Category: Physics Notes PPT

Resistance to essentials is as important as making the materials to be used in the right places in the electrical and electronic components.

Items used as conductors, for example in a standard electrical outlet need to be able to have a low resistance level. This means that in a given cross-sectional area, the resistance of the fence will be lesser. Choosing the right material depends on knowing its properties, one of which is its resistivity.

For example, copper is a good conductor as it offers a low level of resistance, its cost is not very high, and it also provides other physical features that are useful in many electrical and electronic functions. 

Copper is often the most preferred material. Material like copper and aluminum imparts low resistance levels which makes them suitable for the use of power cords and cables. Silver and gold have very low resistivity, but as they are very expensive, they are not widely used. However, silver is sometimes used to refine wires where its low resistance is important, and gold light is used in the joints of many electronic connectors to ensure advanced contacts. Gold is also good for electrical connectors as it does not contaminate or emit oxygen like other metals.

What is Resistivity?

Resistivity is the measure of how much an electrical conductor opposes the flow of current through it.

Resistance has an application in protecting the circuit from high current flow.

When a potential difference (acceleration) is applied across the conductor (to car), the electrons start moving from the negative to the positive electrode).

The current flow increases, the resistance acts as a speed breaker to the accelerated car (high current flow).

The magnitude of the resistance is called resistivity.

Hence it is the magnitude of the resistance of a given size of a specific material or a conductor to electrical conduction.

Resistivity Formula

The resistivity of a material is defined in terms of the measurement of the electric field (E) across it that generates current density (J). 

The formula for resistivity is given by,          

       

Where ρ is the proportionality constant known as the resistivity of the material which  is the characteristic property of each material.

A = Area of cross-section

L = Length of the material of a conductor

Derive Resistivity

The resistivity of a material depends upon the following factors:

1. Length

Consider two conductors each of length ‘L’ and the area of cross-section ‘A’

Let V be the same potential difference applied across the ends of two slabs. 

The current ‘I’  flowing across each slab will be I/2. 

Then resistance via each slab is,

R = V/I (Ohm’s law)

Rs = V/ I/2 = 2 R

So, R increases with the increase in length 

R α L …(1)

2. Area of Cross-section 

Each slab of length ‘L’ has a cross-sectional area of A/2.

Similarly, on halving the area of the conductor, the resistance through each of the half slabs will be

R’  =   V/ I/2 = 2 R

R increases with the decrease in the area of each half slab.

R α 1/A…(2)

Combining (1) and (2) we get

R   α L/A    

Removing the proportionality sign we get 

   

Here, ρ is called the electrical resistivity or specific resistance of the material.

Resistivity Definition

The formula for the resistivity is given by,

R = ρ L/A…(a)

If L =1, A =1, then  R = ρ 

Thus, the electrical resistivity of a material of a conductor is defined as the resistance offered by the unit length and unit cross-sectional area of a wire of the given material.

Unit of Resistivity

The unit of resistivity is derived from eq(a)

If  R = ρ L/A

Then ρ = R.A/L ….(b)

Given unit of R = Ohm ([(Omega)]),  A = m² and L = m 

Putting in eq(b)  we get

Define Resistivity of a Material

The resistivity is an attribute of each material that is useful in comparing various materials on the basis of their ability to conduct electric currents. 

Let’s Discuss the Resistivity of Some Materials is Discussed Below:

Relation Between Conductivity and Resistivity 

The relation between conductivity and resistivity can be understood through an example.

You water a lot to the plants during the summer seasons.

If you just sprinkle a few drops of water and won’t supply enough water, after some time, they will get dried and hence die.

Therefore, the more is the resistance to a sufficient supply of water to the plants, the lesser will be their growth (conductivity).

Therefore, high resistivity signifies poor conductors.

Resistivity is symbolized by the Greek letter  ‘ρ’ pronounced as ‘rho’ and the conductivity as σ.

So,  σ =  1/ ρ  or ρ = 1/ σ

Since conductivity is the inverse of resistivity.

