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ELECTRICITY

Electricity
Electricity is a set of physical processes associated with the presence and flow of electric charge. Electricity gives a wide variety of well-known effects, such as lightning, static electricity, electromagnetic induction and the flow of electrical current. In addition, electricity permits the creation and reception of electromagnetic radiation such as radio waves. In electricity, charges produce electromagnetic fields which act on other charges. Electricity occurs due to several types of physics:

• Electric charge: is a property of some subatomic particles, which determines their electromagnetic interactions. Electrically charged matter produces electromagnetic fields.

• Electric current: a movement or flow of electrically charged particles, typically measured in amperes.

• Electric field: This is a simple type of electromagnetic field which is produced by an electric charge even when there is no electric current. The electric field also produces a force on other charges that are within its own area of jurisdiction. Moving charges additionally produce a magnetic field.

• Electric potential: the capacity of an electric field to do work on an electric charge, typically measured in volts.

• Electromagnets: electrical currents generate magnetic fields, and changing magnetic fields generate electrical currents

Uses of Electricity
The use of electricity gives a very convenient way to transfer energy, and because of this it has been adapted to a huge, and growing, number of uses. The invention of a practical incandescent light bulb in the 1870s led to lighting becoming one of the first publicly available applications of electrical power. Although electrification came along with its own dangers, replacing the naked flames of gas lighting greatly reduced fire hazards within homes and factories. Public utilities were set up in many cities to target the growing market for electrical lighting.

Through electricity, the light bulb although an early application of electricity, operates by Joule heating i.e the passage of current through resistance and thereby generating the required heat and light energy for the bulb to function.

The Joule heating effect employed in the light bulb also sees more direct use in electric heating. While this is versatile and controllable, it can be seen as wasteful, since most electrical generation has already required the production of heat at a power station. A number of countries, such as Denmark, have issued legislation restricting or banning the use of electric heating in new buildings. Electricity is however a highly practical energy source for refrigeration, with air conditioning representing a growing sector for electricity demand, the effects of which electricity utilities are increasingly obliged to accommodate.

Electricity is a necessity in all telecommunications companies. The electrical telegraph which was produced in 1837 by Cooke and Wheatstone was one of its earliest applications. With the construction of intercontinental and transatlantic telegraph systems in the 1860s, electricity had advanced communications in minutes across the globe. Although optical fibre and satellite communication technology have taken a share of the market for communications systems, electricity is still expected to remain an essential part of the process.

The effects of electromagnetism are most visibly employed in the electric motor, which provides a clean and efficient means of motive power. A stationary motor such as a winch is easily provided with a supply of power, but a motor that moves with its application, such as an electric vehicle, is obliged to either carry along a power source such as a battery, or to collect current from a sliding contact such as a pantograph, placing restrictions on its range or performance.

Electronic devices make use of the transistor, perhaps one of the most important inventions of the twentieth century, and a fundamental building block of all modern circuitry. A modern integrated circuit may contain several billion miniaturized transistors in a region only a few centimetres square.

Electricity is also used to fuel public transportation, including electric buses and trains.

MAGNETISM

Magnetism
Magnetism is a class of physical events that includes forces exerted by magnets on other magnets. It has its origin in electric currents and the fundamental magnetic moments of elementary particles. These give rise to a magnetic field that acts on other currents and moments. All materials are influenced to some extent by a magnetic field. The strongest effect is on permanent magnets, which have persistent magnetic moments caused by ferromagnetism. Substances that are negligibly affected by magnetic fields are known as non-magnetic substances. They include copper, aluminum, gases, and plastic. Pure oxygen exhibits magnetic properties when cooled to a liquid state.

The magnetic state of a material depends on temperature and other variables such as pressure and the applied magnetic field and so, a material may exhibit more than one form of magnetism depending on its temperature, etc.

Sources of magnetism
There are two sources of magnetism namely;

Electric current

Nuclear magnetic moments of atomic nuclei

Types of magnetism

Diamagnetism
Diamagnetism appears in all materials, and is the tendency of a material to oppose an applied magnetic field, and therefore, to be repelled by a magnetic field. However, in a material with a tendency to enhance an external magnetic field, the paramagnetic behavior dominates. Thus, despite its universal occurrence, diamagnetic behavior is observed only in a purely diamagnetic material. In a diamagnetic material, there are no unpaired electrons, so the intrinsic electron magnetic moments cannot produce any bulk effect. In these cases, the magnetization arises from the electrons' orbital motions, which can be understood classically as follows:

Paramagnetism
In a paramagnetic material there are unpaired electrons, i.e. atomic or molecular orbitals with exactly one electron in them. While paired electrons are required by the Pauli Exclusion Principle to have their intrinsic ('spin') magnetic moments pointing in opposite directions, causing their magnetic fields to cancel out, an unpaired electron is free to align its magnetic moment in any direction. When an external magnetic field is applied, these magnetic moments will tend to align themselves in the same direction as the applied field, thus reinforcing it.

Ferromagnetism
A ferromagnet, like a paramagnetic substance, has unpaired electrons. However, in addition to the electrons' intrinsic magnetic moment's tendency to be parallel to an applied field, there is also in these materials a tendency for these magnetic moments to orient parallel to each other to maintain a lowered-energy state. Thus, even when the applied field is removed, the electrons in the material maintain a parallel orientation. Some well-known ferromagnetic materials that exhibit easily detectable magnetic properties are nickel, iron, cobalt, gadolinium and their alloys.

Anti ferromagnetism
In an anti ferromagnet, unlike a ferromagnet, there is a tendency for the intrinsic magnetic moments of neighboring valence electrons to point in opposite directions. When all atoms are arranged in a substance so that each neighbor is 'anti-aligned', the substance is anti ferromagnetic. Anti ferromagnets have a zero net magnetic moment, meaning no field is produced by them. They are less common compared to the other types of behaviors, and are mostly observed at low temperatures. In varying temperatures, they can be seen to exhibit diamagnetic and ferro magnetic properties.

