• # Physics

• ## Mechanics

• ### Kinematics

• #### Introduction to kinematics

Rest or motion? It depends on the referential!
• #### Basic motions

Consider a car that is pouring oil, so that oil drips at equal intervals of time. The positions of the oil marks on the track can be used to understand the movement of this car. In the following animation, see what happens if we plot the moment the drop of oil fell, $$t$$, versus the position, $$s$$. Test the limit cases: zero acceleration and an initial velocity other than zero; initial zero speed and non-zero acceleration. (The acceleration is constant throughout the movement)
• #### Vertical launch

Vertical launch is the rectilinear and vertical motion that an object describes when it is only under the gravitational force action and where the air resistance is neglected.
• #### Vector kinematics

When a movement occurs in two dimensions or more, one will need to work with vectors, i.e., one must use the vector kinematics. One example of movement in two dimensions is a car describing a circular path.
• #### Circular motion

Circular motion is the movement whose trajectory describes a circular arc.
• #### Relative motion

When we observe a phenomenon in nature, we can do this from different places and ways. For example, when watching the movement of a car, we can observe it by standing on a sidewalk or we can observe inside another moving car. Be that as it may, it is important that the analyses of the movement be consistent, regardless of whose referential we adopt.
• #### Oblique throw

The launch of any object whose initial velocity forms an angle (other than $$90^o$$ ) with the Earth's surface is called oblique throw. Here, we consider only the case without friction; that is, the air resistance is neglected. We also neglect the variation of gravity in relation to the height. This study is for objects that have such formats that suffer little aerodynamic drag, such as an arrow, and only for movements near the surface of the Earth. This methodology cannot be used to treat the movement of a rocket, for example. In the case of the movement of a rocket, the gravity will change with the altitude and the aerodynamic friction will depend on the shape of the rocket, and it is not possible to ignore such characteristics of the movement.
• ### Dynamics

• #### Forces

Force is an agent capable of producing acceleration and/or deformation of a body.
• #### Newton's laws

Once one knows the forces acting on an object, you can use Newton's laws to understand whether the body will be in movement and the characteristics of this dynamic.
• #### Contact forces

The forces between surface, or contact forces, are essential for the analysis of mechanical systems. They are divided into two components: the normal forces and frictional forces.
• #### Elastic forces

In nature, it is possible to find different types of materials with different properties. Here we will cover the elastic properties of the materials, which is the tendency to return to its initial state (equilibrium) when deformed. Examples of objects with such properties are: springs, rubber bands, fishing rod, and many others.
• #### Universal gravitation

The simple fact of having mass causes objects to attract each other. In some cases, you can consider to be constant the gravitational force that a planet exerts on objects. However, for the celestial bodies, such as the Earth-Sun system, it is necessary to use the Law of Universal Gravitation.
• #### Work and power

Work is a process by which energy can be transformed from one form to another or transferred from one object to another, due to the action of a force.
• #### Mechanical energy

Energy is the capacity to do work.
• #### Impulse and quant. of mov.

The study of momentum and impulse is useful to solve problems of collisions and explosions.
• #### Collisions

A collision is an isolated event where two or more bodies exert forces on each other, in a relatively short time interval.
• ### Static

• #### Static of a particle

Static is a branch of mechanics that studies the forces acting on objects that are at rest. The static is particularly important in the construction of buildings, bridges, viaducts and other structures that should be at rest (static).
• #### Moment of a force

The moment of a force is a measure of the tendency of a body to rotate around an axis due to application of a force.
• #### Center of mass

Center of mass is the point of a particle system that moves as if all the mass and external forces are concentrated on it.
• #### Static of solids

There are two simple ways of movement in a rigid system: translation and rotation. Any other possible form of movement, as complex it may be, can always be considered as the combination of a rotation and a translation.
• #### Mechanical equilibrium

Depending on the forces acting on a body, this disturbance can lead to different behaviors.
• #### Simple machines

A simple mechanical machine is a device that changes the direction or/and magnitude of a force. A simple machine can be defined as the most simple mechanism which can provide mechanical advantage.
• ## Thermophysics

• ### Temperature

• #### Thermometry

Molecular Agitation and Temperature
• #### Dilatation of solids

Thermal expansion is the phenomenon where changes in the volume of a body is caused by variation of its temperature. It generally occurs due to the increase in the degree of agitation of its molecules and thus there is an increase in average distance between them.
• #### Expansion of liquids

Both liquid and solid containers undergo a volume change with a change in temperature.
• ### Heat

