All the fundamental laws of physics are expressed using different physical quantities.
To solve physical problems, like how much force is needed to send the rocket into space? How fast is the car moving? We need physical quantities. These physical quantities are expressed using numbers and units.
In this article, we will learn what physical quantities are and their different types. We will also study their SI units and conventions to indicate them.
This will eventually help us understand the fundamental laws of physics that explain nature and use them in our everyday lives.
What are Physical Quantities?
Physical quantities are measurable properties of a physical phenomenon that can be expressed numerically and described using appropriate units.
For example, we use a physical quantity, speed, to tell how fast something is moving in meters per second, temperature, how hot or cold an object is in Kelvin, and time, to organize the events or to find the duration in seconds.
For something to be measurable, there must exist 2 things
- Number (1,2, 2.3, 3, and so on)
- Unit (A standard (reference) against which something is measured)
Types of Physical Quantity
There are 2 types of physical quantities:
- Base or Fundamental Quantities
- Derived Quantities
Base or Fundamental Quantities
Base or Fundamental quantities are conventionally accepted quantities that are independent of other quantities. They are not derived from any other quantity, but by combining them, the other quantities are derived.
There are only seven fundamental physical quantities that exist. These are time, length, mass, amount of substance, temperature, luminous intensity, and electric current.
Derived Quantities
Derived quantities are the quantities that are made by combining fundamental quantities.
For example, speed (a derived quantity) is made by combining the fundamental quantities length and time.
There are countless derived quantities that exist. Some of them are speed, force, electric charge, acceleration, and many others.
There used to be a third type of physical quantities called supplementary quantities. These were plane angle and solid angle, but now they are known as dimensionless derived quantities.
Units in Physical Quantities
Once we know what physical quantities are, it is important to understand how these quantities are expressed.
For example, if you want to measure the distance between two cities, how would you express it?
As mentioned earlier, the physical quantities are expressed using numbers and units.
A unit is a fixed amount of quantity that is used as a reference to measure other quantities of the same kind.
Based on the type of quantity, the units of fundamental quantities are known as base or fundamental units, and units of derived quantities are known as derived units.
A collection of all the units (fundamental and derived units) is called a system of units.
In physics, if you’re using some reference or standard as a unit, it should have two qualities:
- It is accessible (Anyone, anywhere, should be able to reproduce it)
- It is invariable (It should remain the same over time or place)
If we define a human’s foot as a unit of length, it is easily accessible, but it will vary from person to person. So, we can’t choose it as a standard for the unit of length.
In physics, we must first ensure that our standard is invariant. Because if it changes with time or place, our measurements will become inaccurate, which has no value for us.
Once invariability is ensured, the standard is made accessible by accurately reproducing it.
International System of Units (SI Units)
Just as the meanings of physical quantities are precisely defined and remain the same everywhere in the world. There must also be an agreement on their units.
So that we can communicate measurement results accurately, and everyone interprets the results in the same way.
To do this, the BIPM organization was established in 1875 to maintain and manage the International System of Units (SI units). It ensures that measurements are the same everywhere in the world.
This organization held the committee of the General Conference on Weights and Measures (Acronym CGPM). Scientists from many countries met through the CGPM to discuss the standards of fundamental units.
During discussions through CGPM, they established seven fundamental units of measurement, which serve as the foundation of the International System of Units (SI).
These units, with their physical quantities, are shown in the table below, along with how these units are defined.
| Physical Quantity | SI Unit Name | SI Unit Symbol | How are they defined? |
|---|---|---|---|
| Time | Second | s | When a cesium-133 atom, in its unperturbed ground state, undergoes a hyperfine transition, it gives off microwave radiation. One second is the time needed to complete 9,192,631,770 vibrations of this radiation. |
| Length | Meter | m | A meter is defined as the distance light covers in a vacuum in exactly 1/299,792,458 of a second. |
| Mass | Kilogram | kg | 1 kg is defined by assigning a fixed value to Planck’s constant, which is 6.62607015 ×10−34 J s. For realization, we use the Kibble balance. The Kibble balance measures voltage and current using quantum electrical standards (Josephson effect for voltage and the quantum Hall effect for resistance). These depend on the Planck constant h and the elementary charge e. It then uses these measured values in the equation: m = VI/g𝛎 to calculate the mass precisely in kilograms. where g is the local gravitational acceleration and 𝛎 is the velocity of the coil. |
| Amount of Substance | Mole | mol | One mole is the amount of substance that contains 6.02214076 * 1023 elementary entities. By elementary entity, we mean the smallest unit of substance that is being measured. It could be an atom, a molecule, an ion, or any other particle. For example, in 1 mole of oxygen gas (O2), the elementary entity is the O2 molecule. The number 6.02214076 * 1023 is known as the Avogadro number (NA). |
| Temperature | Kelvin | K | The kelvin is defined by assigning the exact value to the Boltzmann constant, kB = 1.380649 x 10-23 J K-1. To realize 1 kelvin, you can use any experimental method that directly links measurable physical quantities to the Boltzmann constant (kB) through well-understood physics laws. Because the definition of the kelvin is based on the fixed value of kB, any experiment that uses this constant correctly will produce the same temperature scale. |
| Luminous Intensity | Candela | cd | 1 candela is the brightness in a particular direction of greenish-yellow light (540 × 10¹² Hz) that has a luminous efficacy of 683 lumens per watt and emits 1/683 watt per steradian. |
| Electric Current | Ampere | A | One ampere is defined by taking the fixed numerical value of elementary charge, which is equal to exactly 1.602176634 x 10-19 C. There are several methods to realize an ampere. One of them is Ohm’s law, I = V/R. Where voltage V and resistance R are measured using quantum electrical standards and depend on Planck’s constant h and the elementary charge e. |
All the other units are derived from these fundamental units. Some of the derived units are shown in the table below
| Derived Quantity | SI Unit Name | SI Unit Symbol | How are they defined? |
|---|---|---|---|
| Volume | cubic meter | m3 | Volume = Length x Width x Height = L3, which has the unit of m3. |
| Acceleration | meter per second square | m s-2 | If the velocity of an object changes by 1 m/s in 1 second, it has an acceleration of 1 m/s2. |
| Force | newton | N or kg m s-2 | If we accelerate an object of mass 1kg with 1 m/s2, the force would be 1 N. |
| Energy | joule | J or kg m2 s-2 | One joule represents the energy gained or spent when a 1 newton force moves something across a distance of one meter |
| Pressure | pascal | Pa or N m-2 or kg s-2 m-1 | A pascal is the unit of pressure that occurs when a 1 newton force is evenly distributed across an area of one square meter. |
| Density | kilogram per cubic meter | kg m-3 | If we have a cube of material that is 1 meter on each side and its mass is 1 kg, the density of that material is 1 kg m-3 |
| Power | joule per second | Watt or J s-1 or N m or kg m2 s-3 | If we do 1 joule of work every second, we are using 1 watt of power. |
Fundamental and derived units, together, form the International System of Units, or SI units.