Therefore, its unit is mho .m-1[Omega] m^-1

Another Unit:  Siemens per meter S m¹⁷

On What Does Resistivity Depend?

The amount of resistivity also depends on the temperature of the asset; opposing material tables usually set values ​​at 20 ° C. Resistance to steel conductors usually increases with increasing temperature; but resistance to semiconductors, such as carbon and silicon, usually decreases with increasing temperature.

Conductivity is a reciprocal of resistivity, and, again, reflects things on the basis of how well electricity flows through them. The second-kilometer unit of conductivity is mho meter or ampere per volt-meter. There is high conductivity and low resistance in good electrical conductors. Fine insulators, or dielectrics, have high resistivity and low conductivity. Semiconductors have values ​​between both.

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Rocket science is the primary branch of aerospace engineering, which is the science of building, or designing rockets. 

All the rockets follow Newton’s three laws of motion.

According to Newton’s first law, a rocket will stay on the launch pad until a force blast it off. Once in space, a rocket will proceed to move unless retrorockets are fired to slow down the rocket.

Newton’s Second Law : Force on a body equals the product of its mass multiplied by acceleration.

                       F = m * a

So, the main forces acting on a rocket in flight are the weight of the rocket, thrust of the rocket engines, and drag.

Now, as the rocket moves through the air, during its flight, it undergoes a few operations that its weight gets greatly reduced, therefore; it achieves a greater acceleration. 

Newton’s Third Law of Motion: This law states that it is necessary to keep the rocket moving so that it ejects a high amount of gas at high speeds.

A rocket can lift off from a launchpad only when it ousts gas at high speeds from its engine. The rocket thrusts against the gas, and the gas, in turn, propels the rocket.

What causes Thrust in the Rocket?

Thrust is a force with which the rocket moves upwards. It is given by,

                                   F = – u dm/dt

In space, rocket engines are ordinarily called reaction engines because the law of reaction crusades the spacecraft to move in a direction opposite to that of the engine’s thrust plume.

The negative sign in the formula indicates that thrust on the rocket is in a direction opposite to the direction of escaping gases.

How does a Rocket Work?

The term rocket science is often used to describe a concept that is quite difficult to comprehend.

Let’s understand the technology behind its working in a simple yet scientific manner.

To eject the high-speed mass from the rocket, a liquid fuel oxidizer mixture is burnt in the rocket combustion chamber, the combustion chamber also helps fuel and oxidizer to mix them efficiently.

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A high-speed jet is passed through a rocket nozzle, the function of the nozzle is to increase the exhaust velocity even further thus increasing the rocket’s thrust.

These types of nozzles are called converging-diverging nozzles.

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So, the subsonic flow gets converted to supersonic flow with the help of such a nozzle. 

The liquid fuel before entering the combustion chamber travels around the nozzle body.

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This helps to reduce the nozzle’s cover temperature and also results in some energy savings.

To pump fuel and oxidizer at an adequate flow rate, two pumps are used. They are:

1. Fuel Pump

2. Oxidizer Pump

They both are connected with the same shaft.

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The pump-turbine is referred to as a turbopump. A gas generator produces hot gas which will turn the turbine. A bypass jet of fuel and an oxidizer are fed into the gas generator for combustion; exhaust from the turbine is mixed with the main rocket exhaust. This unit of the rocket is called the rocket engine.

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Here, the rocket engine is peculiarly the liquid propellant rocket engine.

The fuel and oxidizer required for rocket engine are started to two large tanks as shown below:

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During the liftoff, the thrust generated by the main engine may not be adequate.

Generally, a few solid propellant strap boosters are used to assist the liftoff.

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Solid propellant strap boosters

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Inner view of the solid propellant rocket 

The rocket starts with zero speed at the ground.

However, it must accelerate at the final speed of 28000 Kmph to achieve orbit successfully.

The solid propellant strap boosters are burned off very quickly. 

So, to reduce the weight of the rocket, they are abandoned after the burn-off.

This process is known as rocket staging.

