The Physics Knowledge Vault

Master Physics
From First Principles

PhysicsVault delivers expert explanations of every fundamental physics concept — from Newton's laws to quantum mechanics — with interactive simulations, complete formula sheets, and 3,000+ word deep-dive articles written by physicists.

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25+ Expert Articles
7 Physics Topics
4 Simulations
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Core Physics Topics

Seven Pillars of Physics

Explore our comprehensive coverage of every major physics domain, from classical mechanics to the quantum frontier.

Mechanics

Newton's laws, forces, energy, momentum, circular motion, and gravitation — the foundation of all classical physics.

7 Articles

Thermodynamics

Heat, temperature, entropy, and the laws governing energy transfer in gases, liquids, and solids.

5 Articles

Waves & Optics

Sound, light, reflection, refraction, Doppler effect, and wave interference phenomena.

6 Articles

Electromagnetism

Electric fields, Coulomb's law, Ohm's law, magnetic forces, and Maxwell's equations.

3 Articles

Modern Physics

Special relativity, E=mc², the photoelectric effect, and wave-particle duality.

3 Articles

Kinematics

Describing motion with displacement, velocity, acceleration, and the four SUVAT equations.

1 Article

Quantum Mechanics

Wave functions, uncertainty principle, quantum tunneling, and atomic orbitals.

1 Article
Latest Content

Featured Articles

Comprehensive deep-dive articles with real physics content, worked examples, and interactive elements.

Mechanics

Newton's Laws of Motion: Complete Guide

Master all three of Newton's laws — inertia, F=ma, and action-reaction — with real-world examples and worked problems.

📅 2024 ⏱ 15 min read 🎯 Beginner
Modern Physics

Special Relativity: Einstein's Theory Explained

Time dilation, length contraction, E=mc², and why nothing travels faster than light — explained from first principles.

📅 2024 ⏱ 20 min read 🎯 Intermediate
Thermodynamics

Second Law of Thermodynamics: Entropy

Why heat flows from hot to cold, why perpetual motion is impossible, and how entropy shapes the universe.

📅 2024 ⏱ 18 min read 🎯 Intermediate
Modern Physics

Wave-Particle Duality Explained

De Broglie wavelength, the double-slit experiment, and the quantum superposition principle demystified.

📅 2024 ⏱ 17 min read 🎯 Advanced
Waves & Optics

The Doppler Effect: Complete Explanation

Why sirens change pitch, how radar guns work, and how astronomers use redshift to measure cosmic expansion.

📅 2024 ⏱ 14 min read 🎯 Beginner
Mechanics

Conservation of Momentum

Why momentum is always conserved in isolated systems. Elastic and inelastic collisions with full analysis.

📅 2024 ⏱ 16 min read 🎯 Beginner
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Why PhysicsVault

The Smart Way to Learn Physics

We built PhysicsVault for students, self-learners, and curious minds who want rigorous, accurate physics content—not oversimplified summaries.

Expert-Written Content

Every article is written by physicists and reviewed for accuracy. We cite authoritative sources and flag common misconceptions explicitly.

Interactive Simulations

See physics in action with our canvas-based simulations — projectile motion, wave superposition, Newton's cradle, and kinetic theory gas.

Complete Formula Sheets

Downloadable reference sheets for mechanics, thermodynamics, and waves. Every equation explained with variable definitions and units.

Deep Understanding

Articles run 3,000–5,000 words. We explain the physics conceptually and mathematically, with worked examples at multiple difficulty levels.

Practice Questions

Test your understanding with topic-organized multiple-choice questions. Instant feedback and step-by-step explanations included.

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Complete Coverage

Physics Topic Overview

Navigate our hub-and-spoke architecture from broad topics down to specific concept articles.

Classical Mechanics

7 articles

The study of motion, forces, and energy in the macroscopic world. Mechanics underpins all of classical physics.