Ferromagnetism
Like ferromagnetism, ferromagnets retain their magnetization in the absence of a field. However, like anti ferromagnets, neighboring pairs of electron spins like to point in opposite directions. The first discovered magnetic substance, magnetite, is a ferrite and was originally believed to be a ferro magnet; Louis Néel disproved this, however, after discovering ferromagnetism.

Electromagnet
An electromagnet is a type of magnet whose magnetism is produced by the flow of electric current. The magnetic field disappears when the current ceases.

Electromagnets attract paper clips when current are applied creating a magnetic field. The electromagnet loses them when current and magnetic field are removed.

Other types of magnetism are Molecular magnet, Metamagnetism, Molecule-based magnet, Spin glass

OPTICS AND WAVES

Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.

Most optical phenomena can be accounted for using the classical electromagnetic description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice. Practical optics is usually done using simplified models.

The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics.

Historically, the ray-based model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that light waves were in fact electromagnetic radiation.

Some phenomena depend on the fact that light has both wave-like and particle-like properties. Explanation of these effects requires quantum mechanics. When considering light's particle-like properties, the light is modeled as a collection of particles called "photons". Quantum optics deals with the application of quantum mechanics to optical systems.

Optical science is relevant to and studied in many related disciplines including astronomy, various engineering fields, photography, and medicine (particularly ophthalmology and optometry). Practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers, and fiber optics.

Classical optics
Classical optics is divided into two main branches which are geometrical optics and physical optics. In geometrical, or ray optics, light is considered to travel in straight lines, while in physical or wave optics, light is considered to be an electromagnetic wave.

Geometrical optics can be viewed as an approximation of physical optics which can be applied when the wavelength of the light used is much smaller than the size of the optical elements or system being modelled.

Geometrical optics
Geometrical optics, or ray optics, describes the propagation of light in terms of "rays" which travel in straight lines, and whose paths are governed by the laws of reflection and refraction at interfaces between different media.

These laws were discovered empirically as far back as 984 AD and have been used in the design of optical components and instruments from then until the present day. They can be summarized as follows:

• When a ray of light hits the boundary between two transparent materials, it is divided into a reflected and a refracted ray.

• The law of reflection says that the reflected ray lies in the plane of incidence, and the angle of reflection equals the angle of incidence.

• The law of refraction says that the refracted ray lies in the plane of incidence, and the sine of the angle of refraction divided by the sine of the angle of incidence is a constant.

Physical optics
In physical optics, light is considered to propagate as a wave. This model predicts phenomena such as interference and diffraction, which are not explained by geometric optics. The speed of light waves in air is approximately 3.0×108 m/s (exactly 299,792,458 m/s in vacuum).

The wavelength of visible light waves varies between 400 and 700 nm, but the term "light" is also often applied to infrared (0.7–300 μm) and ultraviolet radiation (10–400 nm).

The wave model can be used to make predictions about how an optical system will behave without requiring an explanation of what is "waving" in what medium. Light waves are now generally treated as electromagnetic waves except when quantum mechanical effects have to be considered.

Wave and Sound
Sound is a mechanical wave that results from the back and forth vibration of the particles of the medium through which the sound wave is moving. If a sound wave is moving from left to right through air, then particles of air will be displaced both rightward and leftward as the energy of the sound wave passes through it. The motion of the particles is parallel (and anti-parallel) to the direction of the energy transport. This is what characterizes sound waves in air as longitudinal waves.

Because of the longitudinal motion of the air particles, there are regions in the air where the air particles are compressed together and other regions where the air particles are spread apart. These regions are known as compressions and rarefactions respectively. The compressions are regions of high air pressure while the rarefactions are regions of low air pressure.

The wavelength of a wave is merely the distance that a disturbance travels along the medium in one complete wave cycle. Since a wave repeats its pattern once every wave cycle, the wavelength is sometimes referred to as the length of the repeating patterns - the length of one complete wave. For a transverse wave, this length is commonly measured from one wave crest to the next adjacent wave crest or from one wave trough to the next adjacent wave trough. Since a longitudinal wave does not contain crests and troughs, its wavelength must be measured differently.

A longitudinal wave consists of a repeating pattern of compressions and rarefactions. Thus, the wavelength is commonly measured as the distance from one compression to the next adjacent compression or the distance from one rarefaction to the next adjacent rarefaction.

Since a sound wave consists of a repeating pattern of high-pressure and low-pressure regions moving through a medium, it is sometimes referred to as a pressure wave. If a detector, whether it is the human ear or a man-made instrument, were used to detect a sound wave, it would detect fluctuations in pressure as the sound wave impinges upon the detecting device. At one instant in time, the detector would detect a high pressure; this would correspond to the arrival of a compression at the detector site.

At the next instant in time, the detector might detect normal pressure. And then finally a low pressure would be detected, corresponding to the arrival of a rarefaction at the detector site. The fluctuations in pressure as detected by the detector occur at periodic and regular time intervals. Sound waves traveling through air are indeed longitudinal waves with compressions and rarefactions. As sound passes through air (or any fluid medium) the particles of air do not vibrate in a transverse manner. Do not be misled - sound waves traveling through air are longitudinal waves.

Characteristics of sound waves
A sound wave has the same characteristics as any other type of waveform which includes wavelength, frequency, velocity and amplitude.

Wavelength
Wavelen

gth is the distance from one crest to another of a wave. Since sound is a compression wave, the wavelength is the distance between maximum compressions.
Speed or velocity
The sound waveform moves at approximately 344 meters/second, 1130 feet/sec. or 770 miles per hour at room temperature of 20oC (70oF).

