Classical Mechanics & Newton's Laws

• Physics is a natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and 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, stars, and galaxies.
• It provides extremely accurate results as long as gravity is weak, and the objects are large enough and moving slowly compared to the speed of light.
• Classical mechanics is a branch of physics used to describe 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 acceleration of an object is directly proportional to the net force acting on the object, is in the same direction as the net force, and is inversely proportional to the mass of the object (F = ma).
• Newton's third law states that for every action, there is an equal and opposite reaction.
• Classical mechanics also includes the study of statics, which deals with objects at rest, and dynamics, which deals with objects in motion.
• Important concepts include displacement, velocity, acceleration, force, mass, momentum, energy (kinetic and potential), work, and power.
• Conservation laws are fundamental in classical mechanics, including conservation of energy, momentum, and angular momentum.
• Lagrangian mechanics and Hamiltonian mechanics are more abstract formulations of classical mechanics, providing a more generalized approach to solving complex problems.

Thermodynamics

• Thermodynamics is the branch of physics that deals with heat, work, and energy, and the relationships between them.
• It defines macroscopic variables, such as temperature, energy, and entropy, that characterize materials and radiation.
• The field is based on four laws of thermodynamics which quantify these variables and describe their relations.
• The zeroth law of thermodynamics states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
• The first law of thermodynamics is the application of the conservation of energy principle to thermodynamic systems. Energy can be transformed from one form to another, but cannot be created or destroyed.
• The second law of thermodynamics states that the entropy of an isolated system always increases or remains constant. It introduces the concept of irreversibility in natural processes.
• The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero.
• Key concepts include temperature, heat, work, internal energy, enthalpy, entropy, and free energy.
• Thermodynamic processes include isothermal (constant temperature), adiabatic (no heat exchange), isobaric (constant pressure), and isochoric (constant volume) processes.
• Heat engines, refrigerators, and heat pumps are examples of thermodynamic systems that convert heat into work or vice versa.
• Statistical mechanics provides a microscopic interpretation of thermodynamics, linking macroscopic properties to the statistical behavior of a large number of particles.

Electromagnetism

• Electromagnetism is the branch of physics that deals with the electromagnetic force that occurs between electrically charged particles.
• It studies the interactions between electric and magnetic fields.
• Electricity and magnetism are two aspects of electromagnetism.
• Electric charge is a fundamental property of matter that can be positive or negative.
• Electric fields are created by electric charges and exert forces on other charges.
• Magnetic fields are created by moving electric charges (electric current) and exert forces on other moving charges.
• Key concepts include electric charge, electric field, electric potential, electric current, resistance, capacitance, magnetic field, magnetic flux, inductance, and electromagnetic waves.
• Maxwell's equations are a set of four equations that describe the behavior of electric and magnetic fields and their interactions with matter.
• Electromagnetic waves, such as light, radio waves, microwaves, and X-rays, are disturbances in electric and magnetic fields that propagate through space.
• Electromagnetism has many applications, including electric motors, generators, transformers, radio communications, and medical imaging.
• Electromagnetic force is one of the four fundamental forces of nature, along with the strong nuclear force, the weak nuclear force, and gravity.

Quantum Mechanics

• Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.
• It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science.
• Quantum mechanics governs the behavior of matter and energy at the atomic and subatomic levels, where classical mechanics fails to provide accurate descriptions.
• Key concepts include quantization of energy, wave-particle duality, the uncertainty principle, superposition, and entanglement.
• The Schrödinger equation is a fundamental equation in quantum mechanics that describes how the quantum state of a physical system changes over time.
• Quantum states are described by wave functions, which provide information about the probability of finding a particle in a particular state or location.
• The uncertainty principle, formulated by Heisenberg, states that there is a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position and momentum, can be known simultaneously.
• Quantum entanglement is a phenomenon in which two or more particles become linked together in such a way that the state of one particle instantaneously affects the state of the other, regardless of the distance between them.
• Quantum mechanics has many applications, including lasers, transistors, nuclear energy, and medical imaging.
• Quantum field theory combines quantum mechanics with special relativity to describe the behavior of elementary particles and their interactions.

Relativity

• Relativity is a theory formulated by Albert Einstein that describes the relationship between space and time.
• It consists of two related theories: special relativity and general relativity.
• Special relativity deals with the relationship between space and time for observers moving at constant velocities.
• General relativity deals with gravity as a curvature of spacetime caused by mass and energy.
• Key concepts in special relativity include the constancy of the speed of light, time dilation, length contraction, and the equivalence of mass and energy (E=mc^2).
• Time dilation is the phenomenon in which time passes slower for an object moving at high speeds relative to a stationary observer.
• Length contraction is the phenomenon in which the length of an object moving at high speeds appears shorter in the direction of motion to a stationary observer.
• General relativity describes gravity as a curvature of spacetime caused by mass and energy.
• The curvature of spacetime affects the motion of objects, including light, causing them to follow curved paths.
• General relativity predicts phenomena such as gravitational lensing, black holes, and gravitational waves.
• Gravitational lensing is the bending of light around massive objects, such as galaxies or black holes.
• Black holes are regions of spacetime where gravity is so strong that nothing, not even light, can escape.
• Gravitational waves are ripples in spacetime caused by accelerating massive objects, such as merging black holes or neutron stars.
• Relativity has many applications, including GPS navigation, particle accelerators, and cosmology.