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Rocket staging

When the main engine is burned off, it is also abandoned.

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The main engine abandoned

The next engine takes over the charge. In this way, the rocket’s weight is greatly reduced.

So, by the relation: F = m * a

Mass is reduced, therefore, it achieves greater acceleration.

Finally, after a few stages of operation, the payload is put into the desired orbit.

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The rocket staging up to five have been successfully tested.

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Payload set in its orbit

So how is the rocket able to maneuver its destination?

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So, there is a modern car technique named cabled thrust also called the Gimbaled Thrust.

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Diagram: Gimbaled thrust

Here, the rocket nozzle is tilted with high precision devices.

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Diagram: Gimbaled angle

Any deviation in the normal angle will produce a torque which in turn will make the rocket’s body rotate.

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Therefore, after achieving enough turn, the gimbal angle is set to 0.

What Rocket Scientists do?

Rocket scientists are aerospace engineers who are experts in the designing and manufacturing of spacecraft.

They diligently work with the principles of science and engineering to create vehicles that aviate within or above the Earth’s surface.

The underlying concepts of Physics have a mathematical base. All measurable quantities are physical quantities. The motion of objects can be described by two mathematical quantities: a scalar and a vector.

• A scalar quantity is described completely by magnitude or numbers alone. Examples of scalar quantities are length, mass, distance, energy, volume, etc.

• A vector quantity needs a magnitude as well as a direction to describe it completely. Examples of vector quantities are displacement, velocity, weight, dipole moment, etc.

 

 

Vector Quantities Can Be Multiplied in Two Ways

• Scalar or dot product

• Vector or cross product

 

In this article, we will discuss scalar and vector products and solve a few examples where we will find the scalar and vector product of two vectors.

 

Define Scalar Product of Two Vectors

The scalar product of two vectors gives you a number or a scalar. Scalar products are useful in defining energy and work relations. One example of a scalar product is the work done by a Force (which is a vector) in displacing (a vector) an object is given by the scalar product of Force and Displacement vectors. The scalar product is denoted by a dot(.) and the formula of scalar product is given below:

[widehat{X}] . [widehat{Y}] = XY Cos ፀ, where ፀ is the angle between the vectors.

The scalar product is also called the dot product because of the dot notation used in it. 

 

Properties of Scalar Product of Two Vectors

• The direction of the angle ፀ has no significance in the dot product of two vectors. The angle ፀ can be measured from either of the vectors to the other since Cos ፀ = Cos (-ፀ) = Cos (2ℼ – ፀ)

• If ፀ is more than 90 degrees and less than or equal to 180 degrees then the dot product is a negative value i.e. 900 < ፀ <= 1800

• If ፀ is more than 0 degrees and less than or equal to 90 degrees then the dot product is a positive value. i.e. 00 < ፀ <= 900

• The dot product of two vectors that are parallel to each other is given by  [widehat{X}] . [widehat{Y}]= XY Cos 0 = XY.

• The scalar product of two anti-parallel vectors is given by [widehat{X}] . [widehat{Y}] = XY Cos 180 = -XY.

• The scalar product of a vector multiplied by itself is the square of its magnitude. [widehat{X}] . [widehat{X}] = XX Cos 0 = X2

• The scalar product of two orthogonal vectors is 0 i.e. [widehat{X}] . [widehat{Y}]= XY Cos 90 = 0

 

 

• The dot product is commutative i.e. the order of the two vectors in the product does not matter. So, [widehat{X}] . [widehat{Y}] = [widehat{Y}]. [widehat{X}]

• The dot product is distributive which means [widehat{X}]  ([widehat{Y}]+ [widehat{Z}]) = [widehat{X}] . [widehat{Y}] + [widehat{X}] . [widehat{Z}]

 

Define Vector Product of Two Vectors

When we take the vector product of two vectors, we get a vector. The Vector product is also termed as the cross product as the sign for the vector product is a cross(X)

[widehat{X}] X [widehat{Y}]

The direction of the vector product of two vectors is perpendicular to both the vectors. This means that the cross product of two vectors [widehat{X}] and [widehat{Y}]  lies in a plane that is perpendicular to the plane which contains Xand Y. The formula to give the magnitude of the vector product is:

| [widehat{X}] x [widehat{Y}] | = XY *Sin θ. Here the angle θ between the vectors is measured from the first vector in the formula (here vector X) to the second vector (vector Y) in the formula.

