Fundamentals

Foundations for studying physics: quantities, units, vectors, reference frames, measurement, dimensional analysis and core concepts.

General idea of the topic

This block covers the tools and concepts every physicist needs before entering any specific domain. It does not describe a particular phenomenon, but rather the language and rules of the game used to describe any physical phenomenon.

It is organized in two layers: the formal tools (physical quantities, units, vectors, reference frames, constants, measurement errors and dimensional analysis) and the cross-domain structural concepts (physical system, interactions, net force, equilibrium, conservation, momentum, energy, field and orders of magnitude). Without mastering this foundation, any subsequent formula becomes a symbol without meaning.

What you will truly understand

• How any physical quantity is measured, named and expressed in the SI.
• How to decompose a vector into Cartesian components and recover its magnitude and angle.
• How to choose a reference frame and what consequences that choice has.
• What values the fundamental physical constants have and what they are used for.
• How to handle significant figures, absolute errors and uncertainty propagation.
• How to verify any formula by dimensional analysis before calculating.
• What a physical system is, what its boundary is, and which forces are internal or external.
• What it means for a quantity to be conserved and under what conditions.
• How to distinguish between energy and linear momentum, and when to use each.
• What a physical field is and why it appears in gravitation, electricity and fluids.
• How to estimate any physical result by orders of magnitude without a calculator.

Recommended learning route

1. Physical quantities and units: the foundation of the numerical language of physics.
2. Vectors and components: geometry of directed quantities.
3. Reference frames: axis and sign conventions.
4. Constants and reference values: reference table before any estimation.
5. Measurement errors and uncertainty: how to report real results.
6. Dimensional analysis: automatic verification of formulas.
7. Core structural concepts: system, forces, equilibrium, conservation, momentum, energy, field and scales.

Physical criterion you must acquire

Before substituting numbers into any formula you must be able to: (1) identify which quantities are involved and in what units, (2) check that the dimensions are consistent, (3) define the physical system and its boundaries, and (4) estimate the expected order of magnitude of the result to detect errors before they arise.

Connection with real problems

These foundations appear in every physics problem without exception: in mechanics when forces are added as vectors, in thermodynamics when energy is conserved, in electromagnetism when working with fields, in fluids when pressure is analyzed, and in any laboratory when uncertainties are reported. They are also the foundation of scientific programming, engineering design and the interpretation of experimental data.

Final goal of the topic

To have the criteria and tools to correctly read, verify and interpret any formula or numerical result in physics, regardless of the specific domain in which it appears.