Physical quantities Knowledge-Based Study

Study notes

1. What is a Physical Quantity?

   In physics, any property of an object or phenomenon that can be measured experimentally and quantified using numbers is called a physical quantity. Qualities such as joy, beauty, or color preference cannot be quantified directly and objectively, so they are not physical quantities.

   Every physical quantity must be expressed as a combination of two essential parts:

   • Numerical value (magnitude): A number that indicates the extent or size of the quantity.
   • Unit: A standard reference quantity chosen by convention against which the measurement is compared.

   For instance, if a runner covers a distance of 100 meters, 100 represents the numerical value, and meter is the unit of measurement. Without a unit, a numerical value in physics is physically meaningless.

   Classification by Origin

   Physical quantities are organized into two primary categories depending on how they are defined within the International System of Units (SI):

   1. Base (Fundamental) Quantities

   Base quantities are defined independently and cannot be expressed in terms of other physical quantities. In the SI system, there are exactly seven base quantities:

   • Length (meter, m)
   • Mass (kilogram, kg)
   • Time (second, s)
   • Electric current (ampere, A)
   • Thermodynamic temperature (kelvin, K)
   • Amount of substance (mole, mol)
   • Luminous intensity (candela, cd)

   2. Derived Quantities

   Derived quantities are formed through mathematical relationships (multiplication or division) of one or more base quantities. Common examples include:

   • Speed or Velocity: Length divided by time ($\text{m/s}$)
   • Area: Length multiplied by length ($\text{m}^2$)
   • Density: Mass divided by volume ($\text{kg/m}^3$)
   • Force: Mass multiplied by acceleration ($\text{kg}\cdot\text{m/s}^2$ or newton, N)

   Classification by Directional Properties

   Physical quantities are also classified according to whether their complete description requires spatial direction:

   1. Scalar Quantities

   A scalar quantity is completely described by its magnitude (a numerical value accompanied by an appropriate unit). It does not have or require a direction in space. Mathematical operations with scalars follow ordinary arithmetic.

   • Examples: Mass, distance, time, speed, temperature, volume, and energy.
   • Observation: Saying a box has a mass of 5 kg provides complete information; adding a spatial direction to mass is physically nonsensical.

   2. Vector Quantities

   A vector quantity requires both a magnitude and a specific direction in space to be fully defined. Vectors follow specific rules of vector algebra rather than simple arithmetic.

   • Examples: Displacement, velocity, acceleration, force, and momentum.
   • Observation: Stating that an aircraft moves at 250 m/s describes only its speed (scalar). Specifying that it moves at 250 m/s due North describes its velocity (vector).

   Comparing Categorizations

   It is important not to confuse the two methods of classification. A quantity is simultaneously either base or derived, and either scalar or vector:

   • All seven SI base quantities are defined as scalars.
   • Derived quantities can be either scalars (e.g., speed, kinetic energy, work, density) or vectors (e.g., velocity, acceleration, force, electric field).

   Common Pitfall: Do not confuse distance with displacement, or speed with velocity. Distance and speed are scalars, meaning they only measure how much ground is covered or how fast an object moves regardless of direction. Displacement and velocity are vectors, which strictly depend on direction relative to a reference frame.