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

Average Speed

The average speed of a moving object is the ratio of the distance traveled along its path to the time taken.

Average speed = Δs / Δt

In vector calculus, the average velocity vector of a moving object is the ratio of its displacement vector to the time taken.

v = Δr / Δt

Instantaneous Velocity

The instantaneous velocity of a body is its velocity at a specific point in its trajectory. Its magnitude is called speed.

Acceleration

Acceleration measures how much the velocity of an object changes per unit time. Since velocity is a vector, changes can affect its magnitude, direction, or both.

Average Acceleration

The average acceleration of an object over a time interval is the change in its velocity divided by the time interval.

a = (v - v₀)... Continue reading "Understanding Kinematics: Speed, Velocity, and Acceleration" »

Diffraction Grating Experiment

Subject:

Calculate the d-spacing (d) of diffraction grating and determine wavelengths of different light sources.

Planning:

A diffraction grating is an optical component that separates light into its constituent wavelengths. There are two main types of diffraction gratings: reflection gratings and transmission gratings. A diffraction grating consists of a surface with a series of closely spaced parallel lines or slits. These can be etched onto a flat metal surface (reflection grating) or a glass plate (transmission grating). When monochromatic light (light of a single wavelength) is incident on a diffraction grating, the emerging waves interfere constructively at specific angles, resulting in a pattern of constructive... Continue reading "Diffraction Grating Experiment: Calculating Wavelengths" »

The oil hydraulic controls and actuators have become increasingly important in team building.
There are numerous machines and plants of modern design and greater efficiency that allow the use of oil-hydraulics in systems of command and control.
Today it is not possible without the oleohidráulica which to develop large forces with small volumes of fluid, laden movements from rest, the easy realization of continuous monitoring of speed and thrust, in addition to the versatile use of cycles.
Currently the technology is applied in hydraulic rigs, Cargie, excavators, farm equipment, telescopic legs, drive presses, valves, etc..
This development forces us to knowledge of this area and gain some degree of control over oil hydraulic systems so... Continue reading "Aircraft systems" »

Content

Labor Force, Kinetic Energy, Potential Energy, Conservative and Nonconservative Forces, Power.

Development

Labor Force

A constant force produces work when applied to a body, it moves along a certain distance.
While work is done on the body, there is a transfer of energy to it, so it can be said that work is energy in motion. Moreover, if a constant force produces no movement, no work is done. For example, holding a book at arm's length does not involve any work on the book, regardless of effort. Work is expressed in Joules (J).

When the force is in the direction of motion:

L = Fd

L: Work done by force.

When the applied force has an inclination with respect to movement:

L = Fd cos θ

All the forces perpendicular... Continue reading "Work, Energy, and Power in Physics: Understanding the Basics" »

Rigid Body Definition

A rigid body is a special case of a many-particle system. It is defined by the condition that the distance between the particles of the body remains constant ($R = \text{constant}$), meaning the body is absolutely non-deformable.

Steiner's Theorem (Parallel Axis Theorem)

We can calculate the moment of inertia of a rigid body ($I_O$) about a rotation axis passing through a point $O$, provided we know the moment of inertia about an axis parallel to the first and passing through the center of mass ($I_{cm}$).

This relationship is:

I_O = I_cm + M d²

Where:

• $I_O$ is the moment of inertia of the body about the new axis (passing through $O$).
• $I_{cm}$ is the moment of inertia about the axis through the center of mass ($C$).
• $M$ is the

Capacitor Fundamentals and Functions

A capacitor (also known as a condenser) is a composite element consisting of two metal plates separated by an insulating material called a dielectric. When connected to a battery, it acquires tension between its plates and becomes electrically charged. In conclusion, it acts as a DC open circuit but allows AC to drive through. Capacity refers to the property of a condenser to store more or less electricity.

Magnetism and Electromagnetism

Ferromagnetic materials are substances attracted to a magnet. The poles of a magnet are the end points where magnetism is most powerful. Electromagnetism dictates that any electric current is associated with a magnetic field.

Magnetic Fields in Conductors

In a straight conductor,... Continue reading "Fundamentals of Capacitors and Electromagnetism" »

The Earth in the Universe

Historically, the geocentric model placed our planet at the center of the universe, whereas the heliocentric theory established the Sun as the center.

Distances in the Universe

• Astronomical Unit (AU): The average distance between Earth and the Sun, equivalent to approximately 149,600,000 km to 150,000,000 km.
• Light-year: The distance light travels in one year at a speed of 300,000 km/s.

The Known Universe: Galaxies

Galaxies are defined as large clusters of stars, gas, and dust. They can contain billions or trillions of stars, which often host planetary systems.

Components of Galaxies

• Nebulae: Concentrations of interstellar gas (hydrogen and helium) and dust.
• Star Clusters: Compact groups of stars. When they are very dense,

Geocentrism: Organic & Hierarchical Universe

The geocentric model conceived of an *organic* and *hierarchical* universe, often described as a large body with separate parts. The concept of space was *closed* and *finite*, with Earth at its center.

Aristotle believed the universe was divided into two levels:

• Supralunar Orbit: Beyond the Moon, considered perfect and unchanging.
• Sublunar Orbit: Below the Moon, imperfect and subject to change.

Ptolemy adopted Aristotelian geocentrism, attributing *epicycles* and *deferents* to planetary orbits to explain their apparent displacement.

From a theological perspective, this dynamic universe posited that everything that moves is moved by another object. Hierarchically and orderly, everything is attracted... Continue reading "Cosmological Evolution: From Geocentric to Mechanical Universe" »

Magnetic Force on a Moving Charge: The Lorentz Law

The force exerted on an electric charge has the following characteristics:

• If the charge is at rest, no forces act upon it.
• If the charge moves with velocity v, it experiences a force proportional to the value of the charge q, perpendicular to the velocity v.
• The magnitude depends on the direction of the velocity vector v: if it has a certain direction, the magnetic force is zero; if the vector v is perpendicular to that direction, the magnetic force is maximal.

These properties are summarized in the Lorentz Law:

F = q(v × B)
The module is F = |q|vB sin(α), where α is the angle formed by B and v.

Magnetic Force and Trajectory

The magnetic force acting on a charge is perpendicular to the velocity... Continue reading "Understanding Magnetic Force and Lorentz Law Principles" »