Notes, summaries, assignments, exams, and problems for Physics

Understanding Electric Fields and Potentials

Electric Field

The spatial region where electric forces are produced and exerted.

Electric Field Intensity

Defined as the force experienced by a positive test charge placed under the action of such a field, divided by the value of the charge.

Charged Particle Motion in Uniform Electric Fields

When a point charge of magnitude "q" enters a region where an electric field exists, it will be subjected to a force of magnitude F = qE. If the particle has mass m, the acceleration, a, imparted to it is given by a = F / m = qE / m. This relationship provides both the magnitude and the direction of the acceleration of a particle in an electric field. The magnitude is equal to qE / m, while the direction depends on... Continue reading "Fundamentals of Electric Fields and Potentials" »

Physics Formulas

Speed

V: Average velocity

• V = s / t
• s: Distance traveled
• s = v · t
• t: Time spent
• t = s / v
• Minutes to hours = min / 60

SI units:

• Speed is the distance traveled by a mobile unit per unit of time.
• m / s
• km / h
• cm / s

Acceleration

a: Acceleration

• a = V_f - V₀ / t
• V_f: Final velocity
• V_f = V₀ + a · t
• V₀: Initial velocity
• V₀ = V_f - a · t
• t: Time

SI units:

• Acceleration is the change in speed per unit of time.
• m / s²

Forces

F: Force in newtons

• F = m · a
• m: Mass in kg
• a: Acceleration in m / s²

SI units:

• Force is a physical quantity associated with movement.
• Newton (N)
• Kilogram-force (kgf)
• Pound (lb)
• Dyne (dyn)

Forces in the same direction:

• F_R = F₁ + F₂

Forces in opposite directions:

• F_R = F₁ - F₂

Mass

m: Mass in kg

• m = F / a
• F: Force in newtons
• a: Acceleration in m / s²

SI units:

San Pietro in Montorio, Bramante, 1502

Religious Architecture, Cinquecento, Rome

Introduction: This is an early work of Bramante in Rome. It is a chapel, built between 1502-1503, located in a small courtyard. According to tradition, Saint Peter was crucified on this site. It is a model of a religious building with a central plan, inspired by the Hellenistic *monopteros* temples, and its elevation recalls the Temple of the Sibyl at Tivoli.

Analysis and Features: It is considered the aesthetic ideal of the Renaissance in the 16th century. This architectural ideal is achieved by using:

• A monumental and grandiose architectural language, achieved through a rigorous study of the proportions of each part of the building.
• The creation of a complete architectural

Huygens' Principle: Understanding Wave Propagation

Huygens' Principle is a wave propagation model that helps explain various wave phenomena. It states that a wave propagates as a wave front or surface connecting all points reached by the wave motion at the same instant. Every point of an isotropic medium which experiences a disturbance behaves as a source emitting secondary waves (or wavelets) that propagate in the direction of the disturbance. The surface tangent to all these wavelets at a given instant forms the next wave front. The radius of the wavelets at any instant is vt (velocity × time).

Wave Reflection

When a wave propagating through one medium reaches the boundary with a different medium, part of the wave is reflected and continues... Continue reading "Huygens' Principle: Wave Propagation & Phenomena" »

Modern Physics

This branch of physics considers the theory of relativity and quantum theory in describing microscopic systems like atoms.

Model of Modern Physics

In the late nineteenth century, it was a common belief that all phenomena of nature could be described by Newton's laws, principles of thermodynamics, and the laws of electromagnetism, which were based on a mechanical conception of the universe.

Reaffirmation of Modern Physics

In 1905, Albert Einstein produced a series of works that revolutionized physics, mainly due to the wave-particle duality of light and the theory of relativity, among others.

Classification of Modern Physics

It is generally known to study phenomena that occur at the speed of light or values close to it, or whose spatial... Continue reading "Modern Physics: Relativity, Quantum Mechanics, and Nuclear Processes" »

Understanding Geospatial Concepts

Geographical Coordinates

The geographic coordinate system determines all positions on the Earth's surface using two angular coordinates of a spherical coordinate system, which is aligned with the Earth's axis of rotation. It defines two angles measured from the center of the Earth:

• Latitude: Measures the angle between any point and the Equator. Lines of latitude are called parallels and are circles parallel to the Earth's surface.
• Longitude: Measures the angle along the Equator from anywhere on Earth. In most modern societies, Greenwich, London, is accepted as the 0° longitude. Lines of longitude are great circles passing through the poles and are called meridians.

Aerial Photography (Photogrammetry)

Photogrammetry... Continue reading "Essential Geospatial and Mapping Concepts" »

Force Interactions

Strength: Action of one body on another, or interaction. Net force (resultant) is the vector sum of all forces acting simultaneously on the same body.

Like acceleration and speed, force is a vector quantity, defined by its magnitude and direction.

Force Measurement

To combine forces on a body, add them vectorially. The net force is equivalent to a single force producing the same effect.

Special Forces

Weight

Weight is the gravitational force a planet or star exerts on a body.

Normal Force

The normal force is a contact force preventing an object from passing through a surface, always perpendicular to it.

Friction Force

Friction force is exerted between two surfaces in contact. Its magnitude on solids depends on surface roughness.

F_r =

Fundamentals of Hydrostatics

Hydrostatics is the branch of fluid mechanics that studies fluids at rest.

Key Concepts and Definitions

Fluid

A fluid is a substance that flows easily and changes its shape under the action of low-magnitude forces. Fluids include both liquids and gases.

• Gases: Molecules vibrate randomly and are compressible.
• Liquids: Take the shape of their container; their vibrating molecules are separated.

Pressure

Pressure (measured in Pascals, Pa, or N/m²) is the quotient resulting from dividing the value of a force acting perpendicularly on a surface by the area over which it is exerted.

• The greater the force, the greater the pressure.
• The greater the area, the lower the pressure.

Any body immersed in a fluid experiences pressure, which... Continue reading "Fundamental Principles of Hydrostatics and Fluid Pressure" »

Forces and Motion

An outside influence that changes a body's state of rest or motion is called force.

Types of Forces

Normal Force: The force perpendicular to a surface exerted on a body by that surface.

Friction: A force resulting from physical contact between a body and its surroundings, opposing motion.

Gravity: A force proportional to acceleration, attracting objects with mass towards each other.

Fundamental Forces: Gravity, Electromagnetic, Strong Nuclear, and Weak Nuclear.

Newton's Third Law

Also known as the Law of Action and Reaction.

Inertial Reference Frame

A frame where a body moves with constant speed if no force acts on it.

Work and Momentum

Work

A scalar quantity obtained from the product of force and displacement.

Momentum

Define this formula:... Continue reading "Physics Fundamentals: Forces, Motion, and Vectors" »