Newton's Laws of Motion Projectile Motion Conservation of Momentum Work-Energy Theorem

Thermodynamics

5 articles

Heat, temperature, and the laws governing energy. From steam engines to cosmic heat death.

First Law of Thermodynamics Second Law & Entropy Kinetic Theory of Gases

Waves & Optics

6 articles

The physics of periodic disturbances — sound, light, seismic waves, and electromagnetic radiation.

Transverse Waves The Doppler Effect Snell's Law

Electromagnetism

3 articles

Electric and magnetic fields, circuits, Coulomb's law, and Maxwell's elegant unification.

Electric Fields Ohm's Law Coulomb's Law

Modern Physics

3 articles

The 20th century revolution: special relativity, the quantum of light, and wave-particle duality.

Special Relativity Photoelectric Effect Wave-Particle Duality

Kinematics

1 article

Describing motion mathematically without reference to forces. The four SUVAT equations and their applications.

Kinematics Equations (SUVAT)
Quick Reference

Essential Physics Formulas

The most important equations in physics, organized by topic with clear variable definitions.

Newton's Second Law
F = ma
F = net force (N), m = mass (kg), a = acceleration (m/s²)
Work-Energy Theorem
W = ΔKE = ½mv² - ½mv₀²
Net work equals change in kinetic energy
Gravitational PE
PE = mgh
m = mass, g = 9.8 m/s², h = height above reference
Conservation of Momentum
m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
Total momentum is conserved in isolated systems
Centripetal Acceleration
a_c = v²/r = ω²r
v = tangential speed, r = radius, ω = angular velocity
Universal Gravitation
F = Gm₁m₂/r²
G = 6.674×10⁻¹¹ N·m²/kg², r = separation distance
First Law of Thermodynamics
ΔU = Q - W
ΔU = change in internal energy, Q = heat added, W = work done by system
Ideal Gas Law
PV = nRT
P = pressure (Pa), V = volume (m³), n = moles, R = 8.314 J/(mol·K)
Specific Heat Capacity
Q = mcΔT
m = mass, c = specific heat capacity, ΔT = temperature change
Carnot Efficiency
η = 1 - T_cold/T_hot
Maximum theoretical efficiency of any heat engine
Entropy Change
ΔS = Q_rev/T
For reversible processes; T in Kelvin
RMS Speed of Gas
v_rms = √(3RT/M)
R = gas constant, T = temperature (K), M = molar mass
Wave Equation
v = fλ
v = wave speed (m/s), f = frequency (Hz), λ = wavelength (m)
Period and Frequency
T = 1/f
T = period (s), f = frequency (Hz)
Doppler Effect
f' = f(v ± v_o)/(v ∓ v_s)
v = wave speed, v_o = observer speed, v_s = source speed
Snell's Law
n₁sinθ₁ = n₂sinθ₂
n = refractive index, θ = angle from normal
Sound Intensity Level
β = 10 log(I/I₀)
I₀ = 10⁻¹² W/m² (threshold of hearing)
Critical Angle
sinθ_c = n₂/n₁
For total internal reflection when n₁ > n₂
Coulomb's Law
F = kq₁q₂/r²
k = 8.99×10⁹ N·m²/C², q = charges, r = separation
Electric Field
E = F/q = kQ/r²
E = field strength (N/C), Q = source charge
Ohm's Law
V = IR
V = voltage (V), I = current (A), R = resistance (Ω)
Electric Power
P = IV = I²R = V²/R
P = power (W), I = current (A), V = voltage (V)
Resistors in Series
R_total = R₁ + R₂ + …
Total resistance increases for series connections
Resistors in Parallel
1/R_total = 1/R₁ + 1/R₂
Total resistance decreases for parallel connections
Mass-Energy Equivalence
E = mc²
c = 3×10⁸ m/s, the speed of light in vacuum
Time Dilation
Δt' = γΔt₀
γ = 1/√(1-v²/c²), moving clocks run slower
Photon Energy
E = hf = hc/λ
h = 6.626×10⁻³⁴ J·s (Planck's constant)
De Broglie Wavelength
λ = h/p = h/mv
Every particle has an associated wavelength
Photoelectric Effect
KE_max = hf - φ
φ = work function, minimum energy to eject electron
Length Contraction
L = L₀/γ
Moving objects are shorter along direction of travel
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Common Questions

