Physical Quantities: (AS and A Level Physics) 

Introduction

Physical quantities are the language of physics to describe measurable quantities. Physics always deals with measurements and interactions, and these must be accurate and precise. So, to give a meaningful measurement, the results are expressed in numerical values and units. The measurement is expressed in a common language, and such quantities that can be measured in terms of units are called physical quantities.

Physical phenomena like length, mass, time, motion, energy, force, flow of electricity, etc. are some familiar physical quantities. They all have their unique calculations and units. They have become important in our daily lives for educational or experimental purposes. For example, when we buy groceries, we weigh them; when a person gets a fever, it is very important to track the temperature; fitting a carpet inside a room needs accurate measurement. These measurements give us the right alert about basic things and solve practical problems in daily life.

In practice, physics or any realm of science seems meaningless without measurement, and for measurement, units serve as a communicating language. Further, we will study the concepts, dimensions, types, methods of measurement, applications, etc. in this article.

What Are Physical Quantities?

A physical quantity is the property of an object or a physical phenomenon that can be measured. Physical quantities describe measurable characteristics of the physical world.

A physical quantity includes a numerical value and a unit. The numerical value gives the actual amount at which the quantity is present. Similarly, the unit is a unique standard given to the measurement of that quantity. For example, we measure heights or lengths in meters, mass in kilograms, and time in seconds, which are the units of those physical quantities.

In simple words,

Physical Quantity = Numerical Value + Unit

Not every aspect of an object is measurable. For example, we cannot measure the color or beauty of an object physically. However, its length, mass, temperature, volume, and speed can be measured accurately.

For example:

• Length of a pencil = 15 cm
• Mass of a book = 0.8 kg
• Time taken to complete a race = 12 s
• Temperature of water = 30 °C
• Speed of a car = 60 km/h

Therefore, physical quantities hold special characteristics which are given below:

• They can be measured experimentally.
• They are expressed using standard units.
• They can be compared with one another.
• They can be combined mathematically according to physical laws.
• They help explain natural phenomena accurately.

There are some fundamental quantities in physics as tabulated below:

Many physical laws are derived on the basis of the interrelation between these quantities.

Classification of Physical Quantities

Physical quantities can be classified in several ways.

–Base and Derived Quantities

Some quantities are fundamental and cannot be expressed using other physical quantities. These are called base quantities.

Examples include:

• Length
• Mass
• Time
• Electric current
• Temperature
• Amount of substance
• Luminous intensity

Other quantities are obtained by combining base quantities mathematically. These are called derived quantities.

Examples include:

• Velocity
• Acceleration
• Force
• Work
• Energy
• Density
• Pressure
• Power

-Scalar and Vector Quantities

Physical quantities are also classified according to whether direction is required.

Scalar quantities have only magnitude.

Examples include:

• Mass
• Time
• Distance
• Temperature
• Energy

Vector quantities have both magnitude and direction.

Examples include:

• Force
• Velocity
• Displacement
• Acceleration
• Momentum

This classification is discussed in greater detail later in the article.

Why Standard Units Are Necessary

Imagine one country measuring distance using footsteps while another uses hand spans. Scientific communication would become confusing because everyone’s measurements would differ.

To avoid such problems, scientists agreed upon standard units that remain the same everywhere.

For example:

• The meter measures length.
• Kilogram measures mass.
• Second measures time.

Standard units make measurements reliable, reproducible, and universally accepted.

Numerical Value and Units of Physical Quantities

Physical quantities are expressed in two parts: a numerical value and its unit. Both parts are equally important to identify the measurement of a distinct quantity. 

The numerical value gives the actual quantity of the standard unit contained in the measured quantity. The unit is the unique standard assigned to all the physical quantities, that is accepted world-wide. For example:

• 5 m means a length equal to five meters.
• 12 kg means a mass of twelve kilograms.
• 30 s means a time interval of thirty seconds.

There are also several units given to asame physical quantities on the basis of a measuring system. However, it doesn’t change the quantity of a body. For example:

• 1 meter = 100 centimeters = 1000 millimeters.
• 2 kilograms = 2000 grams.

Types of Units

The two types of units are:

Fundamental Units: Fundamental units are the units of the fundamental physical quantities i.e. length: meter (m), mass: kilogram (kg), and time: second (s).

Derived Units: Derived units are the units of physical quantities derived from the fundamental quantities. For example, force: newton (N or kg·m/s²), pressure: pascal (Pa or N/m²), volume: cubic meter (m³), etc.

