Physics: Kinematics and Dynamics

Mechanics

Kinematics

• Study of motion without considering forces
• Key concepts:
  • Displacement: shortest distance between initial and final positions
  • Velocity: rate of change of displacement
  • Acceleration: rate of change of velocity
  • Time: scalar quantity measuring duration
  • Frames of reference: inertial and non-inertial frames

Dynamics

• Study of motion considering forces
• Key concepts:
  • Force: push or pull causing motion
  • Newton's laws:
    • First law (inertia): objects at rest stay at rest, objects in motion stay in motion
    • Second law (F = ma): force equals mass times acceleration
    • Third law (action and reaction): every action has an equal and opposite reaction
  • Energy:
    • Kinetic energy: energy of motion
    • Potential energy: energy of position or configuration
  • Momentum: product of mass and velocity

Rotational Motion

• Study of rotation around a fixed axis
• Key concepts:
  • Angular displacement: angle of rotation
  • Angular velocity: rate of change of angular displacement
  • Angular acceleration: rate of change of angular velocity
  • Torque: rotational force
  • Rotational kinematics: analogs of linear kinematics for rotational motion

Thermodynamics

Laws of Thermodynamics

• Key concepts:
  • Zeroth law: if two systems are in thermal equilibrium with a third, they are in thermal equilibrium with each other
  • First law (energy conservation): energy cannot be created or destroyed, only converted
  • Second law: total entropy of an isolated system always increases over time
  • Third law: as temperature approaches absolute zero, entropy approaches a minimum value

Thermodynamic Systems

• Key concepts:
  • Isolated systems: no energy or matter exchanged with surroundings
  • Closed systems: energy exchanged, but no matter exchanged
  • Open systems: energy and matter exchanged with surroundings
  • Thermodynamic equilibrium: state of balance among system and surroundings

Thermodynamic Processes

• Key concepts:
  • Isothermal: constant temperature
  • Adiabatic: no heat exchanged
  • Isobaric: constant pressure
  • Isochoric: constant volume
  • Cyclic processes: series of processes returning to initial state

Relativity

Special Relativity

• Key concepts:
  • Time dilation: time appears to pass slower for moving observers
  • Length contraction: objects appear shorter to moving observers
  • Relativity of simultaneity: events simultaneous for one observer may not be for another
  • Speed of light: always constant, regardless of observer motion
  • Lorentz transformation: mathematical framework for relativity

General Relativity

• Key concepts:
  • Gravitational time dilation: time passes slower near massive objects
  • Gravitational redshift: light emitted from massive objects appears redder
  • Equivalence principle: gravity and acceleration are equivalent
  • Geodesic: shortest path in curved spacetime
  • Einstein's field equations: mathematical description of gravity and spacetime curvature

Mechanics

Kinematics

• Displacement is the shortest distance between initial and final positions
• Velocity is the rate of change of displacement, measured in meters per second (m/s)
• Acceleration is the rate of change of velocity, measured in meters per second squared (m/s²)
• Time is a scalar quantity measuring duration, and is a fundamental concept in kinematics
• Frames of reference can be inertial (at rest or moving at a constant velocity) or non-inertial (accelerating)

Dynamics

• Force is a push or pull that causes motion, measured in Newtons (N)
• Newton's first law states that objects at rest stay at rest, and objects in motion stay in motion, unless acted upon by an external force
• Newton's second law states that force equals mass times acceleration (F = ma), and is a fundamental concept in dynamics
• Newton's third law states that every action has an equal and opposite reaction
• Energy has two main forms: kinetic energy (the energy of motion) and potential energy (the energy of position or configuration)
• Momentum is the product of mass and velocity, and is a measure of an object's tendency to keep moving

Rotational Motion

• Angular displacement is the angle of rotation, measured in radians (rad)
• Angular velocity is the rate of change of angular displacement, measured in radians per second (rad/s)
• Angular acceleration is the rate of change of angular velocity, measured in radians per second squared (rad/s²)
• Torque is a rotational force, measured in Newton-meters (N·m)
• Rotational kinematics has analogs of linear kinematics, including angular displacement, angular velocity, and angular acceleration

Thermodynamics

Laws of Thermodynamics

• The zeroth law states that if two systems are in thermal equilibrium with a third, they are in thermal equilibrium with each other
• The first law states that energy cannot be created or destroyed, only converted from one form to another
• The second law states that the total entropy of an isolated system always increases over time
• The third law states that as temperature approaches absolute zero, entropy approaches a minimum value

Thermodynamic Systems

• Isolated systems exchange neither energy nor matter with their surroundings
• Closed systems exchange energy, but not matter, with their surroundings
• Open systems exchange both energy and matter with their surroundings
• Thermodynamic equilibrium is a state of balance among the system and its surroundings

Thermodynamic Processes

• Isothermal processes occur at constant temperature
• Adiabatic processes occur without heat exchange
• Isobaric processes occur at constant pressure
• Isochoric processes occur at constant volume
• Cyclic processes are a series of processes that return to the initial state

Relativity

Special Relativity

• Time dilation occurs when time appears to pass slower for moving observers
• Length contraction occurs when objects appear shorter to moving observers
• Relativity of simultaneity states that events simultaneous for one observer may not be for another
• The speed of light is always constant, regardless of observer motion
• The Lorentz transformation is a mathematical framework for special relativity

General Relativity

• Gravitational time dilation occurs when time passes slower near massive objects
• Gravitational redshift occurs when light emitted from massive objects appears redder
• The equivalence principle states that gravity and acceleration are equivalent
• Geodesics are the shortest paths in curved spacetime
• Einstein's field equations provide a mathematical description of gravity and spacetime curvature