 

 

Properties of Cross Product of two Vectors

• The angle between the vectors,  θ, lies between 0 and 180 degrees.

• The vector product of vectors which are parallel to each other (where  θ = 0) or antiparallel to each other (where  θ = 180) is 0 since Sin 0 = Sin 180 = 0

• The resultant vector of the cross product of the two vectors could lie either on the upward or downward plane. 

• The vectors [widehat{X}] X [widehat{Y}]and [widehat{Y}] X [widehat{X}] are antiparallel to each other hence vector product is not commutative.

• If the order of multiplication is changed, the resultant vector changes in sign i.e [widehat{X}] X [widehat{Y}]= – [widehat{Y}] X [widehat{X}].

• The common mnemonic used to determine the direction of the cross product of vectors is the corkscrew right-hand rule. The direction of the vector is given by turning the corkscrew handle from the first to the second vector.

 

 

 

 

• The cross product of two vectors is distributive i.e. [widehat{X}]  X  ([widehat{Y}]+ [widehat{Z}] ) =  [widehat{X}]  X  [widehat{Y}] +  [widehat{X}] X  [widehat{Z}].

• The multiplication by a scalar satisfies (k *  [widehat{X}]) X  [widehat{Y}] = k * ( [widehat{X}] X  [widehat{Y}]) =  [widehat{X}] X (k * [widehat{Y}])

 

Solved Examples of Scalar and Vector Product of Two Vectors

Let us find the scalar and vector product of two vectors through a couple of examples:

• For which real number r the vectors X and Y in the equation given below are perpendicular to each other: X = (-2, -r) and Y = (-8, r)

Solution – If two vectors are perpendicular to each other then their scalar product is 0. So we get:

(-2)(-8) + (-r)(r) = 0 i.e. r2 = 16, hence r = 4 or -4.

Solution – we first find the magnitude of the two vectors:

A = [sqrt{2^2 + 3^2}] = [sqrt{4 + 9}] = [sqrt{13}]

YB= [sqrt{3^2 + (-4^2)}] =  [sqrt{9 + 16}] = [sqrt{25}] = 5 

The cross product A X B = AB Sin θ = 5 * [sqrt{13}] * Sin 60 = 5*[sqrt{13}]*[sqrt frac {3}{2}]

When an earthquake happens, energy shockwaves known as seismic waves are released from the earthquake’s focal point. They shake the Earth and transform soft deposits like clay into jelly for a short time (liquefaction).

Seismographs are used by seismologists to record how long seismic waves take to travel across different layers of the Earth. Waves can be refracted and reflected as they travel through varying densities and stiffnesses. Seismologists can deduce the sort of material the waves are traveling through based on the differing behavior of waves in different materials.

The findings could provide a glimpse of the Earth’s core structure, as well as aid in the location and understanding of fault planes and the pressures and strains that act on them.

Seismic Waves Types

P-waves, S-waves, and surface waves are the three primary forms of seismic waves. Body waves refer to the combination of P-waves and S-waves.

Waves produced by Earthquakes

When an earthquake happens, it sends forth energy waves known as seismic waves. It’s similar to the ripples that occur when a stone is thrown into the water. Seismic waves are similar to ripples that can flow through the earth’s interior as well as its surface.

Wave Types of Earthquakes

Three primary forms of elastic waves cause earthquake shaking and damage. Two of the three reproduce within a rock mass. The main or P wave is the fastest of these bodily waves. Its motion is similar to that of a sound wave in that it alternately pushes (compresses) and pulls (dilates) the rock as it spreads out. These P waves can pass through solid rock, such as granite mountains, as well as a liquid material, such as volcanic lava or ocean water.