Frequency
The frequency of sound is the rate at which the waves pass a given point. It is also the rate at which a guitar string or a loudspeaker vibrates.

The relationship between velocity, wavelength and frequency is:

Velocity = wavelength x frequency

Amplitude
Since sound is a compression wave, its amplitude corresponds to how much the wave is compressed, as compared to areas of little compression. Thus, it is sometimes called pressure amplitude.

HEAT AND THERMODYNAMICS

Heat Energy and Thermodynamics
In this topic we are going to discuss about heat energy, temperature and its measurement, transfer of heat energy and the effects of heat on matters. It is important that you take out time and read our previous topics in physics because it will help understand what we are going to deal with here.

We will talk about heat and thermodynamics in this topic. We know that word heat but in physics it is important to understand what it means. Heat by definition is a means by which energy is transferred from a hot object to a cooler object.

Remember that objects are made up of matter and matter consists of atoms and particles. Particles that move around in an object possess kinetic energy. Increase in temperature increases the kinetic energy of a particle.

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Let's think of a real life situation that demonstrates energy transfer in form of heat. Imagine if we place a cup of hot tea on top of a table. Let's also assume that the temperature of the tea is 90 degrees Celsius. At that temperature, it is impossible for someone to attempt to drink the tea because it can burn your mouth.

But what happens if the hot cup of tea is left on the table for a long time? Yes I know you guess right. The cup of tea will lose some heat energy which will in return lower the temperature to equal the temperature of its surrounding.

This simple example shows that energy is transfer from the tea which is at a higher temperature to the surrounding which is at a lower temperature.

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We normally talk about a system and its surrounding when we are discussing heat energy and heat transfer. In our case in this example we will regard the cup of tea as our system while the environment where the cup of tea is placed as the surroundings.

This brings us to how we can measure the temperature of an object.

Temperature
Temperature is the measure of the average kinetic energy of the particles in a sample of matter, expressed in terms of units or degrees designated on a standard scale. It is important to note that the higher the temperature of an object the higher the tendency of that object to transfer heat and via-visa.

Temperature of an object can be measured with an instrument called a thermometer. There are three types of thermometers – Celsius thermometer, kelvin thermometer and Fahrenheit thermometer. Each of the thermometers can be used to measure temperature even though they all have different scales.

One of the confusing aspects of heat and temperature is that quite often most students usually interchanged the meaning of heat and temperature as the same. Understanding the difference between heat and temperature is very important in physics.

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One outstanding difference between heat and temperature is that heat is a form of energy while temperature is not.

Secondly, temperature can be measured with a device called thermometer while heat cannot be measured directly with any kind of device.

Heat Transfer
In our initial study of heat, we mention that energy is transfer from a hot object to a cooler object; we will proceed to learn the different ways by which energy can be transferred from one system to another. Note also that the internal energy of a substance is generated from the motion of its individual atoms or molecules.

Heat transfer can take place through the following processes- conduction, convention and radiation. We will go further to discuss each and every one of them in details.

Conduction
Conduction is a form of heat transfer that involves the flow of the internal energy from a region of higher temperature to region with lower temperature without any motion of the material as a whole.

A simple example of heat transfer by conduction is when you heat one edge of a metal on a fire; the increase in temperature of the region in contact with the fire will increase the kinetic energy of its particles. The particles will experience a higher speed and will randomly collide with other particles in the cooler region.

As these particles collide with one another, the particles with higher kinetic energy will transfer some of its energy to particles with lesser kinetic energy. This will continue to happen until there is a thermal equilibrium.

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Convention
Convection is a form of heat transfer in liquids and gases where by the atoms or molecules of a heated substance moves up to the upper region due to decrease in density and the atoms or molecules in the upper region moves to the lower region. This form of circulation will continue until there is a thermal equilibrium.

Radiation
Radiation is quite different from conduction and convention since it does not use any medium for transfer of energy. Radiation is the transfer of heat by means of electromagnetic waves. A simple example of radiation is the heat from sun.

Latent Heat
The energy required to change a gram of a substance from the solid to the liquid state without changing its temperature is commonly called its "heat of fusion". This energy breaks down the solid bonds, but leaves a significant amount of energy associated with the intermolecular forces of the liquid state.

Change of State
Thermodynamics
Thermodynamics is a branch of natural science concerned with heat and its relation to energy and work. It defines macroscopic variables (such as temperature, internal energy, entropy, and pressure) that characterize materials and radiation, and explains how they are related and by what laws they change with time.

Thermodynamics describes the average behavior of very large numbers of microscopic constituents, and its laws can be derived from statistical mechanics. It is also the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency.

The four laws of thermodynamics define fundamental physical quantities (temperature, energy, and entropy) that characterize thermodynamic systems. The laws describe how these quantities behave under various circumstances, and forbid certain phenomena (such as perpetual motion).

Laws of Thermodynamics
The four laws of thermodynamics are:

• Zeroth law of thermodynamics: The zeroth law in its wider sense establishes a notion of internal thermodynamic equilibrium of a system. In a narrow sense, the law states that if two systems are both in thermal equilibrium with a third system then they is in thermal equilibrium with each other. This law helps define the notion of temperature.

• First law of thermodynamics: The first law establishes a notion of internal energy for a thermodynamic system. Heat and work are forms of energy transfer. The internal energy of a thermodynamic system may change as heat or matter is transferred into or out of the system or work is done on or by the system. All the energy transfers must be accounted for to see that there is strict conservation of the total energy of a thermodynamic system and its surroundings. The law implies that perpetual motion machines of the first kind, which would do work without using the energy resources of a system, are impossible.

