SATELLITES

The objects moving around a planet are called the satellites of that planet. The moon moves around the earth hence moon is a satellite of the earth. The moon is a natural satellite of the earth. The centripetal force must be provided for moon to move around the earth . Here the necessary centripetal force is provided by the gravitational force between the moon and the earth.
In the same way by providing necessary centripetal force by by the gravitational force between the earth and the object it is possible to make it to move around the earth . These days there are very large numbers of human beings made satellites i.e. artificial satellite moving around the earth in different orbit saving different purpose,such as transmission of tv and radio programs for the telecommunication purposes etc.
LAUNCHING SATELLITE'S:
When satellite are made to move away from the earth's gravitational field the minimum velocity required is 11.3k/s or 40320 km/hr. Using a single stage rocket it is not possible to have so much velocity. Hence for launching satellites multistage rockets are used. Generally for such purposes 3-stage rockets satellites is always kept at the rckets are used.
In the rockets satellites is always kept at the top of the third stage . During launching of the rockets the burnt fuels comes out from the nozzle of the rocket, Then according to the third law of motion the opposite reaction that exceeds rockets weight lift and moves the rocket in upward direction. The rocket accelerates upwards and rises vertically upward so that it passes through the denser atmosphere with least time. Then first stage of the second stage makes the rocket to move with high velocity. After moving through certain distance attaining the height speed the second stage of the rocket also detached and falls back. Using the final third stage of the rocket the satellites is turned in the horizontal direction and is given proper speed for the satellite so that it remains on the orbit.Then the satellite moves around the earth in a closed orbit.

PHOTOMETRY

Light is a physicaal quantoty. Hence as other physical quantity light is also must be measurable. The branch of light that deals with the measurement of light called photometry. In photometry, we have to know about some definitions as given below.
LUMINOUS ENERGY: Light is a measurable physical quantity. Just as electric current flows through a conducting wire the light is also the flow of flux or radiant energy called the luminous energy.Light can be taken as aform of energy since light can be converted to other forns of energy and similarly other forms of energy can also be converted to light for examples:

1. PHOTOCEL:It converts light to electrical energy.
2. SOLAR BATTERY:It converts light to electrical energy.
3. BULBS:It changes electrical energy to light energy and heat .

Hence according to the principle of conservation of energy, light must be a form of energy.

Terrestrial Magnetism: Exploring Earth's Magnetic Field and Its Significance

Introduction:
In early times people thought that the north started attracting the north pole of the magnetic compass. But later a physician William Gilbert interested in scientific experiments suggested that the earth itself behaves like a huge magnet. For verification, he made a clay sphere and kept a long lode of some magnets inside the sphere with two poles one at the top and the other at the bottom. Then he made a dipping needle compass that could dip and down only and held it near one person of the lodestone. He found that the needle pointed towards the center of the sphere. When he held the dipping needle at the center of the sphere the needle set parallel to the horizontal. When he held the dipping needle near the equator of the lodestone, the needle was itself parallel to the line through the two poles. Gilbert concluded that the earth is a magnet dipping needle that should till down More and more as the needle is carried north and that it should point straight down at the magnetic equator, the dip of the needle is zero. Thus the two poles at which the needle shows 90 degrees are known as the poles of the Earth. They are not at the same points as the geographical poles. The angle between the two lines joining the two magnetic poles and the other joining the two geographical axes makes about 17 degrees. The line joining the points where the angle of inclination is zero is called the magnetic equator.

Characteristics of Earth's Magnetic Field:

Magnetic Dipole: Earth's magnetic field can be approximated as a magnetic dipole, with a north magnetic pole near the geographic South Pole and a south magnetic pole near the geographic North Pole. This results in a magnetic axis that is tilted concerning the rotational axis of the Earth.

Magnetic Declination: Magnetic declination is the angle between true north and magnetic north. It varies based on geographic location and changes over time due to the movement of Earth's magnetic field. Accurate knowledge of magnetic declination is essential for navigation and compass use.

Magnetic Intensity: Magnetic intensity refers to the strength of Earth's magnetic field at a specific location. It is commonly measured in units of tesla (T) or its subunit, nanotesla (nT).

Magnetic Anomalies: Earth's magnetic field exhibits variations known as magnetic anomalies. These anomalies can occur due to variations in the composition and magnetization of rocks beneath the Earth's surface. Studying these anomalies provides insights into geological structures, mineral exploration, and plate tectonics.