The secondary or S wave is the slower wave that travels through the body of rock. An S wave shears the rock sideways at right angles to the direction of motion as it propagates. S waves cannot propagate in the liquid sections of the planet, such as oceans and lakes, since liquids do not rebound back when sheared sideways or twisted.

The density and elastic qualities of the rocks and soil through which seismic waves flow determine their actual speed. The P waves are the first to be felt in most earthquakes. The effect is similar to that of a sonic boom, which rattles and knocks glass. The S waves arrive a few seconds later, shaking the ground surface vertically and horizontally with their up-and-down and side-to-side movements. This is the type of wave motion that causes so much structural damage.

What are Seismic Waves?

The energy that travels under the surface layer of the earth and causes an earthquake is called seismic waves. A crack starts to open on a pre-existing point or line of weakness deep underground when an earthquake takes place. Stress builds over the surface of the earth as the crack grows on to become larger and larger. This energy causing the earthquake is known as seismic waves. Seismic waves transfer energy without moving material.

The crack grows with a speed of 2 to 3 km/sec. The level or size of the earthquake also depends on the area in which it takes place. The magnitude, that is, the size of the waves depends on the level of break or slip that has taken place under the surface. The process of cracks and slips taking place is known as Rupture.

 

So, the elastic waves that are formed are because of the rupturing that takes place deep underground and continues to grow at a very fast pace. The speed of this growth depends on their nature and the properties of the earth. Here is a fact for you: as we go deeper and deeper into the surface of the earth, the seismic waves found there are of higher density, pressure, and velocity.

Types of Earthquake Waves and Their Effects

Let us first categorize the S-waves based on the medium that they travel in, namely: 

1. Body waves 

2. Surface waves

The waves that take place under the surface or through the earth are called body waves. On the other hand, the waves that occur on the surface of the earth are called surface waves.

Body Waves or ‘Through The Earth’ Waves are Further divided into Two: 

Primary waves are faster in pace, and Secondary waves are slower in pace. Surface wave earthquakes are very significant, too, as when they grow, they bring destruction to the surface of the earth where all the buildings and people live. It is mostly the energy formed by surface waves that can knock down big buildings.

P Waves (Primary Waves) 

P waves are the fastest seismic waves of all and are thus called Primary ones. P waves grow or travel at a speed of 5 kilometers per sec through the earth’s crust. P waves are the first ones to reach any particular location or point when an earthquake occurs. The waves have a tendency to flow through all three i.e., solids, liquids, and gases. The materials that they flow through experience a force or energy that slightly pulls them apart and pushes them together. The same energy is experienced by a building when an earthquake occurs.

 

S Waves (Secondary Waves) 

S waves are the second-fastest seismic waves and are thus called Secondary. The speed at which the S waves travel is almost half the speed of Primary Waves. S waves are the ones to reach any location after the primary waves when an earthquake occurs. Unlike Primary Waves, Secondary Waves make the material go through an up and down shaking movement from the sides when it flows through them. Unlike P waves, S waves can travel through rocks only. 

Types of Seismic Waves

How do Seismographs Record Earthquakes?

Seismographs are instruments used to record earthquakes. The seismograph is mounted on the surface of the earth, and when there are tremors, the entire unit shakes. However, it is also an attached mass on the spring, which does not shake. This mass has inertia and hence, remains in the same place. When the seismograph starts shaking under this mass, the device records the relative motion between itself and the rest of the instrument (which is shaking) and records the ground motion.

Simple harmonic motion is a special kind of periodic motion, in which a particle moves to-and-fro repeatedly about a mean or an equilibrium position under a restoring force that is directed towards the mean position.

Consider a particle placed on the circumference of a circle.

Initially, the particle is at point X as you can see in the figure below:

As it moves from X to P, there is an angular displacement (an arc) which is equal to [theta] and at time = t, the particle reaches from point OX to P.

The motion is along the circle with a constant angular velocity ω.

