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# Physical Quantities and Units

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The physical quantities in physics are what we can measure or sense in an object or a phenomenon. Let’s take a rock as a simple example.

A rock has several properties, and we can feel some of them using our senses:

• Mass: the rock is composed of atoms that have mass. When gravity acts upon this mass, it generates what we call ‘weight’.
• Volume: if you hold the rock, it takes up space in your hands. The space that the rock occupies is its volume.
• Length: you can see how large the rock is – how wide, long, or tall.
• Temperature: if the rock is exposed to sunlight on a warm day, you can feel the heat transferred from the light to the rock. On a cold day, you will feel the opposite. The temperature is a measure of thermal energy in the object, which is related to the kinetic energy of the molecules or atoms that compose it.

There are other, more complex properties that you can sense, such as electrical charge or luminosity.

Figure 1. Mass pulled by gravitational force (weight) is one of the easiest properties for us to sense.

## Electrical charge

Another physical quantity that we can sense is the electrical charge of an object.

A classic example of this is when you rub your pullover against a balloon. It will exchange a charge with the balloon via the friction. Small electrical charges from the balloon will stick to the pullover, which will gain more charge than it had before.

If you pass your hand over the pullover close a metal object, the electrical charge will jump to the metal and give you a small shock. This happens because of the charge difference between your pullover and the metal. The more you rub your pullover against the balloon, the larger the electrical discharge will be when making contact with the metal.

This small electrical charge you can feel is commonly named electrostatic charge, and it is defined as a lack or excess of electrons in a material – in this case, your pullover.

## Luminosity

Luminosity is another property we can feel with our senses – in this case, our sense of sight.

If you go for a run in the late afternoon, you will feel the difference in environmental luminosity. The source of this is the sun, and your eyes register the luminosity using light-sensitive cells.

As the light dims towards sunset, less light enters your eyes. This lack of light causes a lower signal to the cells, which informs you about the change in luminosity.

Figure 2. We can sense the change in luminosity at sunset.

## Amount of substance

There are quantities that we cannot sense correctly, such as the number of molecules that compose an object, which is known as the ‘amount of substance’. We can, however, sense the difference in this physical quantity after making some deductions and using our intuition.

We know intuitively that a piece of iron weighs more than a piece of carbon. We might take a sample of both, which have the same number of atoms or ‘X’. Looking at the periodic table, we find that the carbon atom has six neutrons and six protons, while the iron atom has 26 neutrons and protons.

In atomic chemistry and atomic physics, neutrons and atoms are the particles that have most of the atom’s mass, meaning that the sample of iron weighs more even if it has the same X number of atoms as the carbon atom.

This ‘X’ quantity in science is known as the mol.

There is another property that we can measure and sense, which is not related to any object. This property is ‘time’, and its units are seconds.

## Time

Time is the property that tells us in which direction processes should go, as in the following examples:

On a cold day, a warm mug of tea or coffee gets cold because of the heat escaping to the cold air. The process always goes warm to cold if nothing intervenes. The period it takes from warm to cold is what we call a period of time.

The breaking of a mug always occurs in one direction – from having a complete mug to having a broken one.

## Physical quantities and measurements

In science and engineering, we have many different units to measure the properties of an object (its physical quantities). In the modern world, we use a system of units named the SI system.

### Units

Units are values that have been agreed upon, serving to compare the physical quantities of an object. There are units for every physical property, from the mass to the quantity of a substance. The units used for the seven basic physical properties are named basic units, one of which is the kilogram.

### Physical quantities and units

Physical quantities allow us to compare two or more objects or phenomena indirectly by using units we know, such as the metre or kilogram. Here is a simple explanation:

We can define a single length or ‘base length’ to compare all other lengths. If we make arrangements for everyone to use the same length, this becomes a value to measure other lengths against.

That value is what we call a ‘unit’, and the comparison of an object against it is what we know as ‘measuring’. That comparison against a value we know and keep constant is how units help us to measure. Let’s take another simple example that will be useful to define a very well-known unit.

A rock has a certain weight, but we need a reference to compare it against. The reference, in this case, is the weight of a litre of water. The rock can weigh a fraction of this unit, or it can weigh several times more than this unit.

If our rock weighs 2.3 times the weight of the litre of water, it means that its weight is two times the litre of water plus 30%.

Before 2019, the weight of a litre of water was the base for the unit we now call ‘kilogram’ in the SI system of units. In our example above, the rock, therefore, weighs 2.3 kilograms.

### The SI system

The SI system is a standard that contains units for the seven basic properties. The system also uses prefixes and mathematical notations (standard forms) to name and annotate large and small numbers, respectively.

Prefixes are placed before the unit’s name to indicate its value. Examples of this are the millimetre and the decametre.

Standard forms are systems of power to express large and small values. Examples of this are:

## Physical quantities and their SI units

All physical quantities that we can measure have been standardised, and so each property has a related unit:

• Length, measured in metres and its derivatives.
• Mass, measured in kilograms and its derivatives.
• Temperature, measured in Kelvin and other units as the Celsius and Fahrenheit.
• Electrical charge, measured in Amperes.
• Luminosity, measured in candelas.
• Amount of substance, measured in mols.
• Time, measured in seconds.

### Derived units

The SI system of units also contains derived units that are used to measure more complex quantities. The derived units are a combination of the seven basic units. A brief list of some derived units can be found below:

• Area, related to the diameter, which is a form of length.
• Speed or velocity, related to time and length.
• Volume, related to length.
• Density, related to volume and mass.
• Energy, related to mass, time, and length.

Each derived unit measures a more complex property, and some of them have their own names. For example, the unit of energy is the Joule, while the unit of pressure is the Pascal.