Measurement Techniques:

Scientists employ various methods to measure and study Earth's magnetic field:

Magnetometers: Magnetometers are instruments used to measure the strength and direction of magnetic fields. They range from simple handheld compasses to sophisticated devices like fluxgate magnetometers and proton magnetometers, capable of providing detailed magnetic field data.

Magnetic Observatories: Permanent magnetic observatories are established at various locations worldwide to monitor and record Earth's magnetic field over time. These observatories contribute to global magnetic surveys and aid in detecting long-term changes and magnetic disturbances.

Satellite Missions: Space-based missions, such as the European Space Agency's Swarm mission, utilize satellite magnetometers to gather high-precision magnetic field measurements. These missions enable the mapping of Earth's magnetic field on a global scale, providing valuable data for scientific research.

Significance and Applications:

Terrestrial magnetism holds immense significance across scientific disciplines and practical applications:

Geophysics and Earth Science: Studying terrestrial magnetism helps us understand Earth's internal structure, including the composition of the core, mantle, and lithosphere. It provides insights into the dynamics of the Earth's interior, plate tectonics, and the history of the planet.

Navigation and Compass Use: Earth's magnetic field has long been utilized for navigation. Compasses rely on the magnetic field to indicate a direction, allowing mariners, aviators, and hikers to navigate accurately.

Magnetic Field Protection: Understanding the behavior of Earth's magnetic field is crucial for protecting sensitive electronic devices, power grids, and communication systems from the effects of geomagnetic storms and solar flares.

Archaeology and Paleomagnetism: The study of ancient magnetic fields preserved in rocks, sediments, and archaeological artifacts, known as paleomagnetism, helps in reconstructing Earth's past magnetic field. This field provides valuable insights into geological time scales, past continental drift, and the movement of tectonic plates.

Space Weather and Ionospheric Studies: Terrestrial magnetism plays a significant role in space weather research. Variations in Earth's magnetic field interact with charged particles from the Sun, resulting in phenomena such as auroras and geomagnetic storms. Understanding these interactions is crucial for satellite operations, space missions, and radio communications.

Environmental Monitoring: Changes in Earth's magnetic field can be indicative of environmental factors such as underground water flows, volcanic activity, and seismic events. Monitoring magnetic field variations assists in detecting and assessing these environmental changes.

Magnetic Resonance Imaging (MRI): Medical imaging techniques like MRI rely on the principles of magnetic fields and their interaction with atoms in the human body. Terrestrial magnetism provides a foundation for understanding the behavior of magnetic fields in these medical applications.

Conclusion:

Terrestrial magnetism, the study of Earth's magnetic field, is a fascinating field of research with diverse applications. From its origin in the Earth's core to its effects on navigation, geophysics, and space weather, understanding the properties and characteristics of Earth's magnetic field provides valuable insights into our planet's past, present, and future. Through the use of sophisticated measurement techniques and ongoing scientific investigations, we continue to unravel the mysteries of terrestrial magnetism and its profound influence on our lives.

DEPTH KNOWLEDGE MECHANICS

AXIAL VECTOR:
Those vectors related with rotation or responsible for rotation.Example angular momentum,angular velocity etc.
POLAR VECTOR:
Those vector related with translation or responsible for translation .Example force,displacement,velocity etc.

• A vector must be changed if we change its magnitude ,direction or both .
• A vector is not changed if it is slide parallel and due to change of co-ordinate x-axis.

Q} A vector is not changed if
ans: slides parellely.
ADDITION OF TWO VECTORS:

• Resultant of any two vectors lies along major diagonal when the angle between both vector less than 90 degree.
• Resultant lies along minor diagonal when the Angle between both vector is obtuse.
• Minimum number of unequal vectors lying on same plane required to make R=0 is 3.
• Minimum number of unequal vectors not lying on same plane required to make R=0 is 4.
  

CONCEPT IN SOUND

1. WAVE AND SOUND

WAVE:Way is a disturbance,which can be transfer from one place to another place to the another place due to repeated periodic motion of the particles of the medium about their mean position.
LONGITUDINAL WAVE +TRANSVERSE WAVE=ripple wave

• Wave produced in a string=1 dimensional
• Wave produced in water=2 dimensional
• Sound and light wave=3dimensional

Wave are two types :

1. Mechanical wave
   
2. Non mechanical wave

• For the propagation mechanical wave, elasticity as well as density of medium is required that's why mechanical wave is also known as elastic wave.