Unit Conversion

Sometimes unit conversion is required in practical situations to maintain consistency in calculations. Some useful conversions are:

• 1 km = 1000 m
• 1 m = 100 cm
• 1 minute = 60 s
• 1 kg = 1000 g
• 1 L = 1000 mL

SI Base and Derived Quantities

The International System of Units (SI) is a uniform and universally accepted measuring unit. It was developed from the metric system and is now the standard system of measurement. Using a common unit of calculation helps to get and compare the results without confusions along any countries.

SI Base Quantities

The SI base quantities are the fundamental quantities of the SI system. It contains seven base quantities. These are the unique and independent quantities and cannot be expressed in terms of other physical quantities. Each base quantity has a corresponding SI base unit.

Other physical quantities can be measured on the basis of these quantities. 

• Length measures the distance and its measurement is used in construction, transportation, surveying, and engineering.
• Mass measures the amount of a matter and used in every fields like science, management, business etc.
• Time measures durations between the events and its measurement crucial in every physical things.
• Electric current gives the measurement of flow of electric charge.
• Temperature measures how much hot or cold is a body. It is measured in kelvin in SI units but degrees and Celsius are more popular in daily life. 
• Amount of substance measures the number of particles such as atoms or molecules.
• Luminous intensity measures how bright is a light source in a particular direction. 

SI Derived Quantities

Many physical quantities are obtained by combining base quantities mathematically. These are called derived quantities. and their units are known as Estimation of Physical Quantities

In some cases, it is difficult or unnecessary to get an exact measurement. In such situations, estimations are done to provide an approximate value on the basis of experience, observation, or simple calculations. For example: estimating the number of students in a class, estimating the area of land etc.

Good estimation skills is a plus point that helps to make quick decisions before performing detailed measurements. They are also useful in everyday activities like buying groceries, cooking, and construction.

Accuracy, Precision, and Uncertainty

No measurement is perfectly exact. There lies some degree of error due to the limitations of measuring devices, environmental conditions, or carelessness. Therefore, understanding accuracy, precision, and uncertainty is crucial in experimental or scientific activities.

Accuracy

Accuracy means how close our measured value is with the standard or accepted value.

For example, if the actual length of a rod is 50.0 cm and a measurement gives 49.9 cm, the measurement is highly accurate. A measurement with greater accuracy gives less errors.

Precision

Some measurements are repeated and all the values are noted. Precision means how close these recorded measurements are with each other. The value may not be accurate but precise measurement gives consistent results.

Suppose a student measures the length of a table several times and records:

• 25.2 cm
• 25.3 cm
• 25.2 cm
• 25.3 cm

This suggests that the measurements are highly precise. However, if the actual length is 26.0 cm, the measurements are precise but not accurate.

Difference Between Accuracy and Precision

For a perfect or ideal measurement the value must be both accurate and precise.

Uncertainty in Measurement

Our measuring devices are built with certain limits and are not made with infinite precision. This brings uncertainty in measurement. 

Measurement uncertainty may arise from:

• Instrument limitations.
• Human reading errors.
• Environmental factors such as temperature or vibration.
• Experimental methods.

Thus, the final measurement is written with absolute value and an expected error or uncertainty. For example:

Length = (12.5 ± 0.1) cm

This means that the true value is expected to lie between 12.4 cm and 12.6 cm.

Sources of Measurement Error

Measurement errors are generally classified into three categories.

Systematic Errors

These occur due to faults in instruments, incorrect calibration, or defects in experimental methods.

Random Errors

These occur unpredictably because of small uncontrollable variations during measurement.

Gross Errors

These are caused by human mistakes, such as incorrect readings, personal carelessness in recording the value or making calculation errors.

Thus, to minimize these errors using well-calibrated instruments are used and also the measurements are done several times with proper procedures.

Some common examples are shown below.

Advantages of the SI System

The SI system offers several important advantages:

• It is accepted internationally.
• It is based on the decimal system and the conversions are simple.
• It provides consistency in scientific calculations.
• It reduces confusion caused by different local measurement systems.
• It allows accurate comparison of experimental results.

Today, almost every branch of science and technology relies on the SI system for accurate measurement and communication.

Scalar and Vector Quantities

Physical quantities can also be classified according to whether direction is required to describe them completely. Based on this criterion, they are divided into scalar quantities and vector quantities.

Scalar Quantities

A scalar quantity has magnitude only. It gives complete information only with a numerical value and a unit. No direction is required.

Examples of scalar quantities include:

• Mass
• Time
• Distance
• Speed
• Temperature
• Energy
• Work
• Volume
• Density
• Power

These all quantities do not require specific directions to give complete information.

Properties of Scalar Quantities

Scalar quantities:

• Have only magnitude.
• Are represented by ordinary numbers.
• Are added and subtracted using simple arithmetic.
• Do not involve direction.