• Second law of thermodynamics: An isolated physical system, if not already in its own internal state of thermodynamic equilibrium, spontaneously evolves towards it. In an isolated physical system, there is a tendency towards spatial homogeneity. In particular, when an isolated physical system reaches its own internal state of thermodynamic equilibrium, its temperature is spatially uniform. When work is done on or by a thermodynamic system, a certain amount of that energy is lost to inefficiency, related to the difference between the energy level of the input and the output. This loss is described by the notion of entropy, which is often used to express the law. Some of the loss is due to friction when work is done, and some of it may be due to the relaxation of the system towards spatial homogeneity. The law says that these two mechanisms occur always and inevitably. The law implies that perpetual motion machines of the second kind are impossible.

• Third law of thermodynamics: There are various ways of expressing the third law. They derive from the statistical mechanical explanation of thermodynamics. They refer to ideally perfect theoretical models of physical systems. A common expression of the law states that no practicable means can bring a physical system to an exactly zero absolute thermodynamic temperature.

Initially, the thermodynamics of heat engines concerned mainly the thermal properties of their 'working materials', such as steam.

This concern was then linked to the study of energy transfers in chemical processes, for example to the investigation, published in 1840, of the heats of chemical reactions by Germain Hess, which was not originally explicitly concerned with the relation between energy exchanges by heat and work.

Chemical thermodynamics studies the role of entropy in chemical reactions. Also, statistical thermodynamics, or statistical mechanics, gave explanations of macroscopic thermodynamics by statistical predictions of the collective motion of particles based on the mechanics of their microscopic behavior.

MOMENTUM

Momentum
The momentum possessed by a body is generally defined as the product of its mass and velocity.

Momentum is a vector and it also has magnitude as it is the product of the multiplication of the mass and velocity. Momentum also has distance which is found in the velocity of the body used in this context.

From Newton's second law it follows that, if a constant force acts on a particle for a given time, the product of force and the time interval (the impulse) is equal to the change in the momentum.

Conversely, the momentum of a particle is a measure of the time required for a constant force to bring it to rest.

The momentum of any collection of particles is equal to the vector sum of the individual momenta.

According to Newton's third law, the particles exert equal and opposite forces on one another, so any change in the momentum of one particle is exactly balanced by an equal and opposite change of the momentum of another particle.

Thus, in the absence of a net external force acting on a collection of particles, their total momentum never changes; this is the meaning of the law of conservation of momentum

Types of Momentum
Angular Momentum
Angular momentum is obtained by multiplying a body's mass by its angular velocity.

This means that a single body can have two types of angular momentum. For example, planetary bodies such as Earth have a first momentum that is calculated from the results of its motion in relation to the sun, and then an additional momentum calculated from the velocity of its spin on its own axis.

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The smaller the body is, the faster it will spin when it is being moved as a consequence of angular momentum.

This explains why figure skaters spin much faster when they are low to the ground and when their arms are wrapped around themselves, compared to when there are standing tall with arms wide-open.

Linear Momentum
Linear momentum, also known as force, is the quantity of mass associated with a body that moves along a straight path. An outside object, with its own force, can change the trajectory of an object with a linear momentum.

For example, if you are running forward and a dog runs into you by accident, your trajectory will be changed, and you may fall; however, you should not be hurt too badly because the momentum of the dog was similar to yours.

However, if you get hit by a truck, which has a higher linear momentum because of its high weight, you will be lucky to survive. That is because the truck's force is higher than yours.

The study of linear momentum also used to understand and predict how things change trajectory when they collide with another object, such as billiard balls do when hit by the cue ball.

In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object.

For example, a heavy truck moving fast has a large momentum—it takes a large and prolonged force to get the truck up to this speed, and it takes a large and prolonged force to bring it to a stop afterwards.

If the truck were lighter or moving more slowly, then it would have less momentum.

Linear momentum is also a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change.

In classical mechanics, conservation of linear momentum is implied by Newton's laws; but it also holds in special relativity (with a modified formula) and, with appropriate definitions, a (generalized) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity.

Now that we have gathered lots of useful information about momentum, we will go further and tackle real momentum problems in physics with series of examples.

Example 1
Calculate the change in momentum cause by 50-kg car moving at 9 m/s.

Solution
Since M = m x v where m = mass and v is velocity

M = 50 x 9 = 450 kgm/s

Example 2
A lorry has a momentum of 200. What would be the car's new momentum if its velocity is tripled?

Solution
M = M x 3 = 200 X 3 = 600

You can now try your hands on the assignment listed below. Please make sure you attempt all the assignments before moving to the next topic.

Assignments
1. A ball having 5kg mass and 8m/s velocity moves to the west. Calculate the momentum of the ball.

2. A car which has 15m/s velocity and 1500kg mass moves towards north will have a momentum value of?

ENERGY

Energy
Energy can be defined as the ability to do a particular work. A person or thing that is able to carry out a particular task or work is said to have energy.

A farmer tilling his soil or planting seeds in his farm possess energy. Also, a horse ploughing the fields is said to have energy.

The unit of measurement for Energy is the joule and it is the same with the unit of measurement for Work. Energy has many different forms and they are as follows;

Mechanical Energy
This is the amount of energy possessed by an object due to its motion or position. Mechanical energy can be either kinetic energy which is energy of motion or potential energy which is stored energy of position.

Heat or Thermal Energy
Thermal energy is the part of the total potential energy and kinetic energy of an object or sample of matter that results in the system temperature. It is represented by the variable Q, and can be measured in Joules.

Light Energy
Light energy can be described as the potential of work that is gotten from light. It is the energy in the form of light and is the only kind of energy that we can actually see with the naked eye.

It can be converted into other types of energy, like chemical energy. This energy is carried in separate packets called photons.