So, the angle subtended by a particle,  [theta] = ωt

The mean position of the particle is at point O.

Now, we draw a perpendicular from P to a certain point on the diameter XOX’.

So the displacement from O to a certain point is, ‘x’.

The instantaneous acceleration will be directly proportional to this displacement.

                              a α x

Now, if we multiply m on both sides, we get

                              ma α mx

                            or,     F α x

So, we concluded that one-dimensional motion of a particle in a uniform circular motion about its mean position is in simple harmonic motion.

SHM as a Projection of Uniform Circular Motion on any Diameter

Consider a particle P moving with uniform speed along the circumference of a circle with radius a, having center OF. This circle is considered as a circle of reference with particle P as the particle of reference.

Here, if you look at Fig.1, XOX’ and YOU’ are perpendicular diameters of the circle of reference.

As the reference particle moves from X to Y, its projection on diameter YOY’ moves from O to Y.

As this reference particle moves from Y to X’, its projection moves along the diameter from Y to O.

Similarly, when the reference particle moves on the circle from X’ to X via Y’, its projection moves along the diameter from O to Y’ and then from Y’ to O.

Thus, during the time the particle P goes around the circle and completes one revolution, its projection, ‘M’ oscillates about the point O along the diameter YOY’ and completes one vibration. Since the projection of the reference particle is in SHM, and the projection of M on diameter YOY’ is also a simple harmonic motion.

Therefore, simple harmonic motion is defined as the projection of uniform circular motion on any diameter of a circle of reference.

SHM as projection of uniform circular motion

Consider a reference particle moving on a circle of reference with radius, ‘a’ with uniform angular velocity, ‘ω’

From Fig.1

Let the particle at time t = 0, start from point X, and sweep an angular displacement [theta] in time ‘t’ with angular velocity ω, equal to ωt.

Now, let the projection of the particle P on diameter YOU’ be at M.

Then the displacement in SHM at time t is given by,

OM = y

In ΔOPM,

Sin [theta] = OM/OP = y/a 

or,

Now, 

In ΔONP,

Cos[theta] = ON/OP = x./a

or, 

From Fig. 3(a)

Now, if A is the starting position of the reference particle.

Here, ∠AOX = ф₀ and  ∠AOP = ωt and [theta]  = ωt – ф₀

From eq(1) and (2)

             y  = a Sin(ωt – ф₀)

             x =  a Cos(ωt – ф₀)

Here, – ф₀ is called the initial phase of S.H.M.

Here, the phase is a physical quantity that is used to express the position and direction of motion of the particle at an instant concerning time represented by a sine or cosine function.

From Fig 3(b)

If we consider B as the starting position of the particle of reference.

If  ∠BOX = ф₀ and  ∠BOP = ωt

Then, ∠XOP =  ωt + ф₀

Now, from eq(1) and (2), we get

                        y  = a Sin(ωt + ф₀)

                        x =  a Cos(ωt + ф₀)

Here, + ф₀ is called the initial phase of S.H.M.

SHM Circular Motion

A reference particle moving along the circumference of a circle of reference makes a displacement.

Where the maximum displacement of a particle from its position is called the amplitude denoted by, ‘A’. It is equal to the radius of a circle.

If S is the span of S.H.M. Then,

                      

         

SHM in Circular Motion

The velocity of a particle at an instant is the rate of change of displacement.

From (1), 

y = a Sinωt

Differentiating both sides:

d(y)/dt = a d(Sinωt)/dt 

V = a ω Cosωt =  a ω [sqrt{(1-Sin^{2}ωt)}] 

                                    = ω[sqrt{(a^{2} – y^{2})}]

At mean position, y = 0, then 

                  V = a ω

At extreme position, y = a

                   V = 0

Thus, the maximum velocity in SHM for a body in uniform circular motion is called the velocity amplitude.

Modulus of Elasticity

Let us understand the modulus of elasticity using examples in this post. The modulus of elasticity is a measurement of the object’s stress–strain relationship. The modulus of elasticity is the most important factor in calculating the deformation response of concrete when stress is applied.