• In a non -mechanical wave,vibration takes place in both electric field as in magnetic field that's why non-mechanical wave is also known as electromagnetic wave.

• Medium is required for the propagation of mechanical wave. For example wave produce in a string ,spring,sonometer wire, tuning fork and sound wave etc.
• There is no requirement of medium for the propagation of non-mechanical wave.Example:light,X-rays, Gama rays, radiation and radio waves.

1. MECHANICAL WAVE:

Mechanical wave are two types:

• Transverse wave
  
• Longitudinal wave

If wave is longitudinal,it must be a mechanical wave and if wave is mechanical then

• It may be longitudinal wave.
• It may be transverse wave.
• It may or may not be longitudinal.
• It may or may not be transverse.

1. NON-MECHANICAL WAVE:

All non -mechanical waves are only transverse in nature
If wave is non-mechanical then must be a transverse wave and wave is non-mechanical wave then

• It may be mechanical wave .
• It may be non-mechanical wave.
• It may or may not be mechanical wave.
• It may or may not be non-mechanical waves.
  

DEPTH KWOWLEDGE IN ELECTROSTATICS

COLUMBUS LAW:

• Two charges express Columbus force due to interaction electric lines of force produce by charges.
• Magnitude of Coulomb;s force on the two charges will be always equal and opposite direction even charges and their masses may be or may not be equal and charges may be like or unlike.
• Force with negative sign represent attractive force and the convention is applied only in magnitude form.
• Above convention is applied only for Coulomb force, gravitational force and magnitude force between two current carrying wire.
• An electron is accelerating with potential of 1volt. Then find kinetic energy and speed gained by electron. Electron, proton,deuteron,Triton accelerating with potential of 1volt kinetic energy gained=1Ev=1.6^-19J.
• Insulator and conductor commonly called as dielectric is used as between charges to very Coulomb force and other electrostatics quantities.
• For pure water K=81(maximum) where K is relative permittivity or dielectric constant.
• For perfect insulator k=o i.e. perfect insulator cannot be charged by any method.
• Dielectric constant of medium epsilon cannot be equal to 1.
• Coulomb force will be maximum if between the charges is air or vacuum and after putting single dielectric completely between the charges then force, decrees by k time.
• If a conductor is kept completely or partially between the charges than Coulomb force decreases to zero.Since electric lines of force produced by charge cannot interact.
• Conductor constant is defined as property of medium which oppose electric lines of force.
• Conversation of charges is consequence of principle of continuity.
• Another left things i will write in another article.
  

Electric potential

If a small positive test charge is placed at a point in an electric filed due to a positive source charge moves away from the source charge. Similarly, if the positive test charge is placed at a point in an electric field due to negative source source charge, the test charge is is found to move towards the source charge. These statements suggest that every point in an electric field have potential. The potential of a point in an electric field is called electric potential.
The electric potential is analogous to the gravitational potential .The electric potentials at different points in the electric field may be different.When a mass moves from one to another point, the gravitational potential energy of the gravitational field is converted into the kinetic energy of the mass. Similar is the case in case of charge moving in an electric Field. When a charge moves in an electric field., the potential energy of the two points in the electric field is converted into the kinetic energy of the charge. Similarly, if a charge is to move against an electric field, the kinetic energy of the charge is converted into the electric potential energy. The electric potential at a point in an electric field is defined as the amount of work done in bringing a unit positive charge from infinity to that point.

Brief introduction to optics

Light is a from of energy stimulates the sensation of vision and makes us see objects around us. Light is emitted by bodies which are heated to very high temperature,such as glowing electric bulb,burning candles,sun,etc.Light can travel through vacuum, It does not require material medium to travel from one place to other.
When light falls on an object,it is party reflected. We see the objects only when the light reflected from the objects enters into our eyes. Regarding the nature of light,Newton put forward the corpuscular theory of light. According to this theory, light consists of tiny elastic particles called corpuscles. A light source emits such corpuscles in all directions when these cor pules strikes an objects, they are partly reflected and the reflected corpuscles enter into our eyes and we see the objects. On the basis of this theory, phenomena like rectilinear propagation,reflection and refraction of light can be explained. At about the same time Huygens proposed wave theory of light. According to this theory, light is propagated in the form of wave through either which was assumed to be present everywhere.This theory explain besides reflection, refraction of light other phenomena like interference,diffraction and polarisation of light. But because of newton's popularity at that time, his corpuscular theory prevailed, and the wave theory remained in the black ground for over a century.
Later, experiments on the measurements of the velocity of light in different media showed that the velocity of light in denser medium, like water or glass, is smaller than the velocity of light in air. According to Newton's corpuscular theory, the velocity of light in denser medium should be greater than that in rarer medium with these experimental results, wave theory of light become general acceptance from scientific communities.
Still latter, it was found that when light of suitable frequency is incident on certain metals, electrons are emitted. This phenomenon could be explained only by assuming that light is absorbed or emitted in the form of quantum of energy .Each quantum of energy is a packet of energy called photon .Photons behave as particles.