In living plants for example, the light energy is what splits organic molecules to make chemical energy in a process called photosynthesis.

Chemical Energy
It is that part of the energy in a substance that can be released by a chemical reaction

Electrical Energy
Electrical energy results from the movement of an electrical charge, and is commonly referred to as simply "electricity". Electrical energy is the result of the interaction of subatomic particles with this force.

Electricity manifests itself in natural phenomena such as lightning and is essential to life at a fundamental level. The ability of humans to generate, transmit and store electricity is crucial to modern industry, technology and, in most countries, domestic life.

Atomic Energy
Atomic energy is the energy produced by atoms.

Solar Energy
Solar power is energy from the sun and without its presence all life on earth would end.

Measurement of Energy
Energy can be measured in two ways;

Potential Energy (P.E)
Potential Energy is simply referred to as stored energy in a body when in a certain state or position. Such stored energy is used to do work when the body begins to move. Such energy can be seen in a stone sitting on a cliff. When it's rolled over and falls on the windscreen of a vehicle, it breaks the glass. That energy which the stone possesses while it is at rest is what is known as potential energy

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Kinetic Energy (K.E)
Kinetic energy is the energy that is said to be possessed by a particular mass of thing or body when it is on the move or when it is in motion.

An example of Kinetic energy is a student running to school. Also, in the example of a stone falling down from a cliff and breaking the glass of a vehicle, the energy possessed by the stone when it is in motion downwards to the vehicle is what is known as kinetic energy.

Kinetic Energy depends only on the mass and velocity of the body. The formulae for the kinetic energy of a body in motion is given as

K.E = ½ mv2

Where m = mass, v = velocity

Therefore, in a situation where two bodies in motion have the same mass, the faster of the two bodies is in possession of kinetic energy and where they have the same velocity, the body with the greater mass has a greater kinetic energy.

Power
Power is the rate of work done in a unit of time. It can be misunderstood by most of the students. They think that more power full machine does more work. However, power just shows us the time that the work requires.

For example, same work is done by two different people with different time. Say one of them does the work in 5 seconds and the other does in 8 seconds. Thus, the man doing same work in 5 seconds is more power full. The shorter the time the more power full the man. Let's represent it mathematically;

The unit of the power from the equation given above, joule/s, however, we generally use the unit of power as watt.

1joule/s=1watt

Conservation of Energy
The law of conservation of energy stated that energy cannot be created or destroy but it can be transformed from one form to another. This implies that when energy is converted from one form to another, no energy is lost or created during the conversion process.

To help you understand this concept even more, we will take a look at a simple example of energy conservation. When we use iron to iron our dress, we plug the electric iron in a socket. The electrical energy from the socket is converted to heat energy which we use to iron our cloth.

Although when will talk about energy transfer and efficiency, it is important to note that in certain situation so of the energy are converted to non-useful energy but the total converted energy will always be the same with the initial energy.

The formula implies that Initial Energy = Final Energy

CIRCULAR MOTION

Circular and Simple Harmonic Motion
Motion can be defined as a change of position of a body with time. It also involves how things move and what makes them move.

In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation.

The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body.

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Examples of circular motion include: an artificial satellite orbiting the Earth at constant height, a stone which is tied to a rope and is being swung in circles, a car turning through a curve in a race track, an electron moving perpendicular to a uniform magnetic field, and a gear turning inside a mechanism.

Uniform Circular Motion
Uniform circular motion describes the motion of a body traversing a circular path at constant speed. The distance of the body from the axis of rotation remains constant at all times. Though the body's speed is constant, its velocity is not constant. Velocity which is a vector quantity depends on both the body's speed and its direction of travel.

This changing velocity indicates the presence of acceleration; this centripetal acceleration is of constant magnitude and directed at all times towards the axis of rotation.

This acceleration is, in turn, produced by a centripetal force which is also constant in magnitude and directed towards the axis of rotation.

In the case of rotation around a fixed axis of a rigid body that is not negligibly small compared to the radius of the path, each particle of the body describes a uniform circular motion with the same angular velocity, but with velocity and acceleration varying with the position with respect to the axis.

Non-uniform Circular Motion
Non-uniform circular motion is any case in which an object moving in a circular path has a varying speed.

The tangential acceleration is non-zero; the speed is changing. Since there is a non-zero tangential acceleration, there are forces that act on an object in addition to its centripetal force which is composed of the mass and radial acceleration.

These forces include weight, normal force, and friction. In non-uniform circular motion, normal force does not always point in the opposite direction of weight.

Since the object's velocity vector is constantly changing direction, the moving object is undergoing acceleration by a centripetal force in the direction of the center of rotation.

Without this acceleration, the object would move in a straight line, according to Newton's laws of motion.

Differences from uniform circular motion
The way to express non-uniform circular motion is not that different from the techniques used in calculating uniform circular motion.

In uniform circular motion, the magnitude of the tangential acceleration is always equal to zero assuming speed remains constant.

The radial acceleration in uniform circular motion is equal to the centripetal acceleration, which is towards the center of the circle. In non-uniform circular motion, the radial acceleration is the same and equal to towards the center of the circle.

What's different is the tangential acceleration, since speed is non-zero and changing.

Since there is a non-zero tangential acceleration, there are forces that act on an object in addition to its centripetal force (composed of the mass and radial acceleration).

These forces on the object include forces such as weight, normal force, and other forces acted on the object due to the environment it is in such as friction.

Simple Harmonic Motion
We have studied linear and circular motions extensively. Right now we will look at oscillation. Oscillating motion is quite complex compare to linear motion but we will try and simplify it so that it will be quite easy to understand.

We will also take a look at a special kind of oscillation called simple harmonic motion.

If you have not heard of oscillation before in physics do not worry because you will soon realized that it all around us.