Elastic constants are the constants that govern the deformation caused by a specific stress system operating on a material.

Uniform Circular Motion Projection and Simple Harmonic Motion of a Spring

Connect the Ball-and-Spring set to a ring stand. Next to the spring, place the vertical-plane spinning motor. Keep the illuminated slide projector at a position approximately a meter away and then the images of the ball undergoing oscillations must be projected on the spring and the revolving ball on the wall. Begin the mass’s oscillation so that it is in phase with the driven ball.

The movement of an ite
m along a circular path at a constant pace is described as uniform circular motion. This motion’s one-dimensional projection may be represented as simple harmonic motion.

Examples

A point P traveling on a circular route with constant angular velocity is in uniform circular motion. Its x-axis projection exhibits simple harmonic motion. This can be compared to the projection of an oscillating mass’s linear vertical motion on a spring.

If we attach a stone to the end of a string and move it in a horizontal plane around a fixed point at a constant angular speed, the stone will travel in a uniform circular motion in the plane. If we look at the stone from the side, it appears to move back and forth along the horizontal line, with the other end of the string serving as the halfway point.

Similarly, the stone’s shadow or projection of motion would appear to move in a to and fro motion perpendicular to the circle’s plane. Galileo witnessed a similar instance when he found that Jupiter’s four main moons moved back and forth relative to the planet in a simple harmonic motion.

If a particle moves in a uniform circular motion, its projection moves in a simple harmonic motion, where the axis of oscillation is the diameter of the circle, or in other words, we can say that SHM is nothing but the projection of uniform circular motion along the circle’s diameter.

Download the App to discover more about SHM and its similarities to circular motion.

More About SHM and its Similarities to Circular Motion

In SHM the maximum displacement on one side of this position equals the maximum displacement on the other side. Each full vibration is characterized by the same time interval. The force that is responsible for driving the motion exhibits a direction that is towards the equilibrium position and is proportionate to the distance from it. That is, F = kx, where F denotes force, x denotes displacement, and k denotes a constant. A force applied in the opposite direction of displacement to return the system to its rest position. The size of the force is solely determined by displacement, like in Hooke’s law.

Uniform circular motion is defined as the constant-speed movement of an item in a circle. When an item travels in a circle, its direction is continually changing. The item is always traveling tangent to the circle. Due to the fact that the velocity vector’s direction is equal in value as the direction of the motion of the object, the velocity vector is also tangent to the circle.

An item traveling in a circle is gaining speed. Objects that accelerate are those that change their velocity – either the speed (i.e., magnitude of the velocity vector) or the direction. It is seen that any object that undergoes uniform circular motion, is always moving at a constant pace. Despite this, it is speeding as a result of its shift of course. The acceleration is pointing inwards. 

The net force is the ultimate motion characteristic of an item moving in a uniform circular motion. The net force acting on such an item is directed towards the circle’s center. The net force is referred to as an inward force or centripetal force. Without such an internal force, an object would travel in a straight line, never straying from its intended path. However, because the inward net force is oriented perpendicular to the velocity vector, the item is continually changing direction and accelerating inward.

The solar system consists of the Sun, the planets that circle around it, their satellites, dwarf planets, and too many other objects such as asteroids and comets. All of these items move, and we can see them. We can see the Sun rise in the east in the morning and set in the west in the evening. At different seasons of the year, we may see different stars in the sky.

In 1543, Nicolaus Copernicus suggested a theory according to which the other planets and the Earth revolved around the Sun on a regular basis. 

What is Moon, Earth and Sun?

• The Earth is the planet on which we live. It is round, like other planets, and resembles a ball. 

• The Moon is the Earth’s natural satellite. This implies that it revolves around our planet in a large circle known as an ‘orbit.’

 

• Both the Earth and the Moon orbit around the Sun. Our Solar System revolves around the Sun, which is a star at the centre of it. The Sun is responsible for the light and heat you feel during the day. This energy keeps everything life on our planet alive.

