## What are Units for Measuring?

Measuring is the comparison of a particular physical quantity with its reference value. A unit is a fixed physical quantity. The length is a physical quantity. A physical quantity is the product of a unit and the numerical value we need to compare with.

There are standard units where we usually call it SI units which is a unit selected for measuring a physical quantity satisfying certain conditions. The types of units include fundamental and derived units. Fundamental units are the physical quantities that are independent that is they do not depend on other quantities like mass, length, time. There are plenty of quantities in our life which need to be measured and compared. From the fundamental units the derived units can be obtained.

## Why Standard unit of Measurement Needed?

To progress our day-to-day lives, we need to convert things to make them common for all, so the conversion factor is essential. Since there are plenty of conversions happening for a number of factors, the units are always converted to their standard measurement. Hence the STANDARD CONVERSIONS are needed. There are plenty of systems that use various units like measuring quantities of the object's length, area, and weight. The seven base units for conversion to its standard units are:

- Length- meter
- Mass-kilogram
- Time-seconds
- Temperature-Kelvin
- Electric current-Ampere
- Amount of substance-mole
- Luminous intensity is candela

These are the fundamental units from where other units are derived.

## Types of Unit Systems

There are three types of unit systems or metric systems we use in Mathematics and Physics, which are** CGS unit systems **where the unit of length is centimeter, unit of mass is gram, and unit of time is seconds. The **FPS system** includes foot (for length), pound (for mass) and second (for time). The **SI unit **is the international system of units where it is like the MKS unit where the units include meter (for length), kilogram (for mass) and second (for time). The SI system also called the rational system of units is most commonly used. The fundamental SI units are Meter, Kilogram, Second, Ampere, Kelvin, Candela, and Mole.

### Metric system

This system was introduced in the early 1800s. It is the system used for measuring quantities like distance, weight, temperature, and length The fundamental; units of metrics are meter, kilogram, and second where it is used for measuring the length, mass, and time respectively.

## What is the British Gravitational (BG) System of Units?

It is a system of units used by mathematicians, scientists, and engineers during the 19th century especially in English-speaking countries like Britain. It consists of the units: foot for measuring the length or the distance, slug for the mass or weight of an object and second for time. This system is a non-SI base unit system where it is similar to the FPS unit system, FPS is foot, pound-force, and second for length, force, and time as base units respectively.

**The BG system or the FPS system**

The British engineers and mathematicians mainly use the units of force instead of mass hence the BG system uses the kilogram-force as a base unit in their system of measurement. The BG units for the primary units are

Mass-Slug, Length-feet, Time-seconds, and Temperature-Fahrenheit

One slug is a 32.2lbm unit. In the BG system, the mass unit is slug which is defined from Newton's second law of motion. It is derived from the pound-force as the mass will accelerate with 1 foot per second per second when one pound-force acts on it.

1 lbf=(1 slug)(1 ft/s^{2})

So 1 lbf pound-force acts on 1 slug of mass will give the mass an acceleration of 1 ft/s^{2}

The pound-force is referred to the force of gravity exerted on a mass of one pound of the given mass on the surface of Earth. During 18th century, this unit has been used in low precision unit measurement. The pound avoirdupois is the unit of mass and weight normally used by the English scientist. A single yard and pound became the official units in English countries like US and UK. The value of the pound is constant, where its value is 0.4535kg. The BG system uses the Fahrenheit unit for temperature, so let's say we need to use the thermodynamic temperature, the SI unit of energy is joule but it is actually a derived unit where it is defined as three base units-kg, m and s. But the thermodynamic temperature is expressed in Kelvin. Hence we can convert Kelvin to Fahrenheit temperature which can become the British gravitation system of the unit.

The weight of a mass that is the force can be calculated in the British gravitation unit as

F(lbf)=m(slugs)a(ft/s^{2})

where the a is the standard gravity or representing the BG unit of gravitational constant. Hence a=32.174 ft/s^{2}.

**Common standards of measuring units **

The conversion factors are

1 feet | 0.3048 m |

1 lbm | 0.453kg |

1 slug | 32.2 lbm |

1 Newton <mmmmm/td> | 0.2248 lbf |

1 Joule | 0.737 ft-lbf |

1 Watt | 0.737 t-lbf/s |

1 hp | 0.7457 Watt, 550 ft-lbf/s |

ºC (Celsius) | $\frac{5}{9}\left(\xb0F-32\right)\left(Farenheit\right)$ |

ºR (Rankine) | $\frac{9}{5}K\left(Kelvin\right)$ |

NOTE: 1 kg of gravitation force is equal to 9.8 N=2.2 lbf

## Practice Problem

1) Convert the length of 32 miles, weight 32 kg and 42 seconds to the BGS system units.

Solution: $168960ft,2.19264slugand42seconds$

$32miles=32miles\times \frac{5280ft}{1mile}$

$=168960ft$

$32kg=32kg\times \frac{0.06852slug}{1kg}$

$=2.19264slug$

42 seconds is 42 seconds itself in BG system.

2) Find which one of these belong to the BG system units

(a) Foot (b) inch (c) miles (d)pounds (e) milligram (f) yard (g) gallon (h) coulomb

Solution: (a) foot

Foot is the primary unit used to measure length in BG system.

## Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

- Bachelors in Technology/Engineering
- Masters in Technology/Engineering
- Bachelors in Science (Physics and Chemistry)
- Masters in Science (Physics and Chemistry)

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