Electric Measurement

Basically, electric measurement means measurement of current, voltage and resistance in a circuit.We have already discussed that a voltmeter is used for measuring current. Both of these instruments work on ohm's law. The fundamental law in current electricity. Certainly, we did not discuss about the measurement of resistance. The instrument to the a resistance is called ohmmeter. An ohmmeter ,in fact, is a combination of a voltmeter and ammeter. It is important to note that all of these electrical instruments use energy from the source of electricity of which they are doing the measurement. It is, therefore, there fore, the measurements taken by them are slightly different from the actual measurements . In other words, some accuracy of measurement is lost with these instrument.
Hence , if we need move accuracy in the electrical measurement,we use potentiometer and Wheatstone bridge for the measurement of electricity. These devices use elaborate circuits for the measurement. However, these devices are much more accurate them the other.
In this sub-unit,we discuss in detail the principle and applications of accurate electrical devices.

Transfer of heat

Heat is a form of energy. Heat energy can be transfered from one place to another. Now , we talk about the mechaniisms of transfer of heat by conduction method. Conduction is one of the mechanisms of heat transfer. This takes place usually in solids. When ther exists temperature difference betwwen two points in solid, transfer of heat akes place from the point at high temperature to the point at low temperature without transferring the mass. This kind of transfer heat without transfer of mass is called heat conduction.

Heat conduction in solids can be explained the basis of kinetic theory of matter.A solid is made of a number of atoms which are fixed at lattice sites and are capable of vibrating about their mean positions.the amplitude of vibration of yhese atoms increases with the increase of temperature of solid.

Suppose that one end of a solid of bar is heated. The temperature if that end increases and the atoms in that region to vibrate with higher amplitudes due ro gain of thermal of heat energy. As a result, they collide with neighbouring atoms in cooler region . During such collision hot atoms transfer thermal energy to tje cold atoms and these atom also will begin to vibrate with higher amplitude. In turn, these neighbouring atoms collide with nextneighbouring vold atoms and so on. Thus, there will be continous transfer of heat thermal of thermal energy towards cold end. Here,heat is transfered from one atom to the other while each atom remaons vibrating about their original positions.

In matals there are many free electrons. The electrions are very small and can travel rapidly. When a bmetal is heated,their vibration increase and the energy is passed on to pther atoms and also the numerous electrons in the metal. The electrons rapidly transfer energy by collision to other electrons and other atoms. Hence the transfer of energy n metals is rapid.In non-metallic solids,there are very few free electrions.Here the only way that hewat can transfer through the solids is by direct transfer of energy from one atom another.Hence,yhe the transfer process slow.

Effects of Refraction of Light: Definition, Examples, Applications, and Everyday Phenomena

What is Refraction of Light?

Refraction of light is the bending or change in the direction of light when it passes from one transparent medium to another due to a change in its speed.

Light travels at different speeds in different media. When it moves from one medium to another-such as from air to water or from air to glass-its speed changes, causing the light ray to bend.

Definition:

Refraction of light is the change in the direction of light as it passes from one transparent medium to another because of a change in its speed.

Effects of Refraction of Light

Refraction produces several interesting optical effects that we observe in our daily lives. Some of the most common effects are discussed below. 

1. A Swimming Pool Appears Shallower Than It Actually Is

One of the most familiar effects of refraction is that a clear swimming pool or pond appears shallower than its actual depth.

Why does this happen?

Light rays coming from the bottom of the pool travel from water (denser medium) into air (rarer medium). As the rays emerge from the water, they bend away from the normal.

Our brain assumes that light travels in a straight line. Therefore, the bottom of the pool appears to be at a higher position than it actually is.

