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

The Theory of Relativity: Revolution in the Macrocosm

Einstein published the theory of special relativity in 1905. Space and time are, therefore, a four-dimensional continuum. Einstein generalized this theory with the theory of general relativity. One of the underlying principles of relativity is that nothing can go faster than light, even gravitational interaction. It was, therefore, necessary to develop the theory of gravitation, taking this limit into account. To achieve this, Einstein introduced the idea of a gravitational field. In the proximity of a large body, space is curved, and time passes more slowly. If space is curved, the planets draw an orbit around it. Thus, the theory of relativity explains the orbital motions of the planets.... Continue reading "Relativity, Universe Expansion, and Wave-Particle Duality" »

Classification of Optical Methods

Non-Spectroscopic Techniques

• Refractometry
• Polarimetry

Spectroscopic Techniques

• UV-Vis Spectrophotometry
• Atomic Absorption
• Flame Photometry

Classification of Spectroscopic Methods

Spectroscopic methods are categorized by absorption or emission.

Absorptiometry

This electromagnetic method uses light, which has both corpuscular and wave-like characteristics. Light is broken down into different wavelengths, arranged in what is called the electromagnetic spectrum.

Wave Constitution

A wave consists of two fields—electric and magnetic—perpendicularly intersecting each other and propagating in the direction of the wave.

Speed of Wave Propagation

In a vacuum, the speed of light (c) is 3x10¹⁰ cm/sec. This speed can change when... Continue reading "Spectroscopic Techniques in Optical Methods: A Comprehensive Guide" »

Understanding Uniform Circular Motion

In uniform circular motion, an object's body movement describes circular arcs of equal length (n equal times). The magnitude of the linear velocity (dl) is constant, but its direction changes continuously.

Linear Speed

Linear speed (s) is the angular velocity multiplied by the radius vector (xl).

Centripetal Acceleration

Centripetal acceleration is perpendicular to the path (dl) and is always directed toward the center of the circle.

Period and Frequency

In uniform circular motion:

• Period (T): The time it takes for an object to complete one full revolution.
• Frequency (f): The number of revolutions an object completes per unit of time.

Centripetal Force

Centripetal force is the force responsible for maintaining circular... Continue reading "Understanding Uniform Circular Motion: Concepts & Theories" »

Kinetic Energy and Potential Energy

Kinetic Energy (KE) Calculation:

A body with a mass of 50kg has a velocity of 20 m/s.

KE = (1/2) * M * V²

KE = (1/2) * 50kg * (20 m/s)²

KE = (1/2) * 50 * 400

KE = 10000 Joules

Total Energy Calculation:

A body with a mass of 5kg is at a height of 10m and moving at a speed of 20 m/s. Calculate its total energy.

Mass (M) = 5kg

Height (H) = 10m

Velocity (V) = 20 m/s

Potential Energy (PE) = M * g * H = 5kg * 9.8 m/s² * 10m = 490 Joules

Kinetic Energy (KE) = (1/2) * M * V² = (1/2) * 5kg * (20 m/s)² = 1000 Joules

Total Energy = KE + PE = 1000 Joules + 490 Joules = 1490 Joules

Heat Transfer and Temperature Conversion

Kelvin to Celsius Conversion:

How to convert 300 Kelvin to Celsius, as applicable to converting 100 Celsius to Kelvin.... Continue reading "Kinetic Energy, Heat Transfer, and Algebraic Equations" »

Kinematics Formulas

Position Vector

r = xi + yj

• x = r cos
• y = r sin
• r = √(x² + y²)
• tan θ = y / x

Displacement

Δr = r - r_initial

Speed, Average Speed, Instantaneous Speed

• Average Speed: v_av = Δr / Δt
• Instantaneous Speed: v = dr / dt

Average Acceleration, Instantaneous Acceleration

• Average Acceleration: a_av = Δv / Δt
• Instantaneous Acceleration: a = dv / dt

Uniform Rectilinear Motion (MRU)

• v = Δx / Δt
• v_mean = (v₀ + v) / 2
• v = v₀ + at
• x = x₀ + vt
• x = x₀ + v₀t + (1/2)at²
• v² - v₀² = 2aΔx
• v² = v₀² ± 2as