## Dimensional formulas

Units possess dimensions, which is the name given to the physical quantities they describe. The metre and kilogram have dimensions of ‘length’ and ‘mass’, respectively. Each of the seven basic physical properties we can measure works as a dimension:

• Metre, dimension ‘length’.
• Kilogram, dimension ‘mass’.
• Second, dimension ‘time’.
• Kelvin, dimension ‘temperature’.
• Mol, dimension ‘quantity of substance’.
• Ampere, dimension ‘electrical charge’.
• Candela, dimension ‘luminosity’.

Each derived unit possesses a combination of dimensions. This expression is sometimes named dimensional formula and expresses the properties composing the units.

### Dimensional expressions of derived units

To express any quantity in its dimensional form, we need to express it in its basic units and then replace this with the dimensions. Two basic examples are given below:

Express the speed in its dimensional form. As speed is expressed in metres per second or m/s, its dimensions are length and time, expressed as L and T.

Express density in its dimensional form. Density is equal to kilograms over volume; kilograms have dimensions of mass or M, and volumes have dimensions of cubic meters or length L at the 3rd power.

Each unit has its own dimensional form.

## Physical quantities and units - Key takeaways

• Physical properties are the things we can measure in an object, better known as the properties of an object.
• There are seven basic properties that we can sense and measure. They are temperature, mass, length, luminosity, electrical charge, time, and the amount of substance the object is composed of.
• To measure an object’s properties, we use units. Unit values are agreed on and used to measure the object’s properties.
• Nowadays, we use the SI system, which is composed of units to express the seven basic properties and uses prefixes and mathematical notation to express large and small quantities.
• There are also derived units made of the basic units, which are used to express an object’s more complex behaviours, such as velocity.

## Frequently Asked Questions about Physical Quantities and Units

The physical quantities of a physical object or a phenomenon are the properties you can sense or measure in an object.

In the SI system, the seven basic units are: metre, kilogram, ampere, mol, candela, second, and kelvin.

Each unit has its own dimensional formula.

## Final Physical Quantities and Units Quiz

Question

What is a unit?

A unit is a standard reference used for measuring.

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Why are units important?

Units are important because they allow us to reproduce measurements.

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What is the SI system?

The SI system is a standard system of units used for measurements.

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How many basic units does the SI have?

The SI has seven basic units.

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How are derived units composed?

They are composed of the SI basic units.

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What are the seven basic units of the SI?

The second, mole, kilogram, kelvin, metre, candela, and ampere.

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What is hertz the derived unit of?

Hertz is the derived unit of the second.

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Does the SI system use Celsius or Kelvin to measure temperature?

Kelvin.

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If you use the length of an object to measure another object, are you measuring by reference or using units?

You are measuring by reference.

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What is the symbol for a metre?

m.

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What is the symbol for an ampere?

A.

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The speed of an object is measured using which units?

Speed is measured in metres and seconds.

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Which measurements do you need to combine in order to measure speed?

Distance and time.

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What is the purpose of the kilogram as a unit of measurement?

The kilogram is used to measure the mass of an object.

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What is the symbol of the kilogram?

kg.

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What is the symbol for a candela?

Cd.

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What is measured in candelas?

Candelas measure the amount of light.

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Is the newton a derived unit?

Yes, it is derived from kilograms, metres, and seconds.

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What is the symbol for a mole?

mol.

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Is Kelvin a derived unit or a basic unit?

It is a basic unit.

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What is a physical quantity?

A property that we can measure.

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How are physical quantities and units related?

One is the property we measure, while the other is the amount of that property.

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Can time and mass as physical quantities be negative?

No, they cannot.

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Physical quantities can be extensive or …?

Intensive.

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Does an extensive property depend on the mass and size of the object?

Yes, it does.

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Do intensive properties depend on an object’s mass and size?

No, they don’t.

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Is force an elemental physical quantity?

No, it isn’t.

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How are derived physical quantities composed?

Derived physical quantities are composed of elemental physical quantities.

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Can a physical quantity be zero?

Yes, it can.

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Define the mass of an object.

Mass is the amount of matter in an object.

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Are physical quantities and units related in physics?

Yes, they are.

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Are weight and mass the same, or are they different?

They are different. Mass is the amount of matter an object contains. Weight includes the pull of gravity, and is a force.

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What is a scalar quantity?

A scalar quantity can be described without knowing its direction. The quantity is called a magnitude and is just a number.

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What is a vector?

A vector is a quantity where you need the direction and value to know what is happening. The value of the quantity is known as magnitude.

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Is time a scalar quantity?

Yes, it is.

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Is speed a scalar quantity?

Yes, it is.

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Is velocity composed of scalar or vector quantities?

Velocity is composed of length and time. Both are scalar quantities.

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Can a physical quantity be negative?

No, it can’t.

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What happens in a negative flow of charge?

Charge flows in the opposite direction.

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Can a temperature measurement be less than zero?

Yes, it can. It depends on the temperature reference.

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Why is the SI unit system important?

It provides a standard to measure quantities.

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How do you interpret one pascal using basic SI units?

One pascal = one kilogram accelerated at one metre per second.

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Is there another way to read one Pascal?

Yes, as one Newton over a square metre.

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Does one Pascal equal one Newton over one square metre?

Yes, it does.

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How many ways does the SI system provide to represent quantities?

Three: prefixes, form factors (standard form), and symbols.

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What are the three ways the SI system represents quantities?

Prefixes, form factors, and symbols.

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Which countries still use systems of units other than the SI?

USA, Canada, Liberia, Thailand, and the United Kingdom.

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What are prefixes?

Prefixes are the words used in the SI system to replace full quantity names, e.g. one kilogram (prefix kilo) instead of one thousand grams.

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Give an example of a prefix.

All of these.

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Is cm the abbreviation or the symbol for centimetres?

It is both.

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