Result

• Apparent depth is less than the real depth.
• The pool appears shallower.

2. A Coin in Water Appears Raised

If a coin is placed at the bottom of a transparent container filled with water, it appears to be lifted upward.

Explanation

The light reflected from the coin bends away from the normal when it passes from water into air.

As a result, the eye sees the image of the coin at a position above its actual location.

Observation

• Actual position → Lower
• Apparent position → Higher

This is why the coin seems raised.

3. A Stick Partially Immersed in Water Appears Bent

A straight stick placed partly in water appears bent or broken at the water surface.

Reason

The portion of the stick inside water is viewed through refracted light rays.

Since the submerged part appears raised while the part above water remains unchanged, the stick appears bent at the interface between air and water.

This is one of the easiest demonstrations of refraction.

4. The Sun Appears Flattened During Sunrise and Sunset

During sunrise and sunset, the Sun often appears slightly flattened instead of perfectly circular.

Why does this happen?

The Earth's atmosphere consists of many layers of air with different densities.

• Air near the Earth's surface is denser.
• Air higher in the atmosphere is less dense.

As sunlight travels through these layers, it undergoes continuous atmospheric refraction.

The lower part of the Sun is refracted more than the upper part because its light passes through denser layers of the atmosphere.

As a result:

• The lower edge appears raised more than the upper edge.
• The vertical diameter appears shorter.
• The horizontal diameter remains nearly unchanged.

Therefore, the Sun appears flattened near the horizon.

5. Stars Twinkle at Night

he twinkling of stars is another beautiful consequence of atmospheric refraction.

Explanation

The Earth's atmosphere is made up of layers of air with continuously changing temperatures and densities.

As starlight passes through these layers:

• The amount of refraction changes continuously.
• The apparent position of the star shifts slightly from moment to moment.
• The intensity of light reaching our eyes also fluctuates.

This continuous change makes stars appear to twinkle.

Why don't planets twinkle as much?

Planets appear as small discs rather than point sources of light. The light from different parts of the disc averages out the fluctuations caused by atmospheric refraction, making planets appear steadier than stars.

Atmospheric Refraction

Atmospheric refraction is the bending of light as it passes through different layers of the Earth's atmosphere.

It is responsible for several natural phenomena, including:

• Twinkling of stars
• Flattened Sun at sunrise and sunset
• Advanced sunrise
• Delayed sunset
• Apparent shifting of celestial objects

Everyday Applications of Refraction

Refraction is used in many scientific instruments and technologies.

Application	Use of Refraction
Spectacles	Correct vision defects
Camera lenses	Produce clear images
Magnifying glass	Enlarges objects
Microscopes	Observe tiny objects
Telescopes	Observe distant celestial bodies
Binoculars	Magnify distant objects
Fiber optic communication	Transmit light signals efficiently

Summary of the Effects of Refraction

Effect	Cause
Swimming pool appears shallow	Bottom appears raised due to refraction
Coin appears raised	Image forms above the real coin
Stick appears bent	Submerged part appears shifted upward
Sun appears flattened	Unequal atmospheric refraction
Stars twinkle	Continuous atmospheric refraction

Frequently Asked Questions (FAQs)

What is refraction of light?

Refraction is the bending of light when it passes from one transparent medium to another because its speed changes.

Why does water appear shallower?

Light from the bottom of the water bends away from the normal as it enters the air, making the bottom appear raised.

Why does a stick look bent in water?

The submerged part appears higher than its actual position due to refraction, making the stick seem bent.

Why does the Sun appear flattened during sunrise and sunset?

The lower part of the Sun is refracted more than the upper part because the lower rays pass through denser atmospheric layers. This compresses the Sun's vertical diameter.

Why do stars twinkle but planets usually do not?

Stars are point sources of light, so atmospheric refraction causes noticeable fluctuations in their apparent brightness and position. Planets appear as small discs, and these fluctuations average out, making them appear steadier.

Conclusion

Refraction of light is a fundamental optical phenomenon that affects many aspects of our daily lives and our observations of the natural world. It explains why swimming pools appear shallower, coins in water seem raised, sticks look bent, the Sun appears flattened at sunrise and sunset, and stars twinkle in the night sky. Beyond these everyday observations, refraction is the working principle behind essential optical devices such as cameras, microscopes, telescopes, spectacles, and fiber-optic communication systems. Understanding the effects of refraction helps us appreciate both the beauty of nature and the science behind modern optical technology.

