A physical quantity is a property of an object, something we can measure with instruments or even by using our senses.
Two simple examples of physical quantities are the mass of an object or its temperature. We can measure both with instruments, but we can also sense them using our hands by lifting the object or touching it.
Fig. 1 - Mass is a physical quantity of an object. Mass per acceleration of gravity gives us the weight of the object.
What are the different physical quantities?
There is a range of physical properties that we can measure. All these properties are related to an object’s dimensions or its constitution. The seven elemental physical quantities are:
- Mass: this is the property that tells us how much matter is contained in the object. An object with a larger quantity of matter has a larger mass. Weight is the force exerted over an object’s mass. Mass and weight are often confused. The equation for weight is: \(weight = mass \cdot 9.81m / s ^ 2\).
- Length: this is the property that tells us how long an object is. This property is related to the properties of area and volume.
- Time: this property is related to the flow of events, and it always increases. Like mass, time is one of the properties that cannot be negative. Time tells us the flow of things in the universe.
- Electrical charge: this is a physical quantity that can be positive or negative, only affecting polarity. It causes a force to act upon the matter when placed in an electric field.
- Temperature: this is the property that measures the quantity of heat in a substance or object. Heat is related to the movement of the particles in the object.
- Mole: this is a fixed physical quantity that measures the number of molecules in a substance. The property represents an exact number of particles or molecules equal to \(6.02214076 \cdot 10 ^ {23}\) molecules of the substance.
- Luminosity: this is an energy measure, just like temperature. Luminosity measures the quantity of electromagnetic energy emitted by an object as light per unit time.
The difference between weight and mass
People confuse weight and mass all the time. The best way to explain the difference is by using an example featuring a ball.
A ball has a different weight on Mars than it does on Earth. However, the matter that composes the ball remains the same. And if the matter does not change, then neither does the mass.
Weight is the amount of force that gravity exerts on mass; it is force per mass. A scale, therefore, measures the gravitational force that pulls down the mass of an object.
This can also be explained using the gravity force formula that determines the weight of an object:
\[\text{weight} = \text{mass} \cdot \text{gravity}\]
The amount of matter in the ball does not change, so mass is a constant. The main difference is the gravity because gravity on Earth is higher than gravity on Mars:
\[\text{gravity (Earth)} > \text{gravity(Mars)}\]
Therefore, the weight on Earth will be higher than on Mars:
\[\text{mass} \cdot \text{gravity (Earth)} > \text{mass} \cdot \text{gravity(Mars)}\]
What are extensive and intensive quantities?
Physical quantities have two categories: extensive quantities and intensive quantities. This classification is related to an object’s mass. Extensive quantities depend on an object’s mass or size, while intensive quantities do not.
Examples of extensive physical quantities
Mass and electrical charge are examples of extensive physical quantities.
Mass depends on the size of the object. If you have two weights made of steel and one is double the size of the other, the larger one will have double the mass.
Another example concerns electrical charge. If the particles of an object have some electrical charge, their number tells us how much electrical charge the object has. If the object increases its mass, thus increasing its number of particles, the electrical charge will be larger.
Examples of intensive physical quantities
Intensive physical quantities do not depend on the object’s mass or size. Simple examples of this are time and temperature.
We can measure the time it takes for two objects of different mass to move from position A to position B. In both cases, time flows in the same way, independent of the composition or size of the objects.
Imagine we have an object with a temperature of 100 Kelvin, which we divide in half. In ideal circumstances where there is no heat transfer, the two halves will each still have the same temperature of 100 K.
What are derived physical quantities?
Derived physical quantities are the properties of an object that result from two elemental physical quantities. Derived quantities can result from a relationship of the same physical quantity (e.g. area) or by relating two different ones (e.g. velocity). See below for some examples of derived physical quantities.
Area and volume: related to length:
\[Area = length \cdot width; \space Volume = length \cdot width \cdot height\]
Velocity and acceleration: related to length and time:
\[Velocity = \frac{length}{time}; \space Acceleration = \frac{length}{time^2}\]
Density: related to length and mass:
\[Density = \frac{mass}{length^3}\]
Weight: related to acceleration and mass (in a planet, acceleration is its gravitational acceleration):
\[Weight = gravity \cdot mass\]
Pressure: related to force and length (for pressure, the force can be the weight exerted by an object, and the area over which this force acts is related to length):
\[Pressure = \frac{force}{length^2}\]
What are some characteristics of physical quantities?
Physical quantities have several characteristics related to their properties, some of which are listed below.
- No physical quantity can be less than zero, except for electrical charge and temperature values.
- Some physical quantities can have a value of zero, such as electrical charge or mass. In these cases, the object is electrically neutral (has no charge) or is massless (light).
- Some physical quantities are scalar, which means that they have only a value but no direction. Examples of these quantities are volume, mass, and mole.
- Other physical quantities are vectorial, in which case you need the direction to understand what is happening. Examples of vectorial quantities are velocity and acceleration.
Fig. 2 - A thermometer can display a value below zero.
Temperatures below zero are the result of taking the temperature at which water freezes as a zero (0) value. In Celsius, every temperature below the freezing point of water is negative.
How are units and physical quantities linked?
Physical quantities are important because they allow us to describe an object. Objects have a certain mass, a certain length, and a certain amount of atoms. The units are the values of reference we use to measure the properties of objects.
Imagine measuring the weight of two rocks. You can tell by holding them in your hands that one is heavier than the other. However, to determine their precise weight, you need to compare them against a standard value (unit), in this case, the kilogram.
Physical Quantities - Key takeaways
- Physical quantities and units are different. Physical quantities are an object’s physical properties, while units are a reference we use to measure the object’s properties.
- There are two types of physical quantities, elemental quantities and derived quantities. The derived ones are composed of the elemental quantities.
- The seven elemental physical quantities are mass, time, temperature, mole, length, luminosity, and electrical charge.
- Some derived physical quantities are velocity, heat, density, pressure, and momentum.
- Extensive physical quantities depend on the amount of substance or the size of the object.
- Intensive physical quantities do not depend on the amount of substance or the size of the object.
- No physical quantity can be less than zero, except for electrical charge and temperature values.
- Physical quantities are directly related to the units in physics.
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