Fundamental Principles of Physics

General Physics

• Physics studies matter, energy, and their interactions.
• The aim of physics is understanding the universe's governing fundamental regulations.
• Physics covers a wide range of phenomena, from subatomic particles to the cosmos' large-scale structure.

Mechanics

• Mechanics is a physics branch that deals with object motion and the forces causing them.
• Kinematics describes motion concerning displacement, velocity, and acceleration, without considering forces.
• Dynamics relates motion to forces and torques that cause it.
• Newton's laws of motion are mechanics' fundamental principles.
• Newton’s first law: objects at rest stay at rest, and objects in motion stay in motion with the same velocity unless acted upon by a force.
• Newton’s second law: the force on an object equals its mass times its acceleration, shown as F = ma.
• Newton’s third law: every action has an equal and opposite reaction.

Energy

• Energy refers to the ability to do work.
• Kinetic energy, or the energy of motion, is given by 1/2 * mv^2.
• Potential energy is stored energy, like gravitational potential energy (mgh) or elastic potential energy (1/2 * kx^2).
• The work-energy theorem states that work done on an object equals its kinetic energy change.
• Conservation of energy means energy is neither created nor destroyed, only transformed.

Thermodynamics

• Thermodynamics studies heat and its relation to other energy forms.
• Temperature measures the average kinetic energy of particles in a substance.
• Heat involves energy transfer between objects due to temperature differences.
• The laws of thermodynamics describe the behavior of energy in thermodynamic systems.
• The first law of thermodynamics: a system’s internal energy change equals heat added minus work done by the system.
• The second law of thermodynamics: an isolated system's entropy (disorder) always increases or stays constant.

Waves

• Waves are disturbances transferring energy through a medium or space.
• Mechanical waves need a medium to travel through.
• Electromagnetic waves don't need a medium, and can travel through a vacuum.
• Transverse waves feature oscillations perpendicular to wave propagation (e.g., light waves).
• Longitudinal waves feature oscillations parallel to wave propagation (e.g., sound waves).
• Wavelength measures the distance between two successive crests or troughs.
• Frequency refers to the number of oscillations per unit of time.
• Wave speed equals wavelength times frequency (v = λf).
• Interference happens when two or more waves overlap.
• Superposition dictates that the resultant displacement at any point is the sum of individual wave displacements.
• Constructive interference happens when waves are in phase, thus resulting in a larger amplitude.
• Destructive interference happens when waves are out of phase, thus resulting in a smaller amplitude.
• Diffraction refers to the bending of waves around obstacles or through openings.

Optics

• Optics concerns the study of light and its properties.
• Reflection refers to light bouncing off a surface.
• Refraction refers to light bending as it passes from one medium to another.
• Lenses focus or diverge light.
• Convex lenses converge light.
• Concave lenses diverge light.
• Focal length measures the distance from the lens to where parallel light rays converge or appear to diverge.

Electricity

• Electricity is the study of electric charge and its effects.
• Electric charge represents a fundamental property of matter.
• There are two kinds of electric charge: positive and negative.
• Like charges repel, and opposite charges attract.
• Electric current refers to the flow of electric charge.
• Voltage measures the electric potential difference between two points.
• Resistance opposes the flow of electric current.
• Ohm's law states that voltage equals current times resistance (V = IR).

Magnetism

• Magnetism studies magnetic fields and their effects.
• Moving electric charges produce magnetic fields.
• Magnets contain two poles: north and south.
• Like poles repel, and opposite poles attract.
• Electromagnetism refers to the interaction between electric and magnetic fields.
• Electromagnets are magnets created by electric currents.

Nuclear Physics

• Nuclear physics studies the structure, properties, and reactions of atomic nuclei.
• The nucleus contains protons and neutrons.
• Protons feature a positive charge.
• Neutrons are without charge.
• The number of protons determines the element.
• Isotopes are atoms of the same element, but with different numbers of neutrons.
• Radioactivity involves the spontaneous emission of particles or energy from unstable nuclei.
• Alpha decay involves emitting an alpha particle (helium nucleus).
• Beta decay involves emitting a beta particle (electron or positron).
• Gamma decay involves emitting a gamma ray (high-energy photon).

Quantum Mechanics

• Quantum mechanics studies matter and energy behavior at atomic and subatomic levels.
• Quantum mechanics describes matter's wave-particle duality.
• Particles can act like waves, while waves can act like particles.
• The Heisenberg uncertainty principle says it's impossible to know both position and momentum of a particle with perfect accuracy.
• Quantum entanglement links two or more particles; the state of one instantaneously affects the other, regardless of distance.

Relativity

• Relativity describes the relationship between space, time, and gravity.
• Special relativity concerns the relationship between space and time for objects moving at constant velocities.
• General relativity describes gravity as the curvature of spacetime caused by mass and energy.
• Time dilation refers to the slowing of time for objects moving at high speeds relative to an observer.
• Length contraction refers to the shortening of an object’s length in motion direction as its speed approaches light speed.
• Mass-energy equivalence exists, expressed by E = mc^2 (energy equals mass times the speed of light squared).

Cosmology

• Cosmology studies the universe's origin, evolution, and structure.
• The Big Bang theory is the prevailing cosmological model.
• About 13.8 billion years ago, the universe originated from an extremely hot, dense state, and has been expanding/cooling since.
• Dark matter and dark energy make up a considerable portion of the universe's mass-energy.
• Dark matter doesn’t interact with light, but scientists infer its presence from its gravitational effects.
• Dark energy may be responsible for the accelerating expansion of the universe.