Earth's Satellites

A heavenly body that revolves round the earth in a circular orbit is called earth's satellite. For example, the moon is the earth's satellite which revolves round the earth in circular orbit of radius 3.84^5km. The moon takes about 27.3 days to move once round the earth.The earth's satellites are of two types: Natural satellite and Artificial satellite.

• Natural satellites:It is a naturally formed body moving around the earth.The moon is the only natural satellite of the earth.
• Artificial satellite:It is a man made body moving around the earth in an orbit.When a body is taken to a certain height above the earth and given necessary centripetal force,the body keeps on moving around the earth and becomes an artificial satellite.

Now a days, the artificial satellites find widespread application in the present world. The following are the uses of artificial satellite.

1. Artificial satellites are widely used in telecommunication.
2. They are used in studying the atmosphere near the earth surfaces.
3. They are used to forecast weather.
4. They are used to transmit radio and video signals.
5. They are used to know the shape and size of earth.
6. They are used in space flights.
7. They are used to study the radiations conform the sun and the outer space.
8. They are used to find another natural satellites which lies in our universe.
   

METHODS OF CHARGING A BODY

Making a body to acquire property of attracting small objects is called charging(or electrification). A body can by charged by the following ways:

By rubbing: When a body is rubbed with another body, both of them charged. One of the bodies acquires positive charge and the other acquires negative charge. For example, when a glass rod is rubbed with a silk, the glass rod acquires positive charges, and at the same time, the silk, the silk acquires negative charges.

By conduction: When an uncharged body is made in contact with a charged body flow into the non charged body and the body is charged. For example ,if an uncharged sphere A is made in contact with a charged sphere B, the sphere A will be charged sphere B, the sphere A will be charged with the same charge as in the sphere B.

    Figure 2: Charging by conduction

By induction: When a charged particles or body is brought near non charged body without touching, charges are developed in the uncharged body. This method of charging a body is called charging by induction. 

                                                          Figure3 : Charging by Induction

Prevot's Theory of Heat Exchange

According to prevot's theory of heat exchange a body not only radiates heat radiations continuously at all temperature but also absorbs heat continuously from the surroundings. The heat radiates by the body per unit area per unit time does not depend upon the temperature of the surroundings but only on the temperature of the body.However,the heat radiations received by the body from its surroundings.If the body radiates more heat to the surroundings then it receives from the surrounding, the body has a net loss of heat. As a result,the body will have cooling effect. Similarly, if the body radiates less heat to the surroundings than it receives from the surroundings,the body has a net gain in heat energy. As a result,the body has heating effect.If the heat radiated by the body to the surroundings is equal to the heat received by the body from the body to the surroundings is equal to the heat received by the body from the surroundings ,the body will be in thermal equilibrium with its surroundings.
therefore,if there are a large number of bodies at the save temperature, the bodies are in dynamic thermal equilibrium. A body stops radiating energy only at absolute zero of temperature.
This is called theory of heat exchange. This theory can be used to explain why we feel cold in winter and hot in summer if we come outside home.
In the winter, the surroundings temperature is less that our body. As a result, the heat energy we radiate into the surroundings is more than the heat energy we receive from the surroundings .As a result,there is net of energy for us we feel cold. However, in summer,the surroundings temperature is more than that of our body. Therefore,the heat energy we radiate into the surroundings is less than that we receive from the surroundings. As a result, there is net gain in heat energy for us and feel hot.

Evaporation and Boiling

The molecules in a liquid are at random motion. In the random motion, the different molecules have different velocities and hence different kinetic energies. In addition, the molecules of the liquid collide with each other. They may exchange their kinetic energies in the collisions. In the collisions, some of the liquid molecules may get energy enough to be converted into vapour even at low temperature.The conversion of some of the liquid molecules into even blow the boiling point is called evaporation. When evaporation takes place, the molecules which fly off the body of the liquid take the required energy for the evaporation from the remaining molecules of the liquid. Since the kinetic energy of the remaining molecules has been decreased,there is net fall in temperature of the liquid. Thus,cooling is resulted from the evaporation of a liquid.
The evaporation of liquid can be defined as slow and silent conversion of the liquid from its liquid state to gaseous state at all temperature.
It has been found that the rate of evaporation of a liquids depends upon the following:

• Nature of the liquid .
• Temperature of liquid.
• Area of the surface of the liquid.
• Pressure and temperature of the atmosphere.
• Effect of liquid.
• Humidity of the atmosphere.