Vector Quantities

A vector quantity has both magnitude and direction so, we have to mention both to completely describe the quantity. For example:

• Displacement
• Velocity
• Acceleration
• Force
• Momentum
• Weight

Suppose, displacement is the measure of the shortest distance between the two points hence, the direction is very important to mention here.

Properties of Vector Quantities

Vector quantities:

• Have magnitude and direction.
• Are represented by arrows in diagrams.
• Follow special rules of vector addition.
• Change if either magnitude or direction changes.

Difference Between Scalars and Vectors

Dimensions and Dimensional Analysis

Every physical quantity can be expressed in terms of the fundamental quantities. This representation is called the dimension of the quantity.

Dimensions simply indicate the nature of a physical quantity. It doesn’t give the numerical value or unit.

For example:

• Length has the dimension L.
• Mass has the dimension M.
• Time has the dimension T.

Derived quantities are represented as combinations of these fundamental dimensions.

Some common dimensional formulas are:

What Is Dimensional Analysis?

Dimensional analysis is a technique that uses dimensions to check the validity of physical formulas, equations or relationships.

The main principle of dimensional analysis is that the dimension of any equation or relationship must be the same in both LHS and the RHS side. 

For example:

Force = Mass × Acceleration

Dimensions of force:

= M × LT⁻²

= MLT⁻²

Since both sides have identical dimensions, the equation is dimensionally correct.

Applications of Dimensional Analysis

Dimensional analysis is useful for:

• Checking whether equations are mathematically correct.
• Deriving relationships between physical quantities.
• Converting units from one system to another.
• Identifying mistakes in calculations.
• Simplifying scientific formulas.

There are also some handful of demerits of dimensional analysis for example, some constants, numerical values,etc., do not have dimensions but are effective to identify various errors in the measurement before calculations.

Measurement and Estimation of Physical Quantities

Measurement is the process of determining the magnitude of a physical quantity by comparing it with a standard unit. For example, when we measure the length of a table using a meter scale, we compare the table’s length with the standard unit of one meter. 

Measurement is the foundation of science and a part of daily life. It helps to provide accurate experiments in science whereas, helps to conduct fair trade and commerce in daily life. Also several factors like weather conditions, astronomy, geographical conditions, health practices, manufacturing products, construction and designing, everything requires measurement.

Measuring Instruments

Different physical quantities require different measuring instruments. Some common examples are:

Each instrument does specific measurements for specific cases. For example, a Vernier caliper measures small lengths with greater precision than an ordinary ruler. Similarly, a micrometer screw gauge is used to measure the diameter of thin wires and small objects with accuracy.

Direct and Indirect Measurement

Measurements can be classified into two types.

-Direct Measurement

In direct measurement, the required quantity is measured directly using a suitable instrument. For example, a mass measured using a balance.

-Indirect Measurement

In indirect measurement, the desired quantity is calculated using directly measured information and substituting them in the correct formula. For example: force, power, and density, are determined indirectly.

Estimation of Physical Quantities

In some cases, it is difficult or unnecessary to get an exact measurement. In such situations, estimations are done to provide an approximate value on the basis of experience, observation, or simple calculations. For example: estimating the number of students in a class, estimating the area of land etc.

Good estimation skills is a plus point that helps to make quick decisions before performing detailed measurements. They are also useful in everyday activities like buying groceries, cooking, and construction.

Accuracy, Precision, and Uncertainty

No measurement is perfectly exact. There lies some degree of error due to the limitations of measuring devices, environmental conditions, or carelessness. Therefore, understanding accuracy, precision, and uncertainty is crucial in experimental or scientific activities.

Accuracy

Accuracy means how close our measured value is with the standard or accepted value.

For example, if the actual length of a rod is 50.0 cm and a measurement gives 49.9 cm, the measurement is highly accurate. A measurement with greater accuracy gives less errors.

Precision

Some measurements are repeated and all the values are noted. Precision means how close these recorded measurements are with each other. The value may not be accurate but precise measurement gives consistent results.

Suppose a student measures the length of a table several times and records:

• 25.2 cm
• 25.3 cm
• 25.2 cm
• 25.3 cm

This suggests that the measurements are highly precise. However, if the actual length is 26.0 cm, the measurements are precise but not accurate.

Difference Between Accuracy and Precision

For a perfect or ideal measurement the value must be both accurate and precise.

Uncertainty in Measurement

Our measuring devices are built with certain limits and are not made with infinite precision. This brings uncertainty in measurement. 

