Physical Quantities
What Is a Physical Quantity?
Physical quantities are characteristics of the world that can be measured.
Imagine trying to describe an object. Simply saying it’s “big,” “heavy,” or “hot” isn’t enough. You need to be specific. That’s where physical quantities come in: they’re properties of objects or phenomena that we can quantify with a number and a unit of measurement.
Common examples? Length, mass, temperature, speed, time… all things we can measure with tools like rulers, scales, stopwatches, and thermometers.
But if you wanted to measure something subjective like “beauty” or “happiness,” we’d be out of luck. These qualities can’t be turned into objective numbers. There’s no tool to measure how much patience you’ll need to sit through a boring class!
The Two Key Components of Measurement:
Every measurement involves a process and a unit of measurement.
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The measuring process: This refers to how you compare the quantity you're measuring with a reference standard. For example, when you use a ruler to measure the length of a pencil, you’re following a standard procedure to obtain a value. This process is crucial: if you and someone else measure the same thing, you should get the same result. If not… it might be time to replace your ruler!
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The unit of measurement: This is the standard you use to compare your physical quantity. For instance, the most common unit for measuring length is the meter. When measuring mass, the unit is the kilogram. These units aren’t chosen arbitrarily; they must be consistent (unchanging across locations and over time) and accessible to everyone. This ensures that no matter where you are in the world, you’ll get the same result using the same unit of measurement.
Measurement as a Ratio
When you measure something, the value you obtain is always a ratio between the quantity being measured and the unit of measurement. For example, if a pencil’s length is 15 cm, that means the pencil is 15 times the chosen unit (the centimeter). This ratio gives meaning to the measurement.
A number without a unit is called “dimensionless.” In other words, it’s just a number. We can say 15 is a natural, whole, positive, real number, but nothing more. You can only say an object weighs 15 kg or a pencil is 15 centimeters long if you include the unit of measurement.
So, what is length? Length is the distance between two points, and to measure it, we use tools like rulers or measuring tapes. For example, to find out how long a pencil is, you’d use a ruler and see that it measures 15 centimeters.
In this case, the number “15” is the measurement, which represents the ratio between the pencil’s length and the unit of measurement (the centimeter), showing how many times the centimeter fits into the total length of the pencil.
Every time you measure something, you are comparing an attribute of that object to a standard unit of measurement. This is the essence of physical quantities: they allow you to describe the world with precision and consistency, in a way that everyone can understand. Without them, everything would be an uncertain jumble of “more or less” and “maybe.”
Homogeneous and Non-Homogeneous Quantities
Understanding the difference between homogeneous and non-homogeneous quantities is essential when performing calculations. Otherwise, you risk making meaningless statements. Only homogeneous quantities can be mathematically combined, while non-homogeneous ones need to stay in their own category.
Homogeneous Quantities
Homogeneous quantities are those that can be compared and added together because they measure the same physical property. Don’t get confused: “homogeneous” doesn’t mean they have to be equal in value; it just means they refer to the same type of physical quantity.
Example? The length of a table and the length of a pencil are homogeneous quantities because both measure—no surprise here—length. Even if the table is 2 meters long and the pencil is only 15 centimeters, you can compare, add, subtract, or even multiply them. That’s why you can say, “I have a 3-meter-long rope and another that’s 2 meters long. If I tie them together, I’ll have 5 meters of rope.” Easy, right? Since both are lengths, they’re homogeneous and can be mathematically manipulated.
Non-Homogeneous Quantities
Non-homogeneous quantities, on the other hand, are trickier. These are quantities that can’t be compared or added together because they measure different physical properties. It’s like trying to add apples and oranges—it just doesn’t work. If someone tries, they’re misunderstanding the basics.
A classic example? The length of a rope and the mass of a stone. These two quantities can’t be added, subtracted, or directly compared because they measure completely different things. Length is measured in meters or centimeters, while mass is measured in kilograms or grams. It’s like mixing a red sock with a blue one—they just don’t match. You wouldn’t say that 2 meters + 3 kilograms equals something meaningful. Or that 30 minutes + 25 degrees Celsius makes sense. It’s absurd to combine them.
So, when conducting an experiment or making measurements in daily life, you need to know which quantities can be added or compared. If you don’t, your calculations will end up being nonsensical.
Fundamental and Derived Physical Quantities
The International System of Units (SI), established at the 11th General Conference on Weights and Measures in 1960, defines the units of measurement we use to describe nearly everything. There are seven fundamental units that form the core of the system. These are called fundamental physical quantities because they serve as the basis from which all other units are derived.
| Quantity | Unit of Measurement | Symbol |
|---|---|---|
| Length | meter | m |
| Time | second | s |
| Mass | kilogram | kg |
| Electric Current | ampere | A |
| Temperature | kelvin | K |
| Amount of Substance | mole | mol |
| Luminous Intensity | candela | cd |
These units form the foundation of everything we measure in fields like physics, chemistry, and engineering. From these basic units, we derive all other measurement units, known as derived physical quantities, such as the newton for force or the joule for energy.
Using the same system worldwide ensures measurements are accurate and comparable, without ambiguity. Imagine if every country had its own way of measuring things—it would be chaos trying to communicate precise information.
Derived quantities are those that don’t have their own unit in the International System (SI) but are created by combining the units of fundamental quantities to describe more complex physical phenomena.
Speed is a perfect example of a derived quantity because it combines length and time. It’s the ratio of distance traveled to the time taken. Mathematically, speed is expressed as:
$$ \text{Speed} = \frac{\text{distance (in meters)}}{\text{time (in seconds)}} = \frac{m}{s} $$
In this case, the SI unit for speed is meters per second (m/s), which is derived from two fundamental quantities: the meter (for length) and the second (for time). So, speed is a derived physical quantity.
While the International System is the universal scientific standard, there are still “non-SI” units widely used in everyday life, as well as in scientific and technical contexts. For example, we use tons for mass, minutes and hours to measure time (even though technically, the SI only uses the second as the fundamental time unit), and for pressure, we often use bars or atmospheres instead of pascals. In some situations, these non-SI units are more practical or simply more common. Then, there are countries like the United States or Canada that stick to their own systems of measurement. They haven't fully adopted the SI and continue using non-decimal-based units, such as miles for distances, feet for heights, and gallons for liquids. A mile equals 1,609.344 meters! So when you see a sign saying the next exit is “5 miles” away, the European brain instinctively starts calculating. These non-SI units may seem confusing, but they remain in use due to tradition or convenience, and we sometimes have to work with them. So, if you ever visit the United States, get ready to drive in “miles per hour” instead of “kilometers per hour.”