An oscillatory system can be simply define as a system where by a particle moves back and forth. The particle will always come back to its starting position to make a complete oscillation.

This type of oscillating motion is also called a periodic motion.

Unlike in other kinds of motions, in oscillating motion, amplitude, period, and frequency are used to describe the periodic nature of an oscillating motion.

Time Period
Time period is measured in seconds and it is the time taken for an oscillating object to complete a full cycle. There are situations where by many cycles are complete on a specific time, in order to get the time period of the oscillation, the following formula is used.

T (Time Period) = Time in seconds / Number of oscillation

Frequency of Oscillation
The frequency of oscillation is the number of complete oscillating cycle completed in a second. The frequency of oscillation is related to the period by the following equation.

Frequency = 1 / Time Period

The displacement of an oscillating particle is the distance the particle has been moved from its equilibrium position.

The amplitude of an oscillation is the maximum displacement of the vibrating object from the equilibrium position.

There are many examples of simple harmonic motions in real life but one example we will emphasize on is the simple pendulum. When a pendulum is attached on a string and the other end of the string is attached to a top beam, when the pendulum ball is swing sideways, it exhibits a simple harmonic motion.

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When the pendulum ball moves to it central point – which is consider as the equilibrium point, there is no resultant force on the object. At the far-end, the pendulum ball stops before it changes direction. At this point the velocity of the pendulum is zero and the displacement is at its maximum.

The diagram below shows a graphical representation of simple harmonic motion.

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Simple harmonic motion equations can be used to find different parameters of the motion.

Where V = velocity, A = acceleration, E = energy

Y = A sin wt = A sin √ (Kt / m)

V = wAcos wt

A = - w2Asin wt = -w2y

E = KE + PE = 1/2kA2

FORCE

Force
A force is a push or a pull applied to an object as a result of the interaction of the object with another object. Every time there is in interaction involving two objects, there is always a force upon every one of the objects. The force between them ceases to exist when the interaction between them stops. Forces only occur as a result of interaction. Without interaction, there will be no force.

In summary forces are classified broadly into two.

1. Contact forces
2. Resultant Forces as a result of a distance action
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Contact forces
Contact Forces are types of forces that exist between two interacting objects when they are in close contact with each other. The sub-types and examples of contact forces are listed below:

• Frictional forces

• Tensional forces

• Normal forces

• Air resistance forces and

• Applied forces.

Each category of contact force above will be explained in details in our succeeding lessons.

Resultant Forces from a distance action
These are those types of forces that occur when the two objects that are interacting do not have bodily contact with each other; still they are capable of putting forth a push or a pull in spite of their bodily separation. Examples of these types of forces are:

Gravitational forces
Typical example of gravitational force is the force exerted by the sun and the planets irrespective of the wide spatial distance between them. Even when your feet are not in contact with the ground, there still exists a gravitational force or pull between you and the Earth.

Electric forces
These are another example of resultant forces as a result of interactions from remote positions. Examples of electrical forces are the forces that exist between the protons in the nucleus of an atom and the electrons outside the nucleus of an atom. The proton and electron irrespective of the distance from each other exert an electrical force of attraction or pull towards each other.

Magnetic forces
These are another example of resultant forces from a distance action. For instance, two magnets can put forth a magnetic pull against each other even when they are separated by a few centimeters' distance. We will discuss each one of these forces in details in our subsequent lessons.

Examples of contact and action-at-distance forces are listed in the table below.

Contact Forces Distance Forces
Frictional Force Gravitational Force
Tension Force Electrical Force
Normal Force Magnetic Force
Air Resistance Force
Air Resistance Force
Applied Force
Spring Force
Measurement of Force
The standard unit (SI) of measurement of Force is the Newton. A Newton is shortened as an "N." So when you say "10.0 N", it means 10.0 Newton of force.

One Newton is the amount of force required to give 1-kg mass of an object an acceleration of 1 m/s/s. Thus, we could derive the unit of 1Newton as:

A force is a vector quantity not a scalar quantity. A vector quantity is a quantity that has both magnitude and direction.

To completely explain the force acting upon an object, its magnitude and direction must be described. Therefore, 10 Newton is not a complete picture of the force acting on an object.

On the contrary, when you say 10 Newton downward, it is a complete explanation of the force acting on an object; both in terms of the magnitude (10 Newton) and the direction (downward).

Due to the fact that a force is a vector that has a direction, it is regular practice to characterize forces using diagrams in which a force is represented by an arrow.

The size of the arrow is a reflection of the size/magnitude of the force and the direction of the arrow shows the direction on which the force is acting. These types of diagrams are referred to as free-body diagrams.

We are going to see some of the example for force and calculation involving finding a force that acts on an object or finding each component of a force.

Example 1
What force is required to accelerate an object having a mass of 8 kg at 7 m/s2?
Solution:
Force is represented with the following formula

F = ma where m is mass and a is acceleration.

F = 8 x 7 = 56 N

Example 2
A body of mass – 20kg was hit by a force of 200 N, what will be the acceleration of the body due to the impact of the force.

Solution
F = ma

a = F / m

a = 200 / 20 = 10 ms2

With these examples, you have learned how to calculate the components of force. You should try your hands on the assignments given below. It will help you master force in physics.

Assignment
1) What force is required to accelerate an object having a mass of 64 kg at 2 m/s2?

2) What the mass of an object that accelerates with 2m/s2 when hit by a force of 30N.

Newton's first law of motions
Newton's laws of motion are one of the fundamental laws that gave us a new ways to understand our universe. Newton's first law of motion stated that every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

By simple explanation it means that an object at rest will always remain at rest expect it is acting by a nonzero external force.

The idea of a nonzero force will bring us back to our previous topic in vector addition. We define a net force as the resultant force obtained when all the forces acting on an object are summed together. Nonzero force can also be regarded as net force.