However, the boiling (also called equilibrium) is a rapid and noisy conversion of a liquid into vapour at a particular temperature called boiling point.The temperature of the liquid does not change during boiling. No cooling effect is observed.

Gravity and Gravitional

Newton, in 1687, discovered the existence of a force between two masses.For example,two people sitting in a room, a table and a rock lying in a room, the sun and the earth, the earth ans the moon and so on exert force on each other.The force between two masses is called gravitational force. The gravitational force is always attractive. That is each body (or mass) attracts towards if the other body (or mass).This force exists universally among all bodies in the universe.
In gravitational force, we talk about the force of attraction between two bodies, out of these bodies,if one body is the earth the gravitational force is called force of gravity.Thus, the force of gravity is the special case of the force of gravitation.When a stone is released from the top of tower, it falls towards the ground.Similarly, if a body thrown upward, its speed slows down. The speed becomes zero when the body reaches a certain height, the body returns to the ground. Tf a stone is released at the top of a deep well, it goes into the earth. This implies that the earth attracts every body lying near its surface and on its surface towards its centre. The force of attraction of the earth on the bodies which lie on its surface(or near its surface) is called gravity or force of gravity.
Not only the earth but also all the planets or other heavenly bodies have gravity.The gravity of a body depends upon its mass. The gravity of the moon is about 1by6 times the gravity of the earth.

Centripetal Force: Definition, Formula, Examples, Applications, and Real-Life Explanation

What is Centripetal Force?

Centripetal force is the external force that keeps an object moving along a circular path. This force always acts towards the center of the circle, continuously changing the direction of the object's velocity while keeping its speed constant (in uniform circular motion).

Without centripetal force, the object would no longer follow the circular path. Instead, according to Newton's First Law of Motion, it would move in a straight line tangent to the circle.

Definition:

Centripetal force is the inward-directed force that causes an object to move in a circular path by continuously changing the direction of its velocity.

Understanding Centripetal Force

Consider a body moving in a circle with a constant speed.

Although the magnitude of its velocity remains constant, the direction of the velocity changes continuously at every point on the circular path.

Since velocity is a vector quantity, any change in direction means the velocity is changing.

A change in velocity implies that the body has acceleration.

According to Newton's Second Law of Motion, whenever an object accelerates, a force must act on it.

Therefore, an object moving uniformly in a circular path experiences a force at every instant. This force:

• Acts perpendicular to the direction of motion.
• Is always directed towards the center of the circle.
• Changes only the direction of velocity, not its magnitude.

This inward force is called the centripetal force, and the acceleration produced due to this force is called centripetal acceleration.

At every point on a circular path:

• The velocity is always tangent to the circle.
• The centripetal force is directed towards the center.
• Since force and velocity are perpendicular, the force changes only the direction of motion.

Therefore,

• Speed remains constant.
• Direction changes continuously.
• The object keeps moving in a circle.

Centripetal Acceleration

The acceleration experienced by an object moving in a circular path is called centripetal acceleration.

It is always directed towards the center of the circle.

The formula is:

$$a_c=\frac{v^2}{r}$$

where:

• $a_c$ = centripetal acceleration (m/s²)
• $v$ = linear velocity (m/s)
• $r$ = radius of the circular path (m)

Using angular velocity ($\omega$),

$$a_c=r\omega^2$$

Formula of Centripetal Force

From Newton's Second Law,

$$F=ma$$

Substituting centripetal acceleration,

$$F_c=m\frac{v^2}{r}$$

Therefore,

$$\boxed{{\displaystyle F_c=\frac{m{v}^2}{\mathrm{r<span\; class="vlist"><span\; class="boxpad"><span\; class="mord"><span\; class="mord"><span\; class="mord"><span\; class="mfrac"><span\; class="vlist-t\; vlist-t2"><span\; class="vlist-r"><span\; class="vlist-s"></span></span><span\; class="vlist-r"><span\; class="vlist"></span></span></span></span><span\; class="mclose\; nulldelimiter"></span></span></span></span></span><span\; class="pstrut"></span><span\; class="stretchy\; fbox"></span></span><span\; class="vlist-s"></span>}}}}$$

where:

• $F_c$ = centripetal force (N)
• $m$ = mass (kg)
• $v$ = velocity (m/s)
• $r$ = radius (m)

Using angular velocity,

$$\boxed{F_c=mr\omega^2}$$

Characteristics of Centripetal Force

The important properties of centripetal force are:

• Always acts towards the center of the circle.
• Acts perpendicular to the instantaneous velocity.
• Changes only the direction of motion.
• Does not increase or decrease the speed during uniform circular motion.
• Is not a new type of force.
• Can be provided by tension, gravity, friction, or normal reaction depending on the situation.

