Key Concepts in Physics

Kinematics: Describes motion without considering forces. Key equations include
- ( v = u + at )
- ( s = ut + \frac{1}{2}at^2 )
Dynamics: Studies forces and their effects on motion.
- Newton's Laws of Motion:
  1. An object at rest stays at rest; an object in motion stays in motion unless acted upon.
  2. ( F = ma ) (Force equals mass times acceleration).
  3. For every action, there is an equal and opposite reaction.

Work: Defined as ( W = Fd \cos(\theta) ) (force applied over a distance).
Kinetic Energy: ( KE = \frac{1}{2}mv^2 ).
Potential Energy:
- Gravitational: ( PE = mgh ).
- Elastic: ( PE = \frac{1}{2}kx^2 ) (where ( k ) is the spring constant).
Conservation of Energy: Total energy in a closed system remains constant.

First Law: Energy cannot be created or destroyed, only transformed.
Second Law: Entropy of an isolated system never decreases; processes occur in direction of increasing entropy.
Heat Transfer: Three mechanisms:
- Conduction: Heat transfer through a solid.
- Convection: Heat transfer via fluid movement.
- Radiation: Transfer of energy through electromagnetic waves.

Wave properties: Wavelength, frequency, amplitude, speed.
Types of Waves:
- Mechanical: Require a medium (e.g., sound).
- Electromagnetic: Do not require a medium (e.g., light).
Harmonic Motion: Simple harmonic motion described by ( x(t) = A \cos(\omega t + \phi) ).

Ohm's Law: ( V = IR ) (Voltage = Current × Resistance).
Circuit Components:
- Resistors, capacitors, inductors.
- Series and parallel circuits.
Electromagnetism: Interrelation between electricity and magnetism; described by Maxwell's equations.

Quantum Mechanics: Describes behavior of particles at atomic and subatomic levels.
- Heisenberg Uncertainty Principle: Precise position and momentum cannot both be known.
Relativity: Einstein's theories of special and general relativity alter notions of space, time, and gravity.
- Special Relativity: Time dilation and length contraction relative to speed.
- General Relativity: Gravity as curvature of spacetime.

Kinematics studies motion without considering forces.
- Key equations:
  - ( v = u + at ) (final velocity equals initial velocity plus acceleration times time)
  - ( s = ut + \frac{1}{2}at^2 ) (distance equals initial velocity times time plus half acceleration times time squared)
Dynamics examines forces and their impact on motion.
- Newton's Laws of Motion:
  - First Law: An object at rest stays at rest, and an object in motion stays in motion with the same speed and direction unless acted upon by an unbalanced force.
  - Second Law: Force equals mass times acceleration ( ( F = ma ) ).
  - Third Law: For every action, there is an equal and opposite reaction.

Work is the force applied over a distance. It's calculated as ( W = Fd \cos(\theta) ) where ( \theta ) is the angle between the force and displacement.
Kinetic Energy is the energy of motion, ( KE = \frac{1}{2}mv^2 ) where ( m ) is mass and ( v ) is velocity.
Potential Energy is stored energy.
- Gravitational Potential Energy: ( PE = mgh ) where ( m ) is mass, ( g ) is acceleration due to gravity and ( h ) is height.
- Elastic Potential Energy: ( PE = \frac{1}{2}kx^2 ) where ( k ) is the spring constant and ( x ) is the displacement from equilibrium.
Conservation of Energy states that the total energy in a closed system remains constant, it can only be transformed from one form to another.

First Law of Thermodynamics: Energy cannot be created or destroyed, only transformed.
Second Law of Thermodynamics: Entropy of an isolated system never decreases; processes occur in the direction of increasing entropy.
Heat Transfer:
- Conduction: Heat transfer through a solid material.
- Convection: Heat transfer via the movement of fluids.
- Radiation: Transfer of energy through electromagnetic waves.

Wave Properties:
- Wavelength: Distance between two successive crests or troughs.
- Frequency: Number of waves passing a point per unit time.
- Amplitude: Maximum displacement from equilibrium.
- Speed: Rate at which the wave propagates.
Types of Waves:
- Mechanical Waves: Require a medium to travel, like sound.
- Electromagnetic Waves: Do not require a medium, like light.
Harmonic Motion:
- Simple Harmonic Motion: Oscillation described by ( x(t) = A \cos(\omega t + \phi) ) where ( A ) is amplitude, ( \omega ) is angular frequency, ( t ) is time, and ( \phi ) is the phase angle.

Ohm's Law: ( V = IR ) (Voltage is equal to Current times Resistance).
Circuit Components:
- Resistors: Resist the flow of electrical current.
- Capacitors: Store electrical energy.
- Inductors: Oppose changes in electrical current.
Series and Parallel Circuits: Different ways to connect electrical components.
- Series: Components are connected end-to-end.
- Parallel: Components are connected side-by-side.
Electromagnetism: Relationship between electricity and magnetism.
- Maxwell's Equations: Set of equations that describe the relationship between electricity and magnetism.

Quantum Mechanics: Explains the behavior of particles at atomic and subatomic levels.
- Heisenberg Uncertainty Principle: It is impossible to know both the position and momentum of a particle with perfect accuracy.
Relativity: Einstein's theories that revolutionized our understanding of space, time, and gravity.
- Special Relativity: Concerns motion at constant speeds and includes concepts like time dilation and length contraction.
- General Relativity: Describes gravity as a curvature of spacetime.

Kinematic Equations:
- ( v^2 = u^2 + 2as ) (final velocity squared equals initial velocity squared plus two times acceleration times distance)
Work-Energy Principle: ( W = \Delta KE ) (work done equals the change in kinetic energy)
Ideal Gas Law: ( PV = nRT ) (Pressure times Volume equals the number of moles times the ideal gas constant times Temperature)

Practice solving problems regularly to apply the concepts.
Visualize concepts using diagrams like free body diagrams, energy graphs, and electric circuits.
Relate physical principles to real-world examples for better retention.