Physical Quantities: Every day we deal with measurement and analysis in our daily life. The physical quantity example is when we go out to buy fruits or vegetables, we measure the amount of the things we wish to buy and pay for them accordingly. This measured value has a number and a unit associated with it, for example, \(3 \mathrm{~kg}\) mangoes, \(1 \mathrm{~kg}\) tomatoes, \(500 \mathrm{~g}\) coriander etc. Measurement helps us determine the amount of a given set of objects.

To express this measurement, we first need a quantity to associate everything we are measuring, and these quantities must be different for different kinds of measurements. These quantities that help us to express the measured quantity in a way that is understood by all are known as physical quantities. Life before these physical quantities involved ambiguity, and the expression of measurement could not be done uniquely, leading to a lot of confusion and chaos.

What are Physical Quantities?

A physical quantity can be defined as the characteristic property of a system that is generally quantified in terms of measurement. Thus, we can express a physical quantity as the algebraic multiplication involving the product of a numerical value and its unit.

Physical Quantity Example

The physical quantity associated with length can be written as \(x\) \(\text {meter}\), where \(x\) is the numerical value, and the \(\text {meter}\) specifies the unit. Thus, all physical quantities have at least two features: A numerical factor and a unit in which we are expressing the given measurement.

There is an immense number of phenomena and objects that we study in physics and engineering. These range from a tiny duration of the lifetime of an atomic nucleus to the present age of the universe, from the diameter of an amoeba to the diameter of the sun, from the energy required to lift a pen to the energy released post a nuclear reaction, where the small and large quantities may be related to each other in terms of millions of powers of \(10\).

The numerical values provide a much deeper understanding of physical quantities and equations than just the qualitative description. Based on how these quantities are described, physical quantities can be categorized into:

1. Fundamental quantities
2. Derived quantities

Fundamental Units of Physical Quantities

A unit of a physical quantity can be described as a standard chosen arbitrarily, which is used to estimate the physical quantities that belong to the same kind of measurement. Since physical quantities can be minute or even extremely large thus, units play an important role while writing the expression of the given measurement. Although various systems of units have been developed over the years, to avoid any confusion, the international system of units or SI system was developed.

In the absence of such an internationally accepted system, it was tough for scientists to compare the physical quantities and share their findings across boundaries. For example, the length of a room can be expressed in terms of meters, kilometres, centimetres, feet, etc. These units are related to each other and can be converted into each other; without such well-defined units, it would have been difficult to express such a quantity.

Fundamental Quantities

The physical quantities that are independent of other physical quantities are called Fundamental quantities. These are also known as base quantities and are used to express other quantities. These quantities can be broken down further and can be used to determine various other physical quantities. The fundamental quantities are:

1. Length
2. Mass
3. Time
4. Electric current
5. Temperature
6. Amount of substance
7. Luminous Intensity

Supplementary quantities:

1. Plane Angle
2. Solid Angle

Fundamental Units

The units that are associated with fundamental quantities are known as fundamental units. These are the base units that can not be derived from the other units and are defined using an international system of units. The fundamental units are:

