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What are Physical Quantities?
The quantities that can be measured directly or indirectly and by means of which we can define the laws of physics are known as physical quantities.
This is a scientific term and definition, but have you thought when did people realize that they need to be more specific on things and define physical quantities to be more efficient on work and exchange of goods. Before going to this, let’s learn all the basics first.
We all encounter a lot of physical things on a daily basis, of course because we live in a macroscopic world not in a quantum world, we feel physical things such as our own body, its weight, height, or from your toothbrush, table, books to the SpaceX Dragon.
Everything around us that we can see is physical, we can measure their weight, height, heat resistance, surface tension, etcetera. Now, let’s move on.
Physical Quantities are of Two types
- Fundamental Quantities (base quantities)
- Derived Quantities
Fundamental quantities are the quantities that do not depend on any other quantities to define themselves. There are only seven fundamental or base quantities.
- Length
- Mass
- Time
- Electric current
- Thermodynamic temperature
- Luminous intensity
- Amount of substance
While the quantities that can be derived in terms of fundamental quantities are known as derived quantities.
Please note that there is also a third type of physical quantity known as supplementary quantity, it contains on two quantities:
- Plane Angle (radian)
- Solid Angle (steradian)
You can study more about radian and steradian on Wikipedia.
Supplementary quantities are neither classified under fundamental quantities nor derived quantities. They don’t have any dimension as well. These are purely used for calculations and to put meaning in a lot of physical phenomena.
What is a "Unit"?
What is measurement?
Measurement is a process of finding out how large a physical quantity is as compared to a basic reference standard. And the reference standard that is used for any physical quantity is known as the unit of that physical quantity.
I hope you are not taking all these terms lightly, because when I was a student studying all these things, I always got bored easily and didn’t study with full focus. Well, I do regret it sometimes because these are the foundations of our modern world and science.
Do you know that without the concept of measurement, there would be no science, modern medicines, and healthcare. And also there would be no clocks or alarms to wake you up in the mornings. Well, I think it’s not so bad to have no concept of measurement, at least we can sleep long in the mornings and nobody would say that we are gonna be late for school or work.
Jokes aside, you should realize the importance of this subject while you are still making your scientific foundation. Measurement is essential for understanding the world, and it’s a fundamental part of scientific study and development. It allows us to explain the phenomena in the universe using math, and it’s critical for estimating success, failure, and progress.
Here’s a history fact.
Before the 18th century, there was no Universal system of measurement. Countries have their own measuring systems, and units were often based on human body parts, such as foot, hand, or pace. Afterwards, as the trade and industry expanded, the need for a common standard system for units started to become clear.
Fundamental Units are the units of fundamental quantities. Since there are 7 fundamental quantities, hence 7 fundamental units, as given below.
| Name of Quantities | Name of Units |
|---|---|
| Length | meter |
| Mass | kilogram |
| Time | second |
| Electric current | Ampere |
| Thermodynamic temperature | Kelvin |
| Luminous intensity | candela |
| Amount of substance | mole |
Similarly, derived units are the units of derived quantities. Derived units of some physical quantities are given below.
| Physical Quantities | Derived Units |
|---|---|
| Area | Meter2 (m2) |
| Volume | Meter3 (m3) |
| Density | kg/m3 |
| Potential | joule/coulomb or volt |
| Resistance | volt/ampere or ohm |
System of Units
A system of units is a complete set of units which is used to measure all kinds of fundamental and derived quantities.
Some most commonly used system of units are mentioned here as follows
CGS System (Gaussian System of units)
It uses centimeter (cm), gram (g) and second (s) as the fundamental units of length, mass and time, respectively.
FPS System (British Engineering System of units)
It uses foot (ft), pound (lb) and second (s) as the fundamental units of length, mass and time, respectively.
MKS System
It uses meter (m), kilogram (kg) and second (s) as the fundamental units of length, mass and time, respectively. The unit of force in this system is Newton (N).
International System (SI) of Units
It can be considered as a modernized and enhanced version of metric systems like CGS and MKS systems. This system contains 7 fundamental units and 2 supplementary units, as mentioned above.
Here are some units used for measuring small distances.
- 1 cm = 10-2 m
- 1 mm = 10-3 m
- 1 micron (m) = 10-6 m
- 1 nanometer = 10-9 m
- 1 angstrom (Å) = 10-10 m
- 1 picometer (pm) = 10-12 m
- 1 fermi = 10-15 m
And units used for measuring large distances.
- 1 Light year = 9.46 x 1015 m
- 1 Parsec = 3.08 x 1016 m = 3.26 light year
- 1 Astronomical unit (AU) = 1.496 x 1011 m
Dimensions of Physical Quantity
There is 1D, 2D, 3D or you can go however long you want to, it’s just that I can only imagine up to 3D (3rd dimension) in my mind. While going to 4D or higher, my mind goes like what is this? How long will it take me to get a clear picture of these in my mind? And so on.
First you understand 1D, 2D, 3D, 4D and if you still feel good and curious, go for higher dimensions like Kaluza - Klein theory in 5D, Octonian in 8D, or Bosonic string theory which is based on 26 dimensions. Wikipedia is a good source to start from.
Let’s come back to what we need to understand now.
Dimensions of a physical quantity are the powers to which the fundamental quantities are raised to represent the unit of that physical quantity.
For example, let’s see for one derived quantity that is speed.
Speed = distance/time = (length)/(second) = (length) x (second)-1 = [LT-]
So, the dimension for speed is [LT-1].
Refer to this table for dimension of fundamental quantities.
| Fundamental Quantity | Dimension |
|---|---|
| Length | [L] |
| Mass | [M] |
| Time | [T] |
| Electric current | [A] |
| Thermodynamic temperature | [K] |
| Amount of substance | [mol] |
As a part of your study, you can try to make the dimensions of some derived quantities, and see if you have got that correct or not. The important thing is to know the formula, then dimensions can be calculated easily.
Scalar and Vector Quantities
These are some simple terms, scalar means having only magnitude and not direction component, while vector means having both magnitude and a direction component.
Scalar quantities are those quantities that have only magnitude but not direction, such as mass, speed, time, power, work, volume, etcetera.
Vector quantities are those quantities that have both magnitude and direction, such as displacement, velocity, acceleration, force, momentum, torque, etcetera.
In mathematics or as a basics for physics, you should introduce yourself with scalar and vector calculations as well.
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