Introduction to Classical Mechanics and Thermodynamics

• Physics is the study of matter, energy, and their interactions.

Classical Mechanics

• Classical mechanics deals with the motion of macroscopic objects.
• It is based on Newton's laws of motion.
• Newton's first law states that 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.
• Newton's second law states that the force acting on an object is equal to the mass of the object times its acceleration (F = ma).
• Newton's third law states that for every action, there is an equal and opposite reaction.
• Key concepts include displacement, velocity, acceleration, force, mass, momentum, energy, and work.
• Conservation laws, such as conservation of energy, momentum, and angular momentum, are fundamental.
• Examples include projectile motion, pendulum motion, and planetary motion.
• Lagrangian and Hamiltonian mechanics are advanced formulations of classical mechanics.

Thermodynamics

• Thermodynamics is the study of heat and its relation to other forms of energy.
• It deals with the macroscopic properties of matter, such as temperature, pressure, and volume.
• The first law of thermodynamics states that energy is conserved: the change in internal energy of a system is equal to the heat added to the system minus the work done by the system (ΔU = Q - W).
• The second law of thermodynamics states that the entropy of an isolated system always increases or remains constant.
• The third law of thermodynamics states that the entropy of a system approaches a minimum value as the temperature approaches absolute zero.
• Key concepts include temperature, heat, work, internal energy, entropy, and enthalpy.
• Thermodynamic processes include isothermal, adiabatic, isobaric, and isochoric processes.
• Heat engines and refrigerators are examples of thermodynamic systems.
• Statistical mechanics provides a microscopic interpretation of thermodynamic quantities.

Electromagnetism

• Electromagnetism deals with the interactions between electric charges and magnetic fields.
• Electric charge is a fundamental property of matter.
• Coulomb's law describes the force between electric charges.
• Electric fields are created by electric charges and exert forces on other charges.
• Magnetic fields are created by moving electric charges (currents) and exert forces on other moving charges.
• Faraday's law of induction describes how changing magnetic fields create electric fields.
• Ampere's law describes how electric currents create magnetic fields.
• Maxwell's equations are a set of four equations that describe the behavior of electric and magnetic fields.
• Electromagnetic waves, such as light, are disturbances in electric and magnetic fields that propagate through space.
• Key concepts include electric charge, electric field, magnetic field, electric current, voltage, resistance, capacitance, and inductance.

Quantum Physics

• Quantum physics deals with the behavior of matter and energy at the atomic and subatomic levels.
• It is based on the idea that energy is quantized, meaning it can only exist in discrete amounts.
• The wave-particle duality states that particles can exhibit wave-like properties and waves can exhibit particle-like properties.
• The Heisenberg uncertainty principle states that it is impossible to know both the position and momentum of a particle with perfect accuracy.
• The Schrödinger equation is a fundamental equation in quantum mechanics that describes the evolution of a quantum system over time.
• Quantum mechanics is used to describe the behavior of atoms, molecules, and other microscopic systems.
• Quantum field theory extends quantum mechanics to include fields, such as the electromagnetic field.
• Key concepts include wave function, quantum state, energy levels, quantum numbers, and superposition.
• Examples include the photoelectric effect, the Compton effect, and atomic spectra.

Relativity

• Relativity deals with the relationship between space and time.
• Special relativity describes the behavior of objects moving at constant speed.
• General relativity describes the behavior of objects in gravitational fields.
• Key postulates of special relativity are:
• The laws of physics are the same for all observers in uniform motion.
• The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.
• Consequences of special relativity include time dilation, length contraction, and mass increase.
• Mass-energy equivalence (E = mc^2) is a famous result of special relativity.
• General relativity describes gravity as a curvature of spacetime caused by mass and energy.
• Predictions of general relativity include the bending of light around massive objects, the existence of black holes, and gravitational waves.
• Key concepts include spacetime, Lorentz transformation, gravitational field, and black hole.