Newton's first law of motion is quite similar to inertia. Inertia is one of the fundamental concepts used in physics to describe motion of objects and how objects are affected by applied forces.

Understanding inertia also will help you understand to meaning and implementation of Newton's first law of motion.

Inertia is the resistance of any physical object to any change in its state of motion (including a change in direction). In other words, it is the tendency of objects to keep moving in a straight line at constant linear velocity. (Wikipedia)

Newton's Second Law of Motion
The fundamental concept of Newton's second law of motion deals with the relationship between an object mass, the force that acts on the object and its acceleration. It focuses on the velocity of an object when a force acts on an object.

You should remember that we talked about nonzero force when we discussed Newton's first law of motion, imagine if the net force that acts on an object is not zero, the object will experience a change in velocity due to the applied force on the object. This change in velocity is called acceleration.

This implies that there is a linear relation between applied force and acceleration. Increasing the amount of force that acts on an object will increase the acceleration of the object. Since force and acceleration are vector quantities, it means that they have both magnitude and direction. The force and acceleration moves in the same direction.

Let consider the relationship between the applied force on an object and the object itself. If the same amount of force is applied to the object but of different size, the small object will tend to accelerate faster than the bigger object.

We can deduce so far that

Force = mass x acceleration

A simple example to illustrate Newton's second law of motion is shown below.

Diagram
Newton's third law of motion
By now you must have understood the important of laws that Newton described. These laws have redefines our understanding of our universe. We will detail concisely with Newton's third law of motion now.

Newton's third law of motion stated that for every action there is an equal and opposite reaction. Although it sounds simple but we will dive into it and make it even much easier to understand.

Newton's third law of motion emphasis that for every internal force that acts upon an object, there is an opposing force with the same magnitude but in opposite direction at also acts on the object. This implies that an object is not responsible to initiate its own motion. In this case there is no net force.

Newton's third law is predominant in our everyday life.

A typical example of Newton's third law is shown below.

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The force of the small object on top of the big object acts in downward direction but that is also a force with the same magnitude but acts in opposite direction. Since the net force is zero, the small object is at rest on top of the big object.

Normal Force
The concept of normal force is quite confusing for most students new to physics. Some people might think that normal force is just like an ordinary force but it is not true. Let's deal with what normal force means in physics.

Normal force is any force coming from the surface and acting at a right angle to the surface.

In some situation, normal force is just the weight of an object that sits on a level surface. Imagine in a case where the object is inclined to a certain angle on a surface of another object, the normal force is equal and opposite to the perpendicular force.

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Frictional Force
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Friction force always acts in opposite direction to motion and it tends to reduce the net force that acts on an object.

It is important to know that frictional force depends on the material of which an object is made of and also it is affected by normal force.

Frictional force can be defined by this simple equation: Frictional Force = uF

Where u = coefficient of friction and F is the normal force

A simple illustration of frictional force is shown below.

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Equilibrium of Forces
As we have discussion in the vectors and scalar topic and also in Newton's first law of motion, equilibrium of forces is the term used to describe an object with a resultant force of zero. A resultant force of zero is when the upward force is equal to the downward force and the rightward force is equal to the leftward force.

Remember that we do mention of this concept when we treated vector addition, you can back the topic to read more about it.

Equilibrium of forces also implies that the net force that acts on an object is equal to zero. The following conditions are the basis for equilibrium of forces

Leftward force = Rightward force

Upward force = downward force

Net torque = 0

Clockwise torques = Anticlockwise torques

When the net force acting on an object is zero it also implies that the acceleration is equal to zero. You should also know that when acceleration is equal to zero, it does not imply that the object is stationary.

When an object is regarded to be in a static equilibrium it means that the object is at rest. Remember also that an object at equilibrium is either at rest or in motion with the same speed and direction.

Equilibrium of force is an important concept in physics and it has found applications in many different areas. One important area where equilibrium of forces is used is in the construction of structures that carry loads. A typical example is in the construction of bridge. This is necessary to make sure that bridges will maintain equilibrium when many vehicles are line up on the bridge.

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SCALAR AND VECTOR

Scalar and Vector
In physics and mathematics, the words scalar and vectors are commonly used to describe some quantities. Many science students have heard these words many times in the course of their studies but still most might not completely understand its meaning and what they emphasize.

Mathematical quantities are used in different fields to describe certain phenomena. When it comes to moving objects or in mechanics, there are two types of quantities used to describe this object. They are known as scalar and vector.

We will move further to define the meaning of these two quantities and some of the examples of vector and scalar quantities.

Scalars
Scalars are mathematical quantities used to describe objects of one dimensional quantity. In a simple term, they are quantities that are described in numerical terms alone. Scalar quantities have only magnitude.

Example of Scalar Quantities
It is important to list some of the scalar quantities so that it will help your understand while there are called scalar quantities.

Temperature

Time

Speed

Mass

Vectors
Unlike scalar quantities, vector quantities are quantities that can be described by magnitude and direction. This implies that vector quantities are multi-dimensional quantities.

Example of Scalar Quantities
The list below highlights some examples of vector quantities.

Velocity

Acceleration

Force

Vector Representation
Vector representation is a way to represent and fully visualize how to manipulate vectors in physics. There are different ways in which vectors can be represented in physics. The simple and commonly used is the graphical representation of vectors.

When a vector is represented graphically, its magnitude is represented by the length of an arrow and its direction is represented by the direction of the arrow.The direction of a vector is often expressed as a counter-clockwise angle of rotation of that vector from due east. The graphical representations of vectors use the concept of tip and tail. The tip has an arrow which indicates the direction of the vector.

