Table of Contents
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## Newton's Laws ☰

In 1632, the Italian physicist Galileo experimentally demonstrated that in the absence of external force, a body can maintain not only its state of rest but also its uniform straight-line motion. This is known as Galileo's law of inertia. Inertia is the property of a body to maintain its state of rest or uniform straight-line motion.

The English scientist Isaac Newton discovered three laws of dynamics 50 years after Galileo. These laws form the basis of classical mechanics. Newton presented these laws in his work "Mathematical Principles of Natural Philosophy" in 1687.

**1. Newton's First Law:** Any body will maintain its state of rest or uniform straight-line motion unless acted upon by an external force. This is the law of inertia. There are also reference frames in which, if no external forces act on a body or if the acting forces cancel each other out, bodies maintain their state of rest or uniform straight-line motion. Such a reference frame is called an inertial reference frame. Any other reference frame that moves in a straight line and at a constant speed relative to an inertial reference frame is also called inertial.

**2. Newton's Second Law:** The acceleration of a body is directly proportional to the force applied to it and inversely proportional to its mass, and is directed in the same direction as the applied force. The applied force is equal to the product of the mass of the body and its acceleration.

\( \vec{a} = \frac{\vec{F}}{m} \quad \Rightarrow \quad \vec{F} = m \vec{a} \)

**3. Newton's Third Law:** The interaction between two bodies always results in forces that are equal in magnitude but opposite in direction.

\(\vec{F}_{1.2} = -\vec{F}_{2.1}\)

## Law of Conservation of Momentum ☰

The sum of the momenta of bodies that make up a closed system remains constant. This is known as the law of conservation of momentum.

The product of a body's mass and its velocity is called the momentum of that body:

\(\vec{P} = m \times \vec{v}\)

A group of bodies that interact with each other is called a system. The forces of interaction between the bodies that make up the system are called internal forces, while the forces of interaction with external bodies are called external forces. If no external forces act on the system, or if these forces cancel each other out, such a system is called closed.

\(\vec{P} = \sum_{i=1}^{n} (m_i \vec{v}_i) = \text{constant}\)

## Law of Universal Gravitation ☰

According to this law, the gravitational force of attraction between two bodies, whose sizes are very small compared to the distance between them, is directly proportional to the product of their masses and inversely proportional to the square of the distance between them:

\(F = \gamma \frac{m_1 \times m_2}{r^2} \)

Here \(F\) is the gravitational force, \(r\) is the distance between the bodies, \(m_1\) and \(m_2\) are the masses of the bodies (gravitational masses), and \(\gamma\) is the gravitational constant.

Any body with mass \(m\) located on the Earth's surface is attracted to the Earth with a force directed toward its center:

\(F = \gamma \frac{m \times M}{R^2} \)

Here \(M\) is the mass of the Earth, and \(R\) is the distance from the body to the Earth's center (this distance is approximately equal to the Earth's radius at its surface, meaning \(R \approx R_t\)).

## Law of Conservation of Electric Charge ☰

The fundamental property of electric charge is that it exists in two forms, commonly referred to as positive and negative charges. Experiments show that like charges repel each other, while unlike charges attract. Although the exact reason for the existence of opposite charges is unknown, it is clear that the balance between positive and negative electric charges allows the universe to exist.

Unlike electric charges are created and destroyed in equal amounts. The sum of electric charges within a body always remains constant. This is known as the law of conservation of electric charge.

\(Q = \sum_{i=1}^{n} q_i = \text{constant}\)

This law highlights that in any physical process, the total amount of electric charge is conserved, ensuring that the universe remains in a state of equilibrium. For example, in an isolated system, if a charged object loses some of its charge, another object must gain that charge, keeping the overall charge balanced.

## Coulomb's Law ☰

French physicist Charles Coulomb was the first to quantitatively characterize the interaction between electric charges in 1873. The interaction between charged bodies depends on their shape and size. Therefore, the concept of a point charge is used. Point charges are charges whose sizes are very small compared to the distance separating them. Any charged body can be represented as the sum of many point charges.

Coulomb established that the force of interaction between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them, directed along the line connecting both charges.

\(F = k \frac{q_1 \times q_2}{r^2} \)

Here, \(q_1\) and \(q_2\) are the interacting point electric charges; \(r\) is the distance between them. The value of \(k\) depends on the properties of the medium in which the charges are located and the chosen system of units.

