Classical Mechanics: Motion and Forces

• Physics is a natural science that studies matter, its motion, and behavior through space and time, and that studies the related entities of energy and force.

Classical Mechanics

• Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, and stars.
• It predicts the behavior of objects when subjected to forces.
• It is often referred to as Newtonian mechanics after Isaac Newton and his laws of motion.
• Key concepts include:
  • Displacement: Change in position of an object.
  • Velocity: Rate of change of displacement.
  • Acceleration: Rate of change of velocity.
  • Force: Interaction that causes a change in an object's motion.
  • Mass: Measure of an object's resistance to acceleration.
  • Momentum: Product of mass and velocity.
  • Energy: Ability to do work.
• Newton's Laws of Motion are fundamental:
  • First Law (Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a force.
  • Second Law: Force equals mass times acceleration (F = ma).
  • Third Law: For every action, there is an equal and opposite reaction.
• Conservation laws:
  • Conservation of energy: The total energy of an isolated system remains constant.
  • Conservation of momentum: The total momentum of an isolated system remains constant.
  • Conservation of angular momentum: The total angular momentum of an isolated system remains constant.

Thermodynamics

• Thermodynamics is the study of energy, its transformations, and its relation to matter.
• It deals with the macroscopic properties of systems, such as temperature, pressure, and volume.
• Key concepts:
  • Temperature: Measure of the average kinetic energy of the particles in a system.
  • Heat: Transfer of energy between objects due to a temperature difference.
  • Work: Energy transferred when a force causes a displacement.
  • Internal energy: Total energy contained within a thermodynamic system.
  • Entropy: Measure of the disorder or randomness of a system.
• Laws of Thermodynamics:
  • Zeroth Law: If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
  • First Law: The change in internal energy of a system equals the heat added to the system minus the work done by the system (ΔU = Q - W).
  • Second Law: The entropy of an isolated system always increases or remains constant; it never decreases.
  • Third Law: The entropy of a system approaches a constant value as the temperature approaches absolute zero.
• Thermodynamic processes:
  • Isothermal: Occurs at constant temperature.
  • Adiabatic: Occurs without heat transfer.
  • Isobaric: Occurs at constant pressure.
  • Isochoric (or isovolumetric): Occurs at constant volume.

Quantum Physics

• Quantum physics studies the behavior of matter and energy at the atomic and subatomic levels.
• It introduces concepts like quantization, wave-particle duality, and uncertainty.
• Key concepts:
  • Quantization: Energy, momentum, and other physical quantities are restricted to discrete values.
  • Wave-particle duality: Particles (like electrons) exhibit both wave-like and particle-like properties.
  • Uncertainty principle: There is a fundamental limit to the precision with which certain pairs of physical properties, like position and momentum, can be known simultaneously.
  • Superposition: A quantum system can exist in multiple states at the same time.
  • Entanglement: Two or more quantum systems can be linked together in such a way that they share the same fate, no matter how far apart they are.
• Important formalisms and equations:
  • Schrödinger equation: Describes how the quantum state of a physical system changes over time.
  • Heisenberg's uncertainty principle: ΔxΔp ≥ ħ/2, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and ħ is the reduced Planck constant.
• Quantum phenomena:
  • Quantum tunneling: Particles can pass through a potential barrier, even if they do not have enough energy to overcome it classically.
  • Quantum entanglement: Two particles can be linked in such a way that the state of one particle instantaneously affects the state of the other, regardless of the distance between them.

Electromagnetism

• Electromagnetism is the study of the electromagnetic force, which is one of the four fundamental forces of nature.
• It describes the interactions between electrically charged particles and includes the study of electric and magnetic fields.
• Key concepts:
  • Electric charge: A fundamental property of matter that causes it to experience a force when placed in an electromagnetic field.
  • Electric field: A field of force surrounding an electric charge that exerts force on other charges.
  • Magnetic field: A field of force created by moving electric charges (electric current) or magnetic dipoles.
  • Electric current: The rate of flow of electric charge.
  • Voltage: The electric potential difference between two points.
  • Resistance: Opposition to the flow of electric current.
• Maxwell's equations:
  • Gauss's law for electricity: Relates the electric field to the distribution of electric charges.
  • Gauss's law for magnetism: States that there are no magnetic monopoles.
  • Faraday's law of induction: Describes how a changing magnetic field creates an electric field.
  • Ampère-Maxwell's law: Relates the magnetic field to electric currents and changing electric fields.
• Electromagnetic waves:
  • Electromagnetic waves are disturbances in electric and magnetic fields that propagate through space.
  • They travel at the speed of light in a vacuum.
  • Examples include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.

Relativity

• Relativity encompasses two related theories by Albert Einstein: special relativity and general relativity.
• Special relativity deals with the relationship between space and time in inertial reference frames (frames moving at constant velocity).
• General relativity deals with gravity as a manifestation of the curvature of spacetime caused by mass and energy.
• Key concepts of Special Relativity:
  • Principle of relativity: The laws of physics are the same for all observers in uniform motion relative to one another.
  • Constancy of the speed of light: The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.
  • Time dilation: Time passes more slowly for moving objects relative to stationary observers.
  • Length contraction: The length of a moving object appears shorter in the direction of motion to a stationary observer.
  • Mass-energy equivalence: Energy and mass are interchangeable (E = mc²).
• Key concepts of General Relativity:
  • Principle of equivalence: Gravitational mass and inertial mass are equivalent.
  • Spacetime curvature: Gravity is not a force but a consequence of the curvature of spacetime caused by mass and energy.
  • Gravitational time dilation: Time passes more slowly in stronger gravitational fields.
  • Gravitational lensing: Light bends as it passes near massive objects.
  • Black holes: Regions of spacetime where gravity is so strong that nothing, not even light, can escape.