtons (N) = \(4.44822 \times 10^5\) dynes (dyn)

Pressure
1. 1 pascal (Pa) = \(10^{-1}\) baryes (Ba) = \(1.45038 \times 10^{-4}\) pounds per square inch (psi)
2. 1 barye (Ba) = 10 pascals (Pa) = \(1.45038 \times 10^{-5}\) pounds per square inch (psi)
3. 1 pound per square inch (psi) = 6894.76 pascals (Pa) = 68.9476 baryes (Ba)

Energy
1. 1 joule (J) = \(10^7\) ergs (erg) = 0.000947817 BTU (British Thermal Units)
2. 1 erg (erg) = \(10^{-7}\) joules (J) = \(9.47817 \times 10^{-11}\) BTU
3. 1 BTU = 1055.06 joules (J) = \(1.05506 \times 10^{10}\) ergs (erg)

These conversions should cover most of the common physical quantities you might encounter. If you need more specific conversions or additional quantities, feel free to ask!

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(1) MKS (SI-units) CGS – University of Cambridge. https://www.damtp.cam.ac.uk/user/gold/pdfs/teaching/131004-ufk.pdf.
(2) PHYSICAL CONSTANTS, UNIT SYSTEMS, AND CONVERSION FACTORS. https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781118493052.app1.
(3) Fundamental Physical Constants and Unit Conversion in SI (MKS …. https://www.mathworks.com/matlabcentral/fileexchange/23908-fundamental-physical-constants-and-unit-conversion-in-si-mks-gaussian-cgs-units.
(4) CGS System of Units Converter – Omni Calculator. https://www.omnicalculator.com/conversion/cgs-system-of-units.
(5) CGS and MKS Units – The Public’s Library and Digital Archive. https://www.ibiblio.org/units/cgsmks.html.

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