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

Definition of Freefall

Freefall is rectilinear motion in the vertical direction with constant acceleration performed by a body when it is dropped in a vacuum.

Freefall highlights two important features:

• 1) Objects in freefall do not experience air resistance.
• 2) All objects on the surface of the Earth accelerate downward at a value of approximately 10 m/s² (more accurately 9.8 m/s²).

Energy and Uniform Circular Motion

Energy is defined as the ability to do work.

Uniform circular motion describes the motion of a body moving with a constant speed along a circular path.

Laws of Dynamics and Forces

Dynamics is the branch of physics that describes the evolution over time of a physical system in relation to the causes of state changes or motion.

• Force: Any

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:

Understanding Physical Forces

Forces can act on objects even when they are not physically in contact. For example, a magnet attracts another through its magnetic field.

What Effects Do Forces Produce?

Depending on the applied force and the body receiving it, different outcomes can occur:

1. Shape Shifting (Deformation)

When a force is applied to a body, it may deform. There are two primary types of deformation:

• Plastic Deformation (Permanent): This deformation is maintained over time, permanently changing the object's shape. Such bodies are called inelastic. For example, if you press hard on a ping-pong ball, it deforms and does not return to its original shape naturally.
• Elastic Deformation (Temporary): This deformation is only maintained while the

Basic Laws of Cartesian Physics

Descartes invokes God to explain extension and motion: God is the creator of matter and of a certain amount of motion that remains constant, because God is unchangeable both in being and in operation. He therefore regards the universe as a closed system. He formulates three fundamental laws:

Three Fundamental Laws of Motion

1. Law of inertia: Every body tends to remain in its state of rest or of uniform motion in a straight line unless acted on by an external force.
2. Law of straight-line motion: Any body in motion tends to continue moving in a straight line unless an external force intervenes; otherwise there would be no reason to explain a deviation.
3. Law of conservation of motion: Motion is not lost in collisions between

Understanding Hooke's Law

Hooke's Law states that the deformation of an object is proportional to the force applied. When one magnitude or signal is proportional to another, a relationship can be established between both magnitudes by multiplying one of them by a coefficient of proportionality.

In this case, the force applied (F) is proportional to the elongation (x) of a spring. This relationship is expressed as:

F = kx

Where k is the coefficient of proportionality, known as the spring constant. Its value is defined as:

k = F / x

Units and Elastic Characteristics

In the International System of Units (SI), the spring constant is measured in N/m. This constant is a characteristic of the spring's stiffness:

• Hard springs: Have a high k value.
• Lazy (soft)

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

Material Resistance and Stiffness

Resistance is the property that support materials have against the action of forces, while material stiffness is the ability to resist deformation.

Types of Loads

• Static: Applied gradually from zero to maximum.
• Dynamic Load: Applied at a certain speed on the body that must endure it. It is divided into sudden load, shock-free, and forced shock.
• Sudden Load: Applies its maximum value instantly.

Mechanical Efforts

• Effort: An internal force that originates from a resistive element and is transmitted through a flat section of it.
• Tensile Strength: Stress perpendicular to the cross-section of the body that tends to elongate the fibers.
• Compression Effort: A negative voltage, since the load tends to shorten the fibers of

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 and Special Relativity

Postulates of Special Relativity

• First Postulate: The physical laws are identical in all inertial reference systems, and equations are expressed by analogy.
• Second Postulate: The value of the speed of light in a vacuum is 3 x 10^8 m/s. It does not depend on the observer measuring it nor the movement of the light source; it is an absolute velocity.

The Photoelectric Effect

Some metals, when illuminated by electromagnetic radiation with a small wavelength, emit electrons. Light strikes the cathode, resulting in the issuance of electrons reaching the anode and establishing a current detected by the ammeter.

Experimental Results

• Kinetic Energy: Defined in terms of the intensity of the radiation.
• Intensity: At small