Sources of Centripetal Force

Different situations provide centripetal force through different physical forces.

Situation	Force Acting as Centripetal Force
Stone tied to a string	Tension
Satellite orbiting Earth	Gravitational force
Car turning on a road	Friction
Roller coaster	Normal reaction
Planet revolving around the Sun	Gravitational attraction
Electron around nucleus (classical model)	Electrostatic force

1. Stone Tied to a String

When you whirl a stone attached to a string, the tension in the string provides the centripetal force that keeps the stone moving in a circle.

If the string breaks, the stone flies off in a straight-line direction tangent to the circle.

2. Car Taking a Turn

While turning, the friction between the tires and the road supplies the centripetal force.

Without enough friction, the car skids outward.

3. Satellite Orbiting Earth

Earth's gravitational attraction acts as the centripetal force that keeps satellites moving in orbit.

Without gravity, satellites would travel away in straight lines.

4. Roller Coaster Loop

In vertical loops, the track exerts a normal force on the coaster, helping provide the required centripetal force.

5. Washing Machine

During the spin cycle, clothes move in circular paths while water escapes through small holes because it tends to move tangentially.

Factors Affecting Centripetal Force

From

$$F=\frac{mv^2}{r}$$

we conclude:

1. Depends on Mass

Greater mass means greater centripetal force.

$$F\propto m$$

2. Depends on Velocity

Force increases with the square of velocity.

$$F\propto v^2$$

If speed doubles,

Force becomes four times.

3. Depends on Radius

Larger radius requires less centripetal force.

$$F\propto\frac1r$$

Difference Between Centripetal Force and Centrifugal Force

Centripetal Force	Centrifugal Force
Acts towards the center	Appears to act away from the center
Real force	Apparent (pseudo) force
Observed in an inertial frame	Observed in a rotating frame
Keeps object in circular motion	Tendency felt by the observer moving with the object

Applications of Centripetal Force

Centripetal force is used in many fields:

• Satellite communication
• Artificial satellites
• Highway curve design
• Roller coaster engineering
• Ferris wheels
• Centrifuges
• Washing machines
• Medical laboratory equipment
• Space science
• Planetary motion

Numerical Example

Problem

A 2 kg object moves in a circular path of radius 4 m with a speed of 6 m/s.

Find the centripetal force.

Solution

Given,

• Mass = 2 kg
• Radius = 4 m
• Velocity = 6 m/s

Using

$$F=\frac{mv^2}{r}$$ $$F=\frac{2\times6^2}{4}$$ $$F=\frac{72}{4}$$ $$F=18N$$

Answer: The centripetal force is 18 N.

Key Points to Remember

• Centripetal force acts towards the center of a circular path.
• Velocity is always tangent to the circle.
• Force is always perpendicular to velocity.
• It changes only the direction, not the speed, in uniform circular motion.
• It is provided by existing forces such as gravity, tension, friction, or normal reaction.

Frequently Asked Questions (FAQs)

What is centripetal force in simple words?

Centripetal force is the inward force that keeps an object moving in a circular path.

What is the SI unit of centripetal force?

The SI unit is the newton (N).

Is centripetal force a real force?

Yes. It is a real force supplied by gravity, tension, friction, or another physical force depending on the situation.

Why is centripetal force directed towards the center?

Because an inward force is needed to continuously change the direction of the object's velocity and keep it moving in a circle.

What happens if centripetal force disappears?

The object immediately moves in a straight line tangent to the circular path due to inertia.

Conclusion

Centripetal force is the essential force responsible for circular motion. Although an object moving in a circle may have constant speed, its continuously changing direction means it is constantly accelerating. This acceleration requires an inward force directed toward the center of the circle. Whether it is a satellite orbiting Earth, a car taking a turn, or a stone tied to a string, centripetal force plays a crucial role in keeping objects on their circular paths. Understanding this concept provides the foundation for studying mechanics, orbital motion, transportation systems, and many real-world engineering applications.