Moon and Earth System

The Moon orbits the Earth on its axis in the same way as the Earth orbits the Sun. The Moon rotates on its axis in about 27 Earth days and revolves around the Earth in roughly twenty-nine and a half Earth days. 

As the Moon’s period of rotation (total time taken by the moon to complete one rotation) about its own axis and period of revolution (total time taken by the moon to complete one revolution) around the Earth are almost identical, the same side of the Moon always faces the Earth. 

When viewing the Moon from Earth, changes in the Moon’s brightness can be noticed as it rotates around the Earth, allowing more or less Sunlight to be seen. As a result, the Moon appears to alter form. The view of the Earth from the moon looks like a bright ball in space.

Earth, Sun and Moon System

The Earth revolves around the Sun in an orbit and it completes one revolution around in 364 days. The rotation of the Earth on its own axis causes day and night on Earth. In 24 hours, the Earth completes one rotation.

The formation of tides on Earth is mainly caused by the gravitational effects of the Sun and the Moon. The oceans of Earth nearest to the Moon expand outward, towards the Moon when the Moon circles Earth. This bulge represents the high tide. On the other side of the planet, another high tide occurs. Low tides occur in the intervals between high tides.

Eclipse and Its Types

An eclipse happens when one heavenly body blocks the passage of light, causing the light to be projected onto another heavenly body. Solar eclipses and lunar eclipses are the two forms of eclipses that may be seen from Earth. Due to the changing configurations of the Earth, the Sun, and the Moon, both eclipses occur.

• Solar Eclipse: The Sun orbits the Earth, while the moon orbits the Earth. The moon occurs to pass between the Sun and the Earth on their separate courses. It then hides the Sun’s light and casts a shadow on the Earth. People in the shadows are unable to see the Sun. A solar eclipse happens only on a new moon when the Sun, moon, and Earth line up.

• Lunar Eclipse: When the Earth, the Sun, and the moon all line up and the Earth lies between the Sun and the moon, a lunar eclipse occurs. The moon is surrounded by a massive shadow created by the Earth. The moon’s brightness fades to the point where it is scarcely visible.

Solved Questions

1. What is the revolution of the Earth?

Ans: A revolution is a movement of the Earth around the Sun in a definite path. The Earth spins in an anticlockwise orientation, from west to east. In one year or 365.242 days, the Earth completes one rotation around the Sun.

2. Write some facts about the moon in solar system.

Ans: Following are the list of some facts about the moon in the solar system.

• The Moon is the sole natural satellite of Earth and the solar system’s fifth biggest moon.

• The Moon’s existence aids in the stabilisation of our planet’s wobble and the regulation of our climate.

• The Moon has an extremely thin atmosphere known as an exosphere.

• Comet and asteroid impacts have cratered and pitted the Moon’s surface.

3. What are the effects of the Earth’s revolution?

Ans: As the Earth rotates around the Sun, its axis is inclined by 23.45 degrees from perpendicular to the plane of the ecliptic. Every 24 hours, the Earth turns on this axis. Since the axis is slanted, the impacts of the Earth’s revolution change for various portions of the planet.

At certain periods of the year, certain locations are oriented toward or away from the Sun. The four seasons are caused by this tilting. Due to this tilting, the seasons in the Northern and Southern Hemispheres are opposite.

Fun Facts

• Do you know there is water on the Moon?

• The Earth is moved by the Moon, which causes the tides to rise and fall.

• The Moon is receding from the Earth.

Summary

We have discussed the Earth Sun and Moon system and also the Earth and moon system. We have discussed “what is moon”, Earth’s revolution and rotation. The Earth takes 24 hours to complete one rotation and approximately 365 days to complete one revolution. Due to the revolution and tilt of Earth, the formation of different seasons takes place in the northern and southern hemispheres of the Earth.

Learning By Doing

Observe the night sky on a daily basis and see the different shapes of the moon and think about the reason behind the changing of the moon’s shape. Then present these in your class and compare what your peers have written.