Key Concepts in Physics

Newton's Laws of Motion:
1. First Law: An object at rest stays at rest; an object in motion remains in motion unless acted upon by a net external force.
2. Second Law: Force equals mass times acceleration (F = ma).
3. Third Law: For every action, there is an equal and opposite reaction.
Kinematics: Study of motion without considering forces.
- Key equations of motion for uniformly accelerated motion:
  - ( v = u + at )
  - ( s = ut + \frac{1}{2}at^2 )
  - ( v^2 = u^2 + 2as )

Work: Work done by a force is the product of the force and the displacement in the direction of the force (W = F × d).
Kinetic Energy (KE): ( KE = \frac{1}{2}mv^2 )
Potential Energy (PE): For gravitational potential energy, ( PE = mgh )

Laws of Thermodynamics:
1. Zeroth Law: If two systems are in thermal equilibrium with a third, they are in equilibrium with each other.
2. First Law: Energy cannot be created or destroyed; ( \Delta U = Q - W ).
3. Second Law: The entropy of an isolated system always increases.

Wave Properties:
- Amplitude: Maximum displacement from equilibrium.
- Wavelength: Distance between successive crests or troughs.
- Frequency: Number of oscillations per unit time (f = 1/T).
Types of Waves:
- Transverse Waves: Particles move perpendicular to wave direction (e.g., light waves).
- Longitudinal Waves: Particles move parallel to wave direction (e.g., sound waves).

Coulomb's Law: The force between two charged objects is proportional to the product of their charges and inversely proportional to the square of the distance between them.
Electric Field (E): Force per unit charge experienced by a small positive test charge.
Magnetic Field (B): Produced by moving charges/current; affects other moving charges.

Quantum Theory: Describes behavior of particles at atomic and subatomic levels.
- Photoelectric Effect: Light behaves as both a wave and a particle; photons can eject electrons from metals.
Relativity: Introduced by Einstein; includes:
- Special Relativity: Time and space are relative; speed of light is constant for all observers.
- General Relativity: Gravity is a curvature of spacetime caused by mass.

Strong Nuclear Force: Holds protons and neutrons together in the nucleus.
Weak Nuclear Force: Responsible for radioactive decay.
Electromagnetic Force: Affects charged particles; responsible for electricity and magnetism.
Gravitational Force: Attractive force between masses; weakest of all forces.

SI Units:
- Length: meter (m)
- Mass: kilogram (kg)
- Time: second (s)
- Electric Current: ampere (A)
- Temperature: kelvin (K)
Dimensional Analysis: Technique to convert units or check the consistency of equations.

Newton's Laws define the principles of motion, highlighting the relationship between forces and motion.
Kinematics analyzes motion without addressing the forces involved.
Key equations for uniformly accelerated motion include:
- ( v = u + at ): Final velocity as a function of initial velocity, acceleration, and time.
- ( s = ut + \frac{1}{2}at^2 ): Displacement in terms of initial velocity, time, and acceleration.
- ( v^2 = u^2 + 2as ): Relates velocity, displacement, and acceleration.

Work (W) is the result of a force moving an object through displacement in its direction: ( W = F × d ).
Kinetic Energy (KE) quantifies the energy of motion: ( KE = \frac{1}{2}mv^2 ).
Gravitational Potential Energy (PE) is calculated using: ( PE = mgh ), relating mass, gravity, and height.

Zeroth Law establishes thermal equilibrium, indicating that if two systems are in equilibrium with a third, they are mutually in equilibrium.
First Law emphasizes energy conservation: ( \Delta U = Q - W ) shows the relationship between internal energy change, heat added, and work done.
Second Law states that in an isolated system, entropy tends to increase.

Wave properties include amplitude (maximum displacement), wavelength (distance between crests/troughs), and frequency (oscillations per time, ( f = 1/T )).
Transverse waves have particle motion perpendicular to the wave direction (e.g., light).
Longitudinal waves feature particle motion parallel to the wave (e.g., sound).

Coulomb's Law describes the force between charges: proportional to the product of the charges and inversely proportional to the square of their separation.
Electric Field (E) refers to the force experienced by a unit positive charge placed in the field.
Magnetic Field (B) is created by moving charges or electric current and influences other moving charges.

Quantum Theory explains particle behavior at atomic and subatomic scales.
The Photoelectric Effect illustrates light’s dual nature: it can behave as both wave and particle, with photons ejected from metals when light hits them.
Relativity, introduced by Einstein, consists of:
- Special Relativity: Suggests that time and space are relative and that the speed of light remains constant for all observers.
- General Relativity: Proposes that gravity results from the curvature of spacetime caused by mass.

Strong Nuclear Force: Holds protons and neutrons together in atomic nuclei.
Weak Nuclear Force: Governs processes such as radioactive decay.
Electromagnetic Force: Affects charged particles and is responsible for electric and magnetic phenomena.
Gravitational Force: An attractive force between masses, and is the weakest of the four fundamental forces.

SI Units for fundamental measurements:
- Meter (m) for length.
- Kilogram (kg) for mass.
- Second (s) for time.
- Ampere (A) for electric current.
- Kelvin (K) for temperature.
Dimensional Analysis is useful for unit conversion and verifying equation consistency.