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:
\(1,000,000 = 1 \cdot 10^6\)
\(0.000,000,000,000,2 = 2 \cdot 10^{-12}\)
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.
\(Speed = m/s = L/T = L \cdot T^{-1}\)
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.
\(Density = M/L3 = M \cdot L^{-3}\)
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.
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