40 in-depth physics guides
Explore motion, energy, fields, space, time, quantum reality, and the hidden structure of the cosmos. Every concept now opens into its own reading page, with the physical idea first and the mathematics explained only when it clarifies the picture.
The subjects build outward from familiar motion into matter, fields, light, spacetime, and the quantum universe. The chapter bar remains available while you read, so changing direction takes one tap.
The complete physics shelf
Browse concise introductions here, then open any concept as its own full reading page—with the physical reasoning, limits, applications, common mistakes, and mathematics explained in context.
6 concepts shown
Mechanics
Mechanics describes how objects move and why their motion changes, from a sliding block to a spinning planet.
Position only means something relative to a chosen origin, and velocity only means something relative to an observer. Acceleration is different: every observer moving at constant velocity agrees when an object accelerates.
Acceleration says how much velocity changes during each interval of time. A turn counts even at constant speed because the direction of velocity changes.
An object does not need a continuing force to keep moving. It needs a net force to accelerate. When all forces balance, it remains at rest or continues with constant velocity.
The combined, direction-aware force sets the acceleration. More net force produces more acceleration; more inertia makes the same force less effective.
Energy can be stored in motion, height, deformation, fields, chemical structure, or random molecular motion. It can cross a system boundary through work, heating, or radiation, but the total accounting remains balanced.
Net work is energy transferred by forces into or out of an object’s motion. Power asks how quickly that transfer occurs.
Momentum combines mass and velocity. During a collision, enormous internal forces can act, yet the total momentum of an isolated group remains unchanged because those forces arrive in equal-and-opposite pairs.
Impulse is force accumulated over time. The same momentum change can come from a large force briefly or a smaller force acting longer—the principle behind airbags and follow-through.
Where mass sits matters when an object turns. Mass farther from the axis is harder to spin up. With little outside torque, pulling mass inward raises rotation rate so angular momentum remains fixed.
Torque is the rotational effect of a force, rotational inertia describes resistance to angular acceleration, and the lever arm determines how effectively a force turns something.
A satellite is pulled downward by gravity while moving sideways fast enough to keep missing the ground. Gravity weakens with distance but never suddenly turns off, so orbital paths connect falling objects to moons and planets.
Doubling the distance between centers makes gravity one-fourth as strong. The inverse-square pattern comes from influence spreading across the surface of an expanding sphere.
Matter & heat
Macroscopic behavior emerges from huge numbers of microscopic particles colliding, flowing, and sharing energy.
Inside a fluid, random molecular collisions push in every direction. Pressure rises with depth because deeper layers support more fluid above them, and a pressure change in a confined fluid is transmitted throughout it.
The same force creates more pressure when concentrated on a smaller area. Hydraulic systems reverse the idea: equal pressure acting over a larger area produces a larger force.
Because pressure is greater at greater depth, the bottom of a submerged object is pushed upward more strongly than its top is pushed downward. The resulting buoyant force equals the weight of displaced fluid.
A larger displaced volume or denser fluid creates more upward force. An object floats when it displaces enough fluid for buoyancy to balance its weight.
In steady incompressible flow, what enters a pipe must leave it. A narrower section therefore carries fluid faster. Bernoulli’s principle relates that speed to pressure and height, while viscosity and turbulence mark where the ideal model loses accuracy.
Cross-sectional area times flow speed stays constant when density and flow rate are constant. Halving the area doubles the speed.
Temperature describes how energy is distributed among microscopic degrees of freedom. Heat is energy in transit because of a temperature difference. Once equilibrium is reached, the transfer stops even though both objects still contain internal energy.
The energy needed for a temperature change depends on mass and specific heat capacity. The relationship does not cover phase changes, where energy rearranges matter without changing temperature.
A high-entropy state can be realized in far more microscopic ways than a low-entropy state. Systems therefore overwhelmingly evolve toward macrostates with more available arrangements, giving ordinary processes a preferred direction in time.
For an isolated system, total entropy does not decrease. Local order can grow—a refrigerator cools its interior—only while producing at least as much entropy elsewhere.
Solid, liquid, gas, and plasma are not different substances but different patterns of motion and interaction. During a phase change, added energy alters the arrangement or bonding rather than raising temperature.
