# Physics Lesson 1.1.1 - Introduction to Units and Systems of Units

Welcome to our Physics lesson on Introduction to Units and Systems of Units, this is the first lesson of our suite of physics lessons covering the topic of Units. Systems of Units. Fundamental and Derived SI Units, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

## Introduction to Units and Systems of Units

Lets start by considering a practical example that you could do at home. Suppose you are told to measure the length of your sitting room but you don't have any measuring tool at home. Therefore, you decide to go at the garden and take a stick you found there. The stick is quite straight, so you think it is fit for this task. You take the measurements and obtain a result, let's say "8 sticks long" for the length of the sitting room. However, your sister doesn't approve this method of measurement. She decides to use her pencil to measure the room's length. After taking the result, she finds the sitting room of your house is 27 pencils long. If the person who told you to take the measurements asks about the result, he will get confused when hearing two different versions of the answer.

Which of you is right? Why?

Despite the fact you have obtained two different results, you are both right if you made correctly the process of length's measurement (i.e. if you measured the required length in a straight line, or if you placed the rod or pencil at the ending position of the previous measurement, etc. Hence, there something else that is wrong here. Can you guess what?

We will try to answer this question and many others in the following section.

### What is a unit? Why do we need units? Why it is necessary to have commonly accepted systems of units?

In Physics, a unit is a widely accepted standard of measurement. Giving the confusion arisen due to the use of many methods of measurement for the same thing in different parts of the world, scientists decided to hold a meeting in which they established a commonly accepted method (protocol) in measuring things. The aim was to allow all people around the world to understand the result of a certain measurement, in addition and most importantly, it allows the use of the science books published in different countries with the sharing of information in a common standard that can be replicated.

Nowadays, many processes in daily life use universal operating standards. If the RAM of your laptop is faulty, you can easily replace it as many different laptop brands use the same type of RAM. All types of Debit Cards are same size, so they all fit a given ATM whereever it may be located. COVID-19 tests work the same for all people around the world, regardless their nationality, race, gender, etc. These and many more examples show the importance of the standardized methods. Units are one of the most classical examples in this regard.

A correct result of a measurement must contain two elements: the magnitude of measurement (the numerical value) and the unit of measurement. You cannot say, "the length of my scarf is 82." The person who is hearing you will immediately reply, "82 what?" Also, you cannot say "I have a pendant which is some cm long." In both cases, the information you are giving is not complete. You must say, "the length of my scarf is 82 cm (or inches)" and "I have a pendant which is 52 cm long" if you want to provide a full information of what you are referring to.

### What are the main systems of units used in science and daily life?

There are two main systems of units used in science and daily life today:

1. The SI (or metric) System of Units
2. The Imperial (or English) System of Units

The first one (SI System) is recognized in science and technology while the other (Imperial System) is mostly used in daily activities in English-speaking countries.

Below, we will discuss the most important features of each system of units.

#### The SI (or metric) System of Units

By definition, units are classified in two main categories: a) Fundamental and b) Derived units. Fundamental units are considered as each of a set of unrelated units of measurement, which are arbitrarily defined and from which other units are derived. Thus, it is obvious that all derived units are obtained by the combination of two or more fundamental ones.

In this regard, the meeting (congress) we discussed before, in which the most well-known scientists around the world discussed setting up a commonly accepted system of measurements and units, established 7 fundamental units. They are:

1. The meter (symbol: m); it is used to measure length.
2. The kilogram (symbol: kg); it is used to measure mass.
3. The second (symbol: s); it is used to measure time.
4. The ampere (symbol: A); it is used to measure electric current.
5. The kelvin (symbol: K); it is used to measure temperature.
6. The mole (symbol: mol); it is used to measure amount of substance or particles in matter.
7. The candela (symbol: cd); it is used to measure light intensity.

There are also two supplementary units which are neither fundamental nor derived. They are:

1. The radian (unit of the plane angle) (symbol: rad); it is used to measure the amount of surface area enclosed by an angle's boundary lines (sides)
2. The steradian [unit of the solid (space) angle] (symbol: sr; is used to measure the amount of space bordered by a solid (3-D) angle.

The other units not included in the above list, are all derived. As stated before, they are all combinations of two or more fundamental units.

For example, the unit of Area (square metre) is a derived unit as 1m2 = 1m × 1m. Although there is only the unit of length (metre) mentioned here, the square metre is a derived unit because the metre here is mentioned twice, i.e there is a combination of metre and metre itself. Or, the unit of speed (metres / second) is derived as it is obtained by the combination of two fundamental SI units.

#### The Imperial (or English) System of Units

The differences between the Imperial and SI Systems of Units consist in the units of length and mass. The other units are the same. Thus, in the Imperial System of Units, the unit of length is the yard (yd). The conversion factor between yard and metre (which is the corresponding the unit of length in the SI system is 1 yard = 0.9144 m.

The unit of mass in the Imperial system is the pound (lb). The conversion factor is 1 lb = 0.4536 kg.

##### Example 1

Convert the following units into the required ones.

23.0 m = _____ yd

5.40 yd = _____ m

20.400 kg = _____ lbs

230.3 lbs = _____ Kg

##### Solution

The conversion factor between yd and m is 1yd = 0.9144 m. This means 1 m = 1 / 0.9144 yd = 1.09 yd.

Likewise, the conversion factor between lbs and kg is 1lb = 0.4536 kg. Thus, 1 kg = 1/0.4536 lbs = 2.20 lbs.

Therefore, we have:

23.0 m = 23 m / 0.9144 yd/m = 25.15 yd

5.40 yd = 5.40 yd × 0.9144 m/yd = 4.938 m

20.400 kg = 20.400 kg × 2.20 lbs/kg = 44.88 lbs

lbs = 230 lbs × 0.4536 kg/lbs = 104.328 kg

Remark!

In addition to the two abovementioned systems of units, there is also another important system which is based on the first three SI units, i.e. the units of length, mass and time. This system is known as the CGS system (centimetre, gram, second). As you see, the only difference with the SI system is that it considers as units two submultiples of the corresponding SI units (metre and kilogram). The rest of the quantities in both systems are the same. The CGS system is particularly useful when dealing with small amounts of materials or with physical quantities such as density, liquid pressure, etc.

Look at the next Physics Tutorial: Length, Mass and Time. Dimensional Analysis for more info in this regard.

## More Units. Systems of Units. Fundamental and Derived SI Units Lessons and Learning Resources

Units and Measurements Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial
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Notes
Revision
Questions
1.1Units. Systems of Units. Fundamental and Derived SI Units
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
1.1.1Introduction to Units and Systems of Units
1.1.2What are multiples and submultiples of units?

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