• #### Calorimetry

It is a process of transferring thermal energy between systems that are at different temperatures. Since heat is a process, it is not stored in the system, that is, we cannot say that a given system has heat. Heat is the process of transferring thermal energy. What the system acquires in function of this process is energy.
• #### Phase transitions

"Solid, liquid or gas? Substance, temperature and pressure?"
• #### Heat transmission

"Always from those who has more (temperature) to those who have less."
• ### Thermodynamics

• #### Gas study

"The universe is modeled as a gas."
• #### Kinetic theory of gases

"All matter is composed of molecules (atoms) that are in continuous chaotic thermal motion".
• #### First law of thermodynamics

"The total energy of the universe is unchanging."
• #### Second law of thermodynamics

"The perfect machine, which would use the energy generated by its own motion indefinitely, is unattainable."
• ## Optics

• ### Princ. of Geometrical Optics

• #### Principles of geometrical optics

Optics is the branch of physics that studies the phenomena associated with the propagation and interaction of light with matter. In the past, it was not known what light is made of. Would it be a set of particle or a wave? We now know that light is an electromagnetic wave, but sometimes, this wave behaves like particles!
• #### Rectilinear propagation of light

In homogeneous, transparent and isotropic means, light travels in a straight line.
• #### Colors

Color is a property of light related to its frequency. The human eye is able to see only a specific range of all possible frequencies of light, this range is known as the visible spectrum.
• ### Reflection and Mirrors

• #### Reflection

"The angle of incidence is equal to the reflection angle".
• #### Flat mirrors

"The mirror tests the reflection of light and the thoughtlessness of men". Gar-Mar
• #### Spherical mirrors

A spherical mirror is a spherical cap where regular reflection of light occurs.
• ### Refraction, Lenses and Optical Inst.

• #### refractive and refractive means

The speed of light changes when moving from one means to another
• #### spherical lenses

A lens is an optical system composed of three homogeneous and transparent media, separated by two curved surfaces or a curved surface and a flat one.
• #### optical instruments

Understanding geometrical optics allows one to build different optical instruments. There are also many optical instruments in nature, but the most important one, for us, is the eye.
• ## Undulatory

• ### Simple Harmonic Motion

• #### SHM: Basic Concepts

In nature we often find phenomena that recur continuously: the seasons of the year, the phases of the moon and our heart beats are examples of these phenomena. The simple harmonic motion (SHM) is a model that describes several phenomena of this type, so any simple harmonic motion is periodic and oscillatory.
• #### Spring-mass and S. pendulum

The simple harmonic oscillator is an isolated system; that is, it has no external forces. In addition, there is no damping at all. It is also known as mass-spring system. In this system, the only acting force is the elastic force of the spring.
• ### Waves

• #### Waves concepts

Waves carry energy and momentum from one place to another without the transport of matter.
• #### Waves speed

The velocity of any mechanical wave, whether transverse or longitudinal, depends both on the inertial properties of the medium (to store kinetic energy) and its elastic properties (to store potential energy). Thus, we can write, generically, that the velocity of a wave is given by:
• #### Interference and standing waves

It is the combination of two or more waves that are in the same region of space generating a resultant wave.
• #### Waves phenomena

In addition to the phenomenon of interference, presented in the previous section, the waves present a wide range of behavior in different situations. The main ones are presented below.
• ### Acoustic

• #### Sound

Sound waves are longitudinal mechanical waves, capable of stimulating the human ears, which can perceive sounds in the range of 20 Hz to approximately 20,000 Hz (20 kHz). Other animals have different boundaries, listening to more bass or treble sounds.
• #### Doppler effect

When an ambulance approaches an observer, the sound of the siren perceived during the approach is more acute (greater frequency) than the sound perceived when the ambulance moves away, which is a more bass sound (decrease in frequency). In these situations, the apparent frequency $$f'$$, which is perceived by the observer, does not coincide with the frequency $$f$$ of the source. This phenomenon is known as Doppler effect . Doppler effect . The figure illustrates two sources (speakers) emitting waves (sound). When the source is stopped, figure on the left, the sound propagates equally in all directions. When the source moves, figure on the right, the wave events arrive faster and faster in one direction and slower and slower in another. Therefore, depending on the position, the frequency will be different. ANIMATION
• ## Electromagnetism

• ### Electrostatic

• #### Electric charges

The electric charge is a physical quantity that determines the intensity of electrostatic interactions.
• #### Electrization

The electrification is a process by which a body gains or loses electrical charges.
• #### Coulomb's Law