Latent heat is the energy per unit mass required to change phase at the transition temperature. The plateau on a heating curve is structural change in progress.
Oscillations & waves
Waves carry energy and information through coordinated disturbance, while the medium’s particles usually oscillate around home.
When displacement produces a push back toward equilibrium, a system can overshoot and repeat. Ideal simple harmonic motion is the special case where the restoring force grows directly with displacement.
The minus sign means the spring force points opposite the displacement. Stiffer springs oscillate faster; greater attached mass makes the response slower.
For many waves, the medium determines propagation speed. The source chooses frequency. Wavelength adjusts so both can be true when a wave crosses into a new medium.
Wave speed equals cycles per second times distance per cycle. If speed falls while frequency stays fixed, wavelength must shorten.
Where disturbances overlap, their displacements add. Matching peaks reinforce; a peak meeting a trough can cancel. After crossing, ideal waves continue with their original forms.
Superposition is ordinary addition with direction included. Interference is the visible pattern created by that addition.
Reflected waves can repeatedly overlap into stationary nodes and antinodes. Only wavelengths that fit the boundary conditions persist strongly, producing discrete resonant frequencies in strings, air columns, structures, and atoms.
For a string fixed at both ends, an integer number of half-wavelengths must fit its length. Different boundaries produce different allowed patterns.
A moving source crowds wavefronts ahead and spreads them behind. An observer moving through a wave meets fronts at a changed rate. This Doppler shift changes perceived pitch and also reveals motion in radar, medicine, and astronomy.
Approach raises the rate at which wavefronts arrive; separation lowers it. Crossing the wave speed piles fronts into a shock wave.
Small repeated pushes can build a large response when timed near a system’s natural frequency. Damping drains energy and limits the growth, which is why engineers tune both resonance and dissipation.
Each push arrives in step with the existing motion, so energy accumulates efficiently—like pushing a swing at the right moments.
Electricity & magnetism
Electric and magnetic fields are two connected aspects of electromagnetism, the interaction holding atoms and technology together.
Like charges repel and opposite charges attract. In conductors, charges can redistribute; in insulators, bound charges can still shift slightly. Charge is conserved, so charging usually means separation or transfer rather than creation.
Electric force grows with both charges and weakens with the square of separation. Its sign tells whether the interaction attracts or repels.
An electric field assigns a direction and strength to every point: it says how a positive test charge would accelerate there. Fields from many charges add as vectors, building a map before any test charge arrives.
Field strength is force per unit positive charge. The field belongs to the source arrangement; the force also depends on what is placed in it.
Electric potential turns a vector field into an energy landscape. Charges naturally move toward lower potential energy, although the direction depends on the sign of the charge.
One volt is one joule of potential-energy change per coulomb of charge. A battery maintains a potential difference by using chemical energy to separate charge.
A source establishes an electric field throughout a closed path, and charges already present respond. Current is charge flow rate; resistance describes how strongly the material and geometry oppose that flow.
For an ohmic element, greater voltage drives greater current while resistance sets the ratio. Electrical power is the rate at which the circuit transfers energy.
Opposite charge collects on nearby conductors, producing a field between them. Geometry and material determine how much charge can be separated for each volt, while charging and discharging introduce a natural time scale.
Capacitance is charge stored per volt. Larger plate area, smaller separation, or a suitable dielectric usually increases it.
A magnetic field pushes perpendicular to both a charge’s motion and the field. It can bend a path without changing speed, and currents create magnetic fields because current is moving charge.
The force is largest when motion crosses the field and zero when motion runs along it. Because the force is sideways, it normally changes direction rather than kinetic energy.
Changing magnetic flux through a loop induces an electromotive force. The induced current opposes the change that produced it, preserving energy rather than offering free amplification.
Faster flux change creates a larger induced voltage. The minus sign is Lenz’s law: the response resists the change.
Light & optics
Ray models explain everyday images; wave models explain diffraction and interference; photons explain how light exchanges energy.
A smooth surface redirects parallel rays in an orderly way, allowing an image to form. A rough surface sends rays in many directions, yet each microscopic reflection still obeys the same rule.