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Beside graphical representation of vectors, vectors can be expressed in terms of their components. Being able to translate between the two representations is an essential skill in physics. The magnitude of a vector is its length. The direction is usually given in terms of some angle.

The diagrams below show different representation of vectors

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Vector Addition
Vector addition involves the summation of two or more vectors to get the resultant vector. The addition of vectors is one of the many operations that can be performed with vectors. To understand the in-depth of vector addition, let us move back to the Newton's first law of motion which stated that an object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

This implies that the net force experienced by an object is equal to the sum of the resultant forces that act on the object. In some situation, we make use of an unbalance force when we are talking about the forces that act on objects. In its simplicity, unbalance force is when that forces that act on an object in opposite direction is not equal to zero when they cancel each other.

We will go ahead to show a diagram that illustrates vector addition in its simplest form.

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Another important vector addition that is worth mentioning is that Pythagoras theorem can be used to add two vector that are at right-angle to each other.

FLUID AND WEIGHT

Fluid and Weight
Mass and Weight
Mass and weight are some of the common terms we come across in our everyday life. These terms are also confusing to many students new to physics. It is important to understand their meaning and how they differ with each other.

A mass of an object is the amount of matter contained by the object. The mass of an object does not change with location. For example, if the mass of an object is 10kg in earth, the object will have the same mass in moon.

The symbol for mass is m while the standard unit of measurement is kilogram.

Alternatively, weight of an object is the mass of the object acting upon by force of gravity. Since weight is a force, its standard unit of measure is in newton.

Just like mass that is independent of location, the weight of an object depends on the amount of force of gravity being acted upon the object. This implies that the weight of an object in earth will differ in moon since different amount of force of gravity acts on it.

The weight of an object is determined by multiplying the mass with acceleration of gravity.

W = m x a (N)

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Another important phenomenon that is worth mentioning is weightlessness. Weightlessness is regarded as a state of free fall. Basically, the weight of an object depends on the mass and force of gravity which is supported by an object. If the supporting object is removed, weightlessness can be achieved.

Density and Relative Density
Density of an object was first discovered by a Greek scientist called Archimedes. It is simply a measurement of how compact the matter that made up the mass of an object is. If the matter is tightly held together the density of the object will be higher while the reverse is the case.

The density of an object can be obtained by using the mass of the object divided by the volume of the object.

Density = mass / volume (kg/m3)

The SI unit of density measurement is kg per cubic meter (kg/m3). Density can be found in use in many different areas in physics.

The symbol for density is the Greek letter rho, :

The relative density of an object is regarded as the ratio of the material's density to the density of water. An object that has a density higher than density of water will sink in water where else an object will a lower density to that of water will float on water.

Pressure
Pressure is another important element in physics that deserve a thorough explanation - what it is and where it can be applied in real life.

Pressure can be defined as the measurement of a force per unit area. In its simple form, it is the force exerted by an object divided by the surface area on which the force is being acted upon.

It is important to understand the concept of pressure when two solids are involved and when pressure is applied in a fluid

For now let us just assume that we are dealing with two solids. In this situation, pressure can be calculated with the formula shown below.

Note: here that the force is applied perpendicular to the area

Pressure = Force / Area (Pascal)

The SI unit of pressure is called Pascal. The simple diagram below shows that pressure exerted on a solid surface.

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Static Fluid Pressure
In a static fluid – a liquid or gas that is confirmed in a particular container, the pressure exerted by the fluid depends on the depth of the fluid, density of the fluid and the force of gravity.

Static fluid pressure = density x force of gravity x depth of fluid

The pressure in a liquid is exerted in all direction unlike in solid. The static fluid pressure does not depend on the shape, mass and surface area of the liquid.

The pressure at any point in a static fluid takes into consideration the pressure on top of the fluid and the depth of a particular spot on the liquid.

If two points are separated by a height (h) in a static fluid, there will be a high pressure in the lower point compare to the upper point.

The general equation to calculate the pressure in each depth in the fluid is shown below.

P2 = P1 + pgh

Pressure Using Pascal's Principle
Another interesting concept of pressure is the work done by Pascal. Pascal's principle stated that in a fluid that is completely enclosed in a system, a pressure applied at one point in the fluid will be transmitted to all other points in the fluid including the enclosing walls.

Pascal's principle has found application in many equipment and measurement tools. A typical example is when you applied a pressure in a pipe containing liquid; the applied pressure is transmitted throughout the pipe.

Since the area in the container might not be the same so also the force being applied, the pressure will always remain the same. In other to find out the amount of force applied to the areas within the container, the following equation can be used.

P1 = P2 = F1 / A1 = F2 / A2

Pressure Measurement Using Barometer
Manometer is one of the instruments used to measure pressure. The mechanism by which the measurement occurs is by exploiting the relationship between pressure and depth. There are open-tube manometer and closed-tube manometer.

A typical example of a closed-tube manometer is a barometer. A simple diagram of a barometer is shown below.

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A tube with one sealed end is filled with mercury and the open-end side of the tube is inserted into an open rectangle container that is filled with mercury. Since the top surface of the container is open, pressure is exerted by atmosphere pressure. The height from the surface of the container to the height of the mercury in the cylindrical pipe equals the pressure being measured.

The empty space at the end of the tube is at zero pressure. Note that this can only work if there is no air bubble present in the cylinder tube when placed inside the mercury container.

Equilibrium of Bodies
The equilibrium of bodies is a way to identify the forces acting on a body partially or completely immersed in a fluid. One scientist that came with a sound explanation about this concept is called Archimedes.

Archimedes' principle stated that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.

In a simple example, if an object of weight is dropped inside a cylinder container filled with water, if the weight of the water displaced is less than the weight of the object, the object will sink otherwise the object will float.

A diagram that illustrates Archimedes' principle is shown below.

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