Units, Physical Quantities & Vectors

Physical Quantities and Units

Physics relies on the measurement of physical quantities, which are properties of objects or phenomena that can be quantified. Each physical quantity is expressed in terms of a unit, which provides a standard for comparison.

• Physical Quantity: Any measurable property, such as length, mass, time, or temperature.

• Unit: A standard amount used to express a physical quantity (e.g., meter, kilogram, second).

• Fundamental Units: The basic units from which all other units are derived. Common fundamental units include meter (m), kilogram (kg), and second (s).

• Derived Units: Units formed by combining fundamental units according to physical laws (e.g., velocity in m/s, force in newtons).

Dimensional Analysis

Dimensional analysis is a method used to check the consistency of equations and to convert between units. Each physical quantity can be represented by its dimensions, which show how it relates to fundamental units.

• Dimensions: Represented by symbols such as L (length), M (mass), T (time).

• Example: Velocity has dimensions of length divided by time, written as .

• Dimensional Formula: Expresses the dimensions of a physical quantity. For example, acceleration is .

Common Physical Quantities and Their Units

The table below summarizes some common physical quantities, their symbols, units, and dimensional formulas.

Example: Dimensional Analysis of Force

Force is defined by Newton's second law as mass times acceleration:

• Mass has dimension , acceleration has dimension

• Therefore, force has dimension

Additional info:

• These notes are foundational for understanding all subsequent topics in physics, as every physical law involves quantities and units.