Both angles are measured from the line perpendicular to the surface, not from the surface itself.
Frequency remains fixed at a boundary, but wave speed and wavelength change. A tilted wavefront reaches the new medium one side first, causing the path to rotate.
Refractive index compares light’s vacuum speed with its speed in a material. A higher index means slower propagation and usually stronger bending toward the normal.
Converging systems bring parallel rays toward a focus; diverging systems spread them as if they came from one. Image location and size follow from geometry, while aberrations appear because real surfaces are not perfect.
The reciprocal relationship connects focal length, object distance, and image distance. Signs distinguish real from virtual images.
When an opening or obstacle approaches a wavelength in size, light cannot be represented by a single straight ray. Different paths overlap, creating bright and dark regions and setting a fundamental limit on resolution.
For evenly spaced slits, bright directions occur where path differences equal whole wavelengths, so the waves arrive in step.
Radio, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays differ mainly in frequency and wavelength. They share the same field structure and vacuum speed, but interact differently with matter.
A photon’s energy grows with frequency. Intensity controls how many photons arrive; frequency controls the energy each carries.
Modern physics & frontiers
At extreme speed, tiny scale, immense gravity, or cosmic distance, deeper frameworks replace familiar approximations.
Observers in uniform relative motion can disagree about elapsed time, distance, and simultaneity while agreeing on the laws of physics and the speed of light. Spacetime interval replaces separate universal measures of space and time.
The Lorentz factor measures relativistic effects. At ordinary speeds it is almost one; as speed approaches light, time and distance comparisons change dramatically.
In general relativity, mass-energy shapes spacetime and free objects follow its straightest possible paths. What feels like gravitational force can be the geometry of the stage itself.
Einstein’s field equations connect the distribution of mass, energy, pressure, and momentum to spacetime curvature; the full mathematics uses tensors.
A quantum state encodes probability amplitudes, not a hidden miniature classical path. Amplitudes can interfere, and measurement returns one allowed outcome with probabilities the theory predicts.
Quantum amplitudes can be positive, negative, or complex and add before being squared. That is why alternatives interfere even when individual detections arrive as localized events.
A state narrowly localized in position requires a broad mixture of momenta, and a sharply defined momentum requires a spread-out wave. This is not merely bad equipment; it follows from wave structure.
The product of position spread and momentum spread has a lower bound. Similar tradeoffs exist for other incompatible observables.
A bound nucleus has less mass than its separated ingredients because energy was released while it formed. Fission and fusion release energy by moving nuclei toward more tightly bound configurations.
A small change in system mass corresponds to a large energy change because the conversion factor is the speed of light squared.
Modern particle physics treats electron, quark, photon, and Higgs fields as fundamental. What we call a particle is a quantized excitation, while interactions exchange energy and momentum through field processes.
The Standard Model unifies electromagnetic, weak, and strong interactions. Gravity and the nature of dark matter remain outside its completed account.
Gravity compresses a star while hot matter and radiation push outward. Fusion changes composition and supplies energy; when available fuel and pressure support change, stars evolve into white dwarfs, neutron stars, or black holes.
Hydrostatic equilibrium is a layer-by-layer balance. Stellar evolution follows what happens as the source of pressure and energy changes.
The Big Bang model describes an early hot, dense universe followed by expansion and cooling, not an explosion into preexisting space. Light redshifts as space expands, letting observations reconstruct cosmic history.
On large scales, more distant galaxies recede faster. The relationship measures expansion of space; gravitationally bound systems do not simply expand with it.
Nonlinear systems can amplify tiny differences in initial conditions until long-term outcomes diverge. The rules may contain no randomness, yet limited measurement precision creates a practical prediction horizon.
A positive Lyapunov exponent describes how rapidly nearby trajectories separate. Weather is a familiar example; climate statistics can remain meaningful even when exact weather cannot.
Below a critical condition, electrons in some materials form a coordinated quantum state that carries current without ordinary electrical resistance. Superconductors also expel magnetic fields through the Meissner effect.
The key is not simply colder metal. Many particles lock into one phase-coherent state, producing new bulk behavior.
Try a broader term such as energy, motion, field, light, or quantum.
The larger picture