Measurement uncertainty may arise from:

• Instrument limitations.
• Human reading errors.
• Environmental factors such as temperature or vibration.
• Experimental methods.

Thus, the final measurement is written with absolute value and an expected error or uncertainty. For example:

Length = (12.5 ± 0.1) cm

This means that the true value is expected to lie between 12.4 cm and 12.6 cm.

Sources of Measurement Error

Measurement errors are generally classified into three categories.

Systematic Errors

These occur due to faults in instruments, incorrect calibration, or defects in experimental methods.

Random Errors

These occur unpredictably because of small uncontrollable variations during measurement.

Gross Errors

These are caused by human mistakes, such as incorrect readings, personal carelessness in recording the value or making calculation errors.

Thus, to minimize these errors using well-calibrated instruments are used and also the measurements are done several times with proper procedures.

Examples and Applications of Physical Quantities

Physical quantities are used in almost every field of science, technology, and everyday life. They allow us to describe, analyze, and predict natural phenomena with accuracy.

Everyday Life

Many daily activities involve physical quantities.

Examples include:

• Measuring ingredients while cooking.
• Checking body temperature during illness.
• Measuring fuel while filling a vehicle.
• Calculating travel distance and time.
• Weighing fruits and vegetables in markets.

These measurements help people perform routine tasks efficiently.

Engineering

Engineers rely on physical quantities to design safe and efficient structures.

They calculate:

• Force acting on bridges.
• Pressure inside pipelines.
• Electrical power consumption.
• Stress and strain in construction materials.

Accurate measurements ensure that buildings, roads, and machines function safely.

Medicine

Modern healthcare depends heavily on physical quantities.

Doctors measure:

• Blood pressure.
• Body temperature.
• Heart rate.
• Body mass.
• Blood glucose level.
• Oxygen saturation.

Medical imaging techniques such as X-rays, CT scans, and MRI also involve precise physical measurements.

Physics Research

Scientists measure physical quantities to investigate the laws of nature.

Examples include:

• Speed of light.
• Gravitational acceleration.
• Electrical resistance.
• Magnetic field strength.
• Radioactive decay rates.

Accurate measurements allow scientists to test theories and develop new technologies.

Environmental Science

Environmental scientists monitor quantities such as:

• Rainfall.
• Temperature.
• Air pressure.
• Wind speed.
• Humidity.
• Pollution levels.

These measurements help predict weather, study climate change, and manage natural resources.

Industry

Manufacturing industries depend on accurate measurements to maintain product quality.

They measure:

• Thickness of materials.
• Machine speed.
• Production time.
• Electrical voltage.
• Material density.

Precision measurement reduces waste and improves product reliability.

Conclusion

The journey of science starts with physical quantities and their measurement. Hence, they form a strong foundation in physics and every other sector of science. The numerical value and the unit assigned to a physical quantity gives complete information about the presence of that quantity. Hence, it makes a physical world measurable. The measurement language is made common so that people from each corner of the world can communicate accurately in terms of measurement.

The International System of Units (SI) gives a universal standard for measurement. It ensures consistency in scientific research and technological applications across the world. Physical quantities are classified into base and derived quantities, as well as scalar and vector quantities. They serve according to the purpose of scientific analysis.

Dimensions and dimensional analysis are very important parts of scientific relationships. They allow scientists to verify equations, understand their relationships and convert units correctly. Accuracy, precision and estimation are equally important for any experiments, to provide reliable measurement. However, some measurement errors and uncertainties can affect the result and hence the experiments must be done carefully.

In reality, from daily activities to advanced science and technology, we are wounded by physical quantities. We gain confidence and alert over each activities like shopping, transportation, experiments, etc., through their measurements. As research and technology is evolving rapidly, the accurate measurement and proper understanding of physical quantities is crucial to provide a strong foundation for further studies.

References

1. Foken, T., Hellmuth, O., Huwe, B., & Sonntag, D. (2021). Physical quantities. In Springer handbook of atmospheric measurements (pp. 107-151). Cham: Springer International Publishing.
2. Mills, I. M. (2001). Physical quantities and units. Recent Advances in Metrology and Fundamental Constants-Proceedings of the International School of Physics, IOS Press, Amsterdam, 27-50.
3. Duncanson, W. E. (1941). The dimensions of physical quantities. Proceedings of the Physical Society, 53(4), 432-448.
4. Bigelow, J., & Pargetter, R. (1988). Quantities. Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, 54(3), 287-304.
5. https://en.wikipedia.org/wiki/Physical_quantity
6. https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/01:_The_Nature_of_Science_and_Physics/1.02:_Physical_Quantities_and_Units
7. https://scienly.com/what-is-physical-quantity/