Classical Mechanics Overview

Classical Mechanics

• Classical mechanics describes the motion of macroscopic objects, such as planets, cars, and baseballs.
• It is based on Newton's laws of motion, which relate force, mass, and acceleration.
• 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 an unbalanced force.
• Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. (F = ma)
• Newton's third law states that for every action, there is an equal and opposite reaction.
• Classical mechanics assumes that space and time are absolute and continuous.
• It is an excellent approximation for many everyday phenomena, but fails to accurately describe the behavior of objects at very high speeds (close to the speed of light) or at very small scales (atomic and subatomic levels).

Thermodynamics

• Thermodynamics deals with the relationships between heat, work, and energy.
• It is based on a set of fundamental laws, which govern the behavior of thermodynamic systems.
• The zeroth law of thermodynamics defines thermal equilibrium. If two systems are in thermal equilibrium with a third, they are in thermal equilibrium with each other.
• The first law of thermodynamics states that energy can neither be created nor destroyed, only transformed from one form to another. (ΔU = Q - W) where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
• The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. Increases in entropy are associated with natural processes.
• The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero. At absolute zero, the entropy of a perfectly crystalline substance is zero. This law also has implications for the unattainability of absolute zero.

Electromagnetism

• Electromagnetism describes the relationship between electric and magnetic fields.
• Electric fields are generated by electric charges, and magnetic fields are generated by moving electric charges.
• Electromagnetic fields propagate as waves.
• Maxwell's equations describe the behavior of electromagnetic fields and their interaction with matter.
• Electromagnetic forces are responsible for a wide range of phenomena, including light, radio waves, and other forms of electromagnetic radiation.
• Electromagnetic phenomena are crucial in understanding many technologies, such as radio, television, and radar.

Optics

• Optics deals with the behavior and properties of light.
• Light can be described as a wave, exhibiting phenomena such as interference and diffraction.
• Light can also be described as a stream of photons, exhibiting particle-like behavior, such as the photoelectric effect.
• Reflection, refraction, and diffraction are important phenomena in optics.
• Mirrors, lenses, and prisms are optical devices used to manipulate light.

Relativity

• Special relativity deals with the behavior of objects moving at constant velocities.
• It postulates that the speed of light in a vacuum is constant for all observers, regardless of the motion of the light source.
• This leads to several counterintuitive consequences, such as time dilation and length contraction.
  • Time dilation: Time slows down for objects moving at high speeds relative to a stationary observer.
  • Length contraction: Objects moving at high speeds appear shorter in the direction of motion to a stationary observer.
• General relativity deals with gravity and the curvature of spacetime.
• It describes gravity not as a force, but as a curvature of spacetime caused by mass and energy.
• This theory explains phenomena such as gravitational lensing and the precession of Mercury's orbit.

Quantum Mechanics

• Quantum mechanics deals with the behavior of matter at the atomic and subatomic levels.
• It postulates that energy, momentum, and other physical properties of a quantum system are quantized, meaning they can only take on discrete values.
• Quantum mechanics uses wave functions to describe the state of a quantum system.
• The wave function contains all the information about the system, including the probability of finding the system in a particular state.
• Key concepts include wave-particle duality, superposition, and entanglement.