Understanding Physical Quantities and Their Measurement
Physical Size
Definition
Every measurement aims to assign a numerical value to a property of an object, such as length or area. These properties, known as physical quantities, can be quantified by comparison with a standard.
Examples of Physical Quantities
Examples include mass, length, time, density, temperature, speed, acceleration, and energy.
Types of Physical Quantities
Physical quantities can be classified based on several criteria:
- Mathematical form: scalars, vectors, or tensors.
- Additivity: extensive or intensive.
Scalars, Vectors, and Tensors
Scalars
Scalars are completely defined by a number and the units used for measurement. They are represented by a simple mathematical entity, a number. They have a magnitude but lack direction. Their value can be independent of the observer (e.g., mass, temperature, density) or depend on the observer’s position or motion (e.g., kinetic energy).
Vectors
Vectors are characterized by a magnitude (intensity or module), a direction, and a sense. In a Euclidean space, a vector is represented by a directed line segment. Examples include speed, acceleration, force, and the electric field.
Vector quantities do not show invariance of their components when observed from different coordinate systems. To relate measurements from different observers, vector transformation relationships are needed.
Tensors
Tensors characterize physical properties and behaviors modeled by a set of numbers that change according to the chosen coordinate system. They are used to relate measurements from observers with different states of motion or orientation.
Extensive and Intensive Magnitudes
Extensive Magnitudes
Extensive quantities depend on the amount of substance in a body or system. They are additive. For a system consisting of two parts, the total value of an extensive quantity is the sum of its values in each part. Examples include mass, volume, and energy.
Intensive Magnitudes
Intensive quantities do not depend on the amount of matter in the system. They have the same value for a system and its subsystems. Examples include density, temperature, and pressure.
The ratio of two extensive magnitudes often results in an intensive magnitude. For example, mass divided by volume equals density.
International System of Units (SI)
The International System of Units is based on seven base quantities: length, time, mass, electric current, temperature, amount of substance, and luminous intensity. Other quantities are derived from these base quantities through mathematical combinations.
Basic or Fundamental Units of SI
- Length: meter (m). The meter is the distance traveled by light in a vacuum in 1/299,792,458 seconds.
- Time: second (s). The second is the duration of 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of cesium-133.