Conventions for Indicating SI Units
There are certain convention that needs to be taken into account while using SI units. The most important ones are mentioned below
- Only SI units and those recognized for use with SI units should be used to express the value of physical quantities. Use the other units in parentheses with SI units only if necessary for the intended audience. For example, the room is 3 meters (about 10 feet) wide.
- Abbreviations like sec, mps should be avoided. Only the official unit symbol or name, and prefix symbol or name should be used. For example, s (for second), meter per second (for speed).
- Unit symbols should always be represented in singular form. For example, 1 m, 5 m (not 1 m, 5 ms)
- There should not be a period (.) at the end of a unit. Unless they come at the end of a sentence. For example, the height of tree is 5 m. Or the stick is 3 m long.
- A space or middle dot should be used to show the multiplication of units. A slash, a horizontal line, or a negative exponent should be used to indicate division of units. Two or more slashes should not be used in the same unit without parentheses. For example, N m or N・m, m/s or m・s-1, (m/s)/s or m s-2.
- No matter what the other text uses. Symbols for quantities and variables should be written in italic type. The units and the number that is used to represent the quantity should always be written in upright (roman) style. For example, F = 3 N, t = 5 s
- Superscript and subscript should be in italic type if they represent some variable, quantity, or running number. They should be in upright (roman type) if they are descriptive.
Examples:
Quantity: cv (specific heat capacity at constant volume)
Descriptive: mp (mass of proton)
Running Numbers: Fi = miai - The combination of letters ppm, ppb, ppt, and the terms parts per million, parts per billion, or parts per trillion should not be used to express the value of quantities. Only use prefixes that are officially approved in SI units. For example, 3 µs (3 x 10-6 s).
- A unit symbol or name should not be modified by adding extra information to it. It should be written as they are. For example, Tmax = 1000 s (it shouldn’t be T = 1000 smax).
- Information should not mix with unit symbols or names. For example, the acceleration is 10 m/s2 (it shouldn’t be written like 10 m acceleration/s2).
- Unit names and symbols should always be kept separate, and mathematical operations should not be applied to unit names. The proper way to express it is m/s or meter per second rather than meter/s or meter/second.
- The values of quantities should be expressed in Arabic numerals and unit symbols.
- There should be a space between the number and the unit symbol, except in case of superscript units for plane angle (2°).
- If a number has more than four digits on either side of the decimal marker, the digits should be grouped into sets of three using a thin space. To form the groups, start counting the digits from both the left and right of the decimal marker. For example, 12 345.678 901
- The full name of a unit always starts with a lowercase letter, even if the unit is named after a scientist. But the unit symbol has an initial capital letter, like for newton, it is N.
- When using an SI prefix (like kilo-, milli-, centi-) with a unit, write it directly before the unit symbol or name, without any space. Compound prefixes are not allowed like 1µµN.
- When a power is assigned to a base unit, it applies to the prefix as well. Like 1 km2 = 1 (km)2 = 1 x 106 m2
Unit Conversion
We normally express the units as SI units. But there could be a need to convert SI unit to some other system of units and vice versa.
Sometimes we need to compare measurements that use different units. For example, one length is 120 cm and another is 3 m. To see which one is longer, we first need to convert one of the measurements to bring them to the same unit.
Different industries use different systems of units, so if they share their findings with each other, they need to convert units to understand the results better.
Let us take a simple example to understand how the process of unit conversion takes place:
In this example, we’ll convert 3000 grams (g) into kilograms (kg)
- Firstly, identify the units you have. We have Grams.
- Identify the units you desire. We need kilograms.
- Now, we need to identify the conversion factor that relates grams to kilograms. A conversion factor is a ratio that shows how many units of one type are equal to a certain number of units of another type. For example, there are 60 seconds in 1 minute, 1000 meters in 1 kilometer.
- Next, we multiply the given units by the appropriate conversion factor to convert them into the desired units.
Example:
3000 g x 1 kg/1000 g
Here, grams cancel out, and 3000 divided by 1000 gives 3. So, the final result is 3 kg, which is the unit we wanted.
This approach can be applied to any conversion of units.