Electric charges repel or attract each other with a force that decreases rapidly with the distance between them. Aside from the atomic scale, the molecules, solids, liquids, gases and all things involving the interaction of man with the environment, the elemental forces involved are gravity and the electromagnetic force. Frictional forces, chemical bonds, viscosity and many of the forces that make the gears turn in industries are manifestations of forces between charges. Here we shall study the forces between static charges, known as electrostatic force, which is described by Coulomb's Law.
• #### Electric field

It is a region of space where a test charge is subject to the action of a force of electrical origin.
• #### Electric potential

When an electric charge $$q$$, immersed in an electrostatic field $$E$$, is dislocated from one position to another, some work must be performed. This work is due to the existence of an electric force, $$(\vec{F}=q\vec{E})$$ , which acts on the charge at each position in the field.
• #### Electrostatic equilibrium

A necessary and sufficient condition for the electrostatic equilibrium between two or more conductors is: they must have the same electrical potential.
• #### Capacitors

Capacitors are among the most used electronic components. In fact, they are among the fundamental components of the electronics, which is a branch of Electricity.
• ### Electrodynamics

• #### Electric currents

Electrical appliances work due to electrical currents that are ordered flows of electrons. However, the charges of the currents are not consumed in the device, i.e., electrons do not disappear within the apparatus; what is consumed is the energy carried by the current.
• #### Energy and electric power

An electric current, when going through a circuit, can produce several effects: heat a conductor, generate chemical reactions in electrolytic conductors, move the needle of a compass near a circuit and many other effects. In the event that the current moves a real object, a mechanical work is performed. In the case of chemical reactions, a chemical work is performed. Remember that work is the process in which energy is transformed or transferred between systems. Therefore, it is important to understand the transformations involving energy, either electrical, thermal, mechanical or chemical.
• #### Elec. resistance and conductance

In an electric circuit, the component which the main purpose is to make it difficult the flow of electrical currents is called electrical resistance or resistor.
• #### Resistors associations

Resistors can be associated in several ways: parallel, in series or in a mixed combination of parallel and series associations.
• #### Generators

Electric generators are devices that transform other forms of energy into electrical energy.
• #### Receptors

A device that can transform electrical energy into another form is called receiver. Examples of receivers are: iron, fan, electric motor, refrigerator, computer, etc.
• #### Measuring devices

For circuits maintenance and building, measuring equipments are indispensable. The most important devices are the ones that make measurements of current, voltage and electrical resistance.
• #### Circuits

Every route established for movement of electric charges is called electric circuit. For a current to be able to circulate, a closed circuit is required to ensure that electrons can move around.
• ### Magnetism

• #### Magnetic field

We know from everyday experience that magnets attract or repel each other, depending on the relative position between them. We can understand this attraction/repulsion by imagining magnetic fields generated by these magnets, but not only magnets are capable of generate magnetic fields, electric currents can also generate magnetic fields. Thus, we can think of magnetism of the magnets as "micro currents" running inside them. Therefore, the origin of any magnetic field can be attributed to electric charges in motion.
• #### Magnetic force

Unlike other interactions, the forces between two moving charges have certain peculiarities: they are not equal in module and do not have the same direction. Be careful, do not attempt to make analogies with forces from other sources that you have studied.
• #### Magnetic fields of currents

An experiment conducted by Oersted showed that an electric current produces magnetic effects. The movement of electrical charges gives rise to magnetic fields, and hence, magnetic interaction.
• #### Electromagnetic induction

A variable magnetic field induces an electric field and vice versa.
• ## Fluids

• ### Hydrostatic

• #### Hydrostatic concepts

In this section, we will study fluids, which is any substance which has the ability to flow. Typically, liquids and gases have this property and take the form of containers containing them. We can also define a fluid as a substance that, subject to a tangential force (shear), continuously deforms.
• #### Principles of hydrostatics

To describe the behavior of fluids in different situations, it is important to know the basic principles.
• #### Buoyancy

It is essential to understand the forces that an object undergoes when immersed in a fluid. The buoyancy force is one of them. This knowledge enables various applicationsb such as the development of ships, ferries, submarines and other aquatic devices. The easiest way to understand this force is through the principle of Archimedes.
• ### Hidrodinamic

• #### Volumetric flow rate

Fluid Dynamics (Hydrodynamics) is the study of moving fluids (liquids and gases). For example, the flow of water into a pipe, the blood flowing through a person's arteries, the flow of air through airplanes and cars, weather phenomena, etc.
• #### Bernoulli's Equation

"Conservation of energy applied to a flowing fluid."