1. Meter – represented by \(\text {m}\). It is the fundamental unit of length. Initially, One meter was defined as a quantity that is \(1650763.73\) times the wavelength of the light emitted in a vacuum due to electronic transition from \(2 p^{10}\) state to \(5 d^{5}\) state in Krypton-\(86\). The \(17 \,\text {th}\) General Assembly of weights and measures, in \(1983\), adopted a new definition for the meter. This definition was given in terms of the velocity of light. Thus, presently a meter can be defined as the distance covered by a ray of light in a vacuum during a time duration equal to \(1 / 299,792,458\) of a second.
2. Second – represented by \(\text {s}\). It is the fundamental unit of time. One second is defined as the duration of \(9192631770\) periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of caesium-\(133\) atoms.
3. Kilogram – represented by \(\mathrm{kg}\). It is the fundamental unit of mass. One kilogram was initially defined as the mass of a cylinder composed of platinum-iridium alloy, kept in the International Bureau of weights and measures, preserved at Serves near Paris. Now, it is defined using the fixed value of Planck’s constant.
4. Ampere – represented by \(\text {A}\). It is the fundamental unit of electric current. One ampere is the amount of current flowing through each of the two parallel conductors, having an infinite length and negligible area of cross-section when placed one meter apart in a vacuum, each conductor will experience a force equal to \(2 \times 10^{-7}\,\rm{N}\) per unit length.
5. Kelvin – represented by \(\text {K}\). It is the fundamental unit of temperature. One kelvin is defined as the temperature which is equal to the fraction of \(1 / 273.16\) of the thermodynamic temperature of the triple point of water.
6. Candela – represented by \(\text {cd}\). It is the fundamental unit of luminous intensity. One candela is defined as the luminous intensity in the direction which is perpendicular to the direction of a surface of a black body having a cross-sectional area equal to \(1 / 600000 \mathrm{~m}^{2}\), when kept at the temperature of solidifying platinum and under a pressure of \(101325 \,\mathrm{Nm}^{-2}\).
7. Mole – represented by \(\text {mol}\). It is the fundamental unit of the amount of substance. One mole is defined as the amount of a substance of a system containing as many elementary entities as there are atoms in \(12 \times 10^{-3} \mathrm{~kg}\) of carbon \(-12\).
8. Radian – represented by \(\mathrm{rad}\). It is the fundamental unit of plane angle. \(1 \,\mathrm{rad}=57^{\circ} \mathrm{17}^{\prime} 45^{\prime \prime}\). One radian is defined as the angle made by an arc of the circle equal to its radius at the centre.
9. Steradian – represented by \(\text {sr}\). It is the fundamental unit of solid angle. One steradian is defined as the angle subtended at the centre of a sphere of a unit radius by a surface having the area equal to the square having side length equal to the radius of the square. The solid angle of a sphere at its centre is \(4 \pi\) steradians.

Derived Quantities

The physical quantities can not be defined on their own and can be broken down into base quantities. These are dependent quantities. The derived physical quantities are expressed in terms of the fundamental quantities. A few examples of derived quantities are Force, velocity, pressure, volume, density, etc.

Derived Units

The units that are derived using various combinations of fundamental units are called derived units. Since these units are derived using the base units, that is why they are known as “derived” units. These units can be broken down. The units of the derived physical quantities are sometimes assigned a name; for example, the SI unit of pressure is \(\mathrm{N} / \mathrm{m}^{2}\), termed as pascal (Pa) or SI unit of force is \(\mathrm{kg} \,\mathrm{m} \mathrm{s}^{-2}\). Which is also known as newton (N).

How to Find the Derived Unit of a Quantity

• Step 1: Write the formula of the quantity whose unit you wish to derive.
• Step 2: Substitute the units of all the quantities involved in the formula.
• Step 3: All quantities’ units should be written in one chosen system of units, preferably in the fundamental or standard form.
• Step 4: The expression containing all the units is simplified to compute the final unit of the given derived quantity. Simplify for the derived unit of the quantity to compute its final unit.

Let’s try it: Compute the unit of acceleration.

Solution: Acceleration is a derived physical quantity.

\(\text {Acceleration}=\frac{\text { velocity }}{\text { time }}\)

\({\text{S}}{\text{.I}}\,{\text{unit}}\,{\text{of}}\,{\text{acceleration}} = \frac{{{\text{ SI unit of velocity }}}}{{{\text{ SI unit of time }}}} = \frac{{{\text{m}}{{\text{s}}^{ – 1}}}}{{\text{s}}} = {\text{m}}/{{\text{s}}^2}\)

Thus, the SI unit of acceleration is \(\mathrm{m} / \mathrm{s}^{2}\).

