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

**Coulomb's Law: Quantifying Force Between Electric Charges**

The quantification of force between electric charges is attributed to Coulomb, who used a torsion balance. Coulomb's law states that the force of attraction or repulsion between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. This can be expressed as:

F = K • (Q₁Q₂ / r²)

Where:

• F is the force
• K is Coulomb's constant
• Q₁ and Q₂ are the charges
• r is the distance between the charges

The electrical constant, K, is defined in terms of another constant called the permittivity of the medium. Coulomb's law is analogous to Newton's law of universal gravitation. Both forces are proportional to the product of the property... Continue reading "Understanding Electric and Magnetic Fields: Forces and Charges" »

Uniform Circular Motion

Uniform circular motion (UCM) describes the movement of a body along a circular trajectory, covering equal arc lengths in equal time intervals.

Key Concepts in Circular Motion

• Radian: An angle whose arc length is equal to the radius of the circle.
• Linear Path (s): The distance traveled along the circumference.
• Angular Path: The angle swept by the radius vector.
• Revolution: A complete circle or 360 degrees.
• Conversions: 1 revolution = 360 degrees = 2π radians.

Angular Velocity (ω)

In UCM, the angular velocity is constant and measured in radians per second (rad/s).

Linear Speed (v)

Linear speed is the product of angular velocity and the radius vector: v = ω · r.

Centripetal Acceleration (a_c)

This acceleration is always perpendicular... Continue reading "Uniform Circular Motion: Principles and Celestial Models" »

Kinematics: Types of Motion and Key Formulas

Uniform Motion (MU)

Uniform Motion is characterized by constant velocity, meaning zero acceleration.

Fundamental Equations

• Displacement (D): D = |e_final - e_initial|
• Average Velocity (V_m): V_m = D / t
• Position (e): e = e₀ + v · t

Graphical Representation

• In the Position vs. Time (e/t) graph, the line is straight and inclined.
• In the Velocity vs. Time (V/t) graph, the line is straight and horizontal (zero inclination).

Uniformly Accelerated Motion (MUA)

Uniformly Accelerated Motion is characterized by constant acceleration.

Fundamental Equations

• Acceleration (a): a = (v_final - v_initial) / t
• Velocity (v): v = v₀ + a · t
• Position (e): e = e₀ + v₀t + ¹/₂ · a · t²
• Time-Independent Equation: v² - v₀² = 2 · a · Δe.

Vibration: Periodic Motion

Periodic motion occurs when the magnitude that characterizes it repeats at regular intervals of time. Examples include the Moon orbiting the Earth and a piston in an internal combustion engine. In periodic motion, the period is defined as the time that passes until the motion repeats.

Oscillatory Movements

An oscillatory movement is a motion in which the path is covered in two directions. An example is a pendulum. Many oscillatory movements in nature eventually stop due to friction. These oscillations are called damped oscillations, in contrast to those that do not involve friction, which are called free oscillations.

Dynamics of Simple Harmonic Motion

Work Done by a Constant Force

The work done by a constant force is the... Continue reading "Understanding Vibrations and Harmonic Motion in Physics" »

Understanding Vehicle Dynamics: FMR, RR, RP, FMD, and FMU

FMR (Force Moving Resistance): Power required to move machines on a surface, such as through a cut or haul road. The factors determining FMR are:

FMR = RR + RP

Rolling Resistance (RR)

RR (Rolling Resistance): The force opposing the ground at the turn of a vehicle's wheels. To move, the vehicle must counteract this force.

RR = rr x factor pbv

Several factors contribute to RR, the most important being:

A. Internal Friction

Internal friction produced in the powertrain, from the engine to the tires or tracks. Mechanical components like bearings create resistance to movement.

B. Tire Flexion

Flexion of tires increases resistance due to sidewall and tread deformation during spinning. The extent of this... Continue reading "Understanding FMR, RR, RP, FMD, and FMU in Vehicle Dynamics" »

Energy Definition

It is a property of any body or material system which can be transformed by changing its position or state, as well as act on them, originating from other processes of transformation.

Forms of Energy

• Kinetic Energy: Energy possessed by a moving body.
• Potential Energy: Associated with the position of a body relative to a reference point (e.g., the floor).
• Thermal Energy: Due to the vibratory motion of the molecules that constitute matter.
• Radiant Energy: Associated with electromagnetic radiation (such as light or microwaves).
• Nuclear Energy: Associated with the process of fusion (union of nuclei) or fission (rupture of nuclei) that takes place inside atoms.
• Chemical Energy: Associated with chemical reactions (e.g., combustion). This

John Dalton: The First Theory of Matter

John Dalton proposed the first theory of matter.

William Crookes: Perfecting Vacuum Tubes

William Crookes (1832-1919) perfected devices using a glass tube that had undergone a partial vacuum and contained two electrodes, one positive and one negative, connected to a source of high-voltage continuous current.

J.J. Thomson: Discovering the Electron

In 1897, J.J. Thomson proved that the cathode ray consisted of minute particles of negative electric charge that are attracted by the positive electrode. He achieved determining the relationship between charge and mass for these particles. He carefully measured how magnetic and electric fields deviated the electrons' trajectory. Independently of their origin, they... Continue reading "Key Discoveries in Atomic Theory and Radioactivity" »

What is a Wave?

A wave (k) is a perturbation that transports energy, originating from a periodic disturbance. Waves exhibit several key characteristics:

• Frequency: The number of wavelengths or impulses passing a point per unit of time.
• Wavelength: The distance traveled by the wave during one cycle.

Waves extend in all directions. When they encounter an obstacle, they undergo:

• Reflection: A change in direction.
• Refraction: If they enter the obstacle, their speed changes.

Kinds of Mechanical Waves

Waves can be classified based on their origin:

Mechanical Waves

These require a medium to propagate. A sudden pressure change can cause them.

Electromagnetic Waves

These occur due to electrical and magnetic disturbances.

The speed of a wave depends on its nature... Continue reading "Understanding Wave Physics: Characteristics and Interactions" »

Wave Motion

Wave motion refers to the transmission of a disturbance from one point to another without the net transport of matter.

Wave Classification

Based on Direction of Propagation

• One-dimensional waves: Propagate in a single direction.
• Two-dimensional waves: Propagate in two directions.
• Three-dimensional waves: Propagate in three directions.

Based on Medium of Propagation

• Mechanical waves: Require a material medium for propagation. Their speed depends on the characteristics of the medium.
• Electromagnetic waves: Do not require a material medium and can propagate in a vacuum (e.g., visible light).

Based on Direction of Disturbance

• Transverse waves: The direction of propagation is perpendicular to the direction of the disturbance.
• Longitudinal waves:

Geocentric Theory

Aristotle proposed the following:

• The Earth is round and immobile at the center of a celestial sphere, which houses the stars.
• The planets and stars rotate in a celestial sphere with uniform circular motion around the Earth.

Ptolemy improved Aristotle's theory. The Ptolemaic theory was based on circular orbits but later included eccentric orbits and epicycles to describe the movement of the planets. He maintained that the Earth was the center of the universe.

Heliocentric Theory

Copernicus and Galileo, who demonstrated this theory with a microscope he had built, proposed the heliocentric theory. However, Copernicus did not reveal his theory until the 16th century. It affirmed the following points:

• The Sun is at the center of the