## Ohm's Law ☰

**Ohm's Law — for a Section of an Electric Circuit**

According to Ohm's Law, the current in a section of an electric circuit is defined as the ratio of voltage to resistance in that section. Ohm's Law for a circuit section is expressed as follows:

$I=\frac{U}{R}$

Where:

**I** — Current (amperes, A)
**U** — Voltage in the section of the circuit (volts, V)
**R** — Resistance of the circuit section (ohms, Ω)

This formula shows how electrical energy is distributed in a section of the circuit and what current flows through it. If the resistance and voltage in the circuit section are known, the current can be calculated.

**Ohm's Law — for a Complete Electric Circuit**

Ohm's Law also applies to a complete electric circuit, considering both internal and external resistances. Ohm's Law for the complete circuit is expressed as follows:

$I=\frac{\epsilon}{R+r}$

Where:

**I** — Current (amperes, A)
**\(\varepsilon\)** — Electromotive force (volts, V)
**R** — External resistance of the circuit (ohms, Ω)
**r** — Internal resistance (ohms, Ω)

This formula shows the relationship between electromotive force and current in a complete electric circuit. It helps to understand how internal and external resistances affect the current.

## Kirchhoff's Laws ☰

**First Kirchhoff's Law:** At every node where currents branch, the algebraic sum of currents is equal to zero.

**Second Kirchhoff's Law:** The second Kirchhoff's Law applies to complex circuits that can be divided into simple closed loops. When traversing a closed loop in a specific direction, the sum of voltage drops is equal to the sum of electromotive forces (EMFs) in the circuit.

**EMF** — The electromotive force (EMF) of a source is the work done by external forces to move a positive unit charge around a closed loop.

The first Kirchhoff's Law is commonly referred to as the **Current Law**, while the second is known as the **Voltage Law**.

## Faraday's Laws (Laws of Electromagnetic Induction) ☰

**1. First Law of Faraday (Electromagnetic Induction)**

The first law of Faraday states: **A change in magnetic flux induces an electromotive force (EMF) in a conducting loop.** That is, if a wire or conductor moves within a magnetic field or if the intensity of the magnetic field changes, an electric current arises in the wire. This phenomenon is known as **electromagnetic induction.**

**2. Second Law of Faraday (Magnitude of Induced EMF)**

The second law of Faraday expresses the magnitude of the electromotive force (EMF). According to this law:

**The induced electromotive force (EMF) is directly proportional to the rate of change of magnetic flux passing through the loop.**

This law can be mathematically expressed as:

\(\mathcal{E} = -\frac{d\Phi_B}{dt}\)

Where:

**𝓔** — induced electromotive force (volts),
**Φ**_{B} — magnetic flux (webers),
**t** — time (seconds),
**\(\frac{d\Phi_B}{dt}\)** — rate of change of magnetic flux over time.

**The negative sign** is due to Lenz's law, which states that the induced current opposes the change in magnetic flux.

**Magnetic Flux**

Magnetic flux depends on the intensity of the magnetic field and the angle of inclination of the surface through which the field passes. Mathematically, magnetic flux is expressed as:

$\Phi $_{
B
}
=
B
·
A
·
cos
θ

Where:

**Φ**_{B} — magnetic flux (webers),
**B** — magnetic induction vector (tesla),
**A** — area of the surface (square meters),
**θ** — angle between the magnetic field and the normal to the surface.

### Applications of Faraday's Laws

**Generators:** A conductor moving within a magnetic field generates electric current. This is the principle of operation for generators.
**Transformers:** Faraday's laws are used to change voltage and transfer electrical energy.
**Induction Stoves:** Metals are heated at high frequencies due to changing magnetic fields.

## Einstein's Theory of Special Relativity ☰

Einstein's theory of special relativity is based on two postulates:

1. It is impossible to determine whether a system is at rest or is moving in a straight line at a constant speed using any experiment conducted in an inertial system.

2. The speed of light in a vacuum is the same in any inertial system \(c=3\times 10^8 \frac{m}{s}\). This means that the speed of light in a vacuum is constant, regardless of the speed of the source and the observer (the principle of invariance of the speed of light).

The mechanics of bodies moving at speeds close to the speed of light is called relativistic mechanics. In classical mechanics, space and time are considered independent concepts.

However, by observing the Lorentz transformations, we can see that time and space are closely related. Spatial coordinates depend on time, just as time depends on spatial coordinates.