Free Fall

• Velocity: v = gt
• Position (height fallen): y = (1/2)gt²
• Velocity (upward): v = -gt
• Position (height): y = y₀ - (1/2)gt²

Upward Vertical Launch

• Velocity: v = v₀ - gt
• Position (height): y = y₀ + v₀t - (1/2)gt²
• Time to reach maximum height: t = v₀ / g
• Maximum

Magnetic Hysteresis in Ferromagnetic Materials

When a magnetic material is subjected to a changing magnetic field intensity (H), the magnetic induction (B) lags behind. This phenomenon is known as magnetic hysteresis. (See Figure 1). When a ferromagnetic substance is subjected to a cyclical (alternating positive and negative) magnetic field intensity, it traces a hysteresis loop.

Key points on the hysteresis curve (See Figure 1):

• O-B: Magnetization curve.
• O-R: Residual magnetization.
• O-D: Coercive force.

When applying an alternating magnetization intensity (+ and -) to a ferromagnetic substance, the resulting hysteresis loop is shown in the image. The magnetic induction (B) lags behind the magnetic field intensity (H). At point B, even when H = 0,... Continue reading "Magnetic Hysteresis & Autoinduction Explained" »

Fundamental Heat Exchanger Concepts

Key Formulas in Heat Transfer

• Heat Exchanged (q): q = m · Cp · ΔT (Heat absorbed or released by a fluid)
• Heat Transfer Rate (Q): Q = U · A · ΔT (Overall heat transfer rate through an exchanger)
• Energy Balance for Heat Exchangers: M_c · Cp_c · (ΔT_c) = M_f · Cp_f · (ΔT_f) (Heat gained by cold fluid equals heat lost by hot fluid)
• Other Formulas (Context Dependent): ct = w1 + w2 · PC1 · CP2

Definition of a Heat Exchanger

A heat exchanger is a device designed to efficiently transfer heat from one fluid to another. Common examples include:

• Condenser: Transfers heat from a hot fluid to a colder one, causing the hot fluid to condense (e.g., steam to water).
• Evaporator: Transfers heat to a cold fluid, causing it to

Energy

Energy is the capacity of bodies to produce transformations in themselves or other bodies.

Energy Sources

Energy sources are natural resources from which humans can obtain usable energy.

Types of Energy Sources

• Non-renewable: Found in limited quantities and are depleted with use.
• Renewable: Considered inexhaustible as they are continuously renewed.

Energy Principles

• Conservation of Energy: The total energy in the universe remains constant in any process.
• Degradation Principle: With each transformation, energy loses quality and produces new transformations.

Work and Power

Work (W) is done when a constant force (F) is applied to a body, causing a displacement (d) in the same direction as the force: W = F * d.

Power is the rate at which work is done.... Continue reading "Energy, Waves, Sound, Light, and Electricity: Physics Fundamentals" »

Position Vector and Components

The position vector r describes an object's location in space. Its components can be expressed in Cartesian or polar coordinates:

• Position Vector: r = xi + yj
• Cartesian X-component: x = r cos θ
• Cartesian Y-component: y = r sin θ
• Magnitude of Position Vector: r = √(x2 + y2)
• Angle of Position Vector: tan θ = y / x

Displacement

Displacement (Δr) is the change in an object's position:

• Final Displacement: Δr = rfinal - rinitial

Speed and Velocity

Speed is the magnitude of velocity. Velocity is a vector quantity describing the rate of change of position:

• Average Speed: vavg = Δr / Δt
• Instantaneous Speed: v = |dr / dt|
• Average Velocity: vavg = Δr / Δt
• Instantaneous Velocity: v = dr / dt

Acceleration

Acceleration (a) is the... Continue reading "Essential Kinematics Formulas and Motion Principles" »

Law of Gravitation

Every object in the universe that has mass exerts a gravitational attraction on other objects with mass, regardless of the distance between them. According to this law, more massive objects exert a greater force of attraction. In parallel, the closer objects are, the greater the force, following an inverse square law.

Considering two masses whose size is small compared with the distance that separates them, we can summarize this in an equation or law that states that the force exerted by a given object with mass m1 on one with mass m2 is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

A force is central where the position vector r is parallel to the force... Continue reading "Fundamental Physics Concepts Explained" »