Frequently Asked Questions

Physics is the fundamental natural science that studies matter, energy, space, and time — and the forces and interactions that govern them. It is important because it provides the foundational understanding for all other natural sciences. From explaining why planets orbit the sun to designing semiconductors in your phone, physics is the bedrock of modern technology and scientific understanding. Studying physics develops critical thinking, mathematical reasoning, and a deep appreciation for the laws that underpin reality.
The main branches of physics covered on PhysicsVault are: (1) Classical Mechanics — the study of macroscopic motion and forces; (2) Thermodynamics — heat, temperature, and energy transfer; (3) Waves & Optics — periodic motion, sound, and light; (4) Electromagnetism — electric and magnetic fields; (5) Modern Physics — special relativity and quantum phenomena; (6) Kinematics — mathematical description of motion; and (7) Quantum Mechanics — the physics of the very small. Additional branches include astrophysics, condensed matter physics, and nuclear physics.
Newton's Second Law of Motion (F = ma) is arguably the most important because it quantitatively links force, mass, and acceleration. It is the workhorse equation of classical mechanics and underlies the analysis of any physical situation involving forces and motion. Newton's First Law (inertia) defines what happens when forces are balanced, and his Third Law (action-reaction) completes the picture of how forces arise between objects. All three are essential for a complete understanding of classical mechanics.
E = mc² is Einstein's mass-energy equivalence equation from Special Relativity (1905). It states that mass (m) and energy (E) are equivalent and interchangeable, with c² (the speed of light squared, ≈ 9×10¹⁶ m²/s²) as the conversion factor. Since c² is enormous, even tiny masses contain vast amounts of energy. This principle explains how nuclear reactions (fission and fusion) release energy by converting a small amount of mass into kinetic energy. It does not mean mass can be converted to pure energy in everyday situations — it means rest mass itself is a form of stored energy.
Speed is a scalar quantity — it tells you how fast an object moves but not in which direction. Velocity is a vector quantity — it has both magnitude (speed) and direction. For example, "60 km/h" is a speed, while "60 km/h north" is a velocity. This distinction matters enormously in physics: an object moving in a circle at constant speed has changing velocity (because direction changes), meaning it is accelerating and there must be a net force acting on it (centripetal force).
Entropy is a measure of the disorder or randomness of a system. In simple terms, it measures how many different microscopic arrangements (microstates) could produce the same macroscopic state. The Second Law of Thermodynamics states that the total entropy of an isolated system always increases over time — disorder spontaneously increases. This explains why ice melts in a warm room (disordered water molecules are more probable than ordered ice), why heat flows from hot to cold, and why you cannot un-scramble an egg. Entropy gives time its direction — the "arrow of time."
According to Einstein's Special Theory of Relativity, as an object with mass accelerates, its relativistic mass increases. The closer it gets to the speed of light, the more energy is required to accelerate it further. Reaching exactly the speed of light would require infinite energy — which is physically impossible for any object with mass. The equation for relativistic momentum is p = γmv, where γ = 1/√(1-v²/c²) approaches infinity as v approaches c. Massless particles like photons always travel at exactly c because they have no rest mass and exist only at light speed.
PhysicsVault uses a hub-and-spoke architecture. The homepage links to 7 pillar category pages (Mechanics, Thermodynamics, Waves & Optics, Electromagnetism, Modern Physics, Kinematics, Quantum Mechanics). Each category page links to 1–7 in-depth "spoke" articles. Every article follows a consistent template: TL;DR, definition, key insight, formula box, 3,000+ word explanation, misconception box, worked examples, applications, summary table, FAQ section, and related articles. Formula sheets provide quick reference by topic, and practice questions let you test your knowledge.