Writing the Units of Physical Quantities

The following rules must be kept in mind before we write the units of the physical quantities.

• Rule 1: The first letter of the full name of the units must never start with a capital letter, even when the units are named after a scientist. For example, the unit of force is written as- newton, unit of power is written as- watt, unit of current is written as- ampere, unit of length is written as- meter.
• Rule 2: We can represent the unit of a physical quantity using its full name or by the internationally agreed symbol.
• Rule 3: Always avoid writing units in plurals. It is wrong. For example, \(10 \,\text {meter}\) is correct, but \(10 \,\text {meters}\) is incorrect, \(25 \mathrm{~kg}\) is correct, but \(25 \,\mathrm{kgs}\) is incorrect.
• Rule 4: We never add a full stop or a punctuation mark at the end of the symbol of a given unit. For example, \(10 \mathrm{~N}\) is correct, but \(10 \mathrm{~N}\). is incorrect.

Some Important Terms

1. Fermi: Used to measure nuclear distances, \(1\) fermi \(=10^{-15} \mathrm{~m}\)
2. Angstrom: Used to measure the wavelength of light, \(1 \,{\rm{Å}}=10^{-10} \mathrm{~m}\)
3. Astronomical Unit: Used to measure the mean distance between the sun and earth, \(1 \,{\rm{A U}}=1.5 \times 10^{11} \mathrm{~m}\)
4. Light Year: Used for measuring astronomical distances. It is the distance travelled by light in one year, \(1 \,{\rm{l y}}=9.4605 \times 10^{15} \mathrm{~m}\)
5. Parsec: Used to measure the distance between galaxies, \(1 \,\mathrm{Parsec}\) \(=3 \,\mathrm{ly}=3.084 \times 10^{16} \mathrm{~m}\)
6. Barn: Used to measure scattering cross-section area of collisions, \(1 \,\text {barn}\) \(=10^{-28} \mathrm{~m}^{2}\)
7. Two instruments that are used for measuring time are Chronometer and Metronome. Time is the only quantity with the same unit (second) in all the unit systems.

Summary

A physical can be defined as the characteristic property of a system that is generally quantified in terms of measurement. Thus, we can express a physical quantity as the algebraic multiplication involving the product of a numerical value and its unit. A unit of a physical quantity can be described as a standard chosen arbitrarily, which is used to estimate the physical quantities that belong to the same kind of measurement.

The physical quantities that are independent of other physical quantities are called Fundamental quantities. These are also known as base quantities and are used to express other quantities. Fundamental units are meter, kilogram, second, ampere, candela, mole and kelvin. The physical quantities can not be defined independently and can be broken down into base quantities called derived quantities. These are dependent quantities. Examples of derived quantities are force, pressure, acceleration, volume etc. The units are derived using various combinations of fundamental units called derived units, for example, newton, pascal, meter/second, etc.

FAQs on Physical Quantities

Given below are the frequently asked questions regarding Physical Quantities:

Q.1: What are fundamental units?
Ans: Fundamental units are the units of fundamental quantities. These units are independent and can not be broken down into other units.

Q.2: What are derived quantities?
Ans: The quantities that can not be defined on their own and can be broken down in terms of the base quantities are called the derived quantities.

Q.3: What is the unit of amount of substance?
Ans: Mole is the SI unit of substance.

Q.4: Candela is the SI unit of which physical quantity?
Ans: Candela is the SI unit of luminous intensity.

Q.5: Compute the unit of velocity.
Ans: Velocity is a derived physical quantity. 
velocity \(=\frac{\text { distance }}{\text { time }}\)
\(\text {S.I unit of velocity} =\frac{\text { SI unit of distance }}{\text { SI unit of time }}=\frac{m}{s}=\mathrm{m} / \mathrm{s}\)
Thus, the SI unit of velocity is \(\mathrm{m} / \mathrm{s}\).

Learn About Relative Density Here

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