[Physics Class Notes] on Newton's Laws of Motion – First Law Pdf for Exam

According to Aristotle, a constant continuous force is required to keep a body in uniform motion which is not actually true. It is called Aristotle’s Fallacy, and Newton’s Laws come under Aristotle’s Fallacy.  Galileo Galilei takes a different angle to explain the laws of motion. According to him, resistance (inertia) or friction affects a body in motion or at rest. While there are many theories on motion given by scholars and ancient scientists, Newton’s Laws of Motion are the most popular.

The three laws of motion proposed by Newton are three physical laws, which together form the basis of classical mechanics. The three laws of motion describe the relationship between a body and the forces acting upon it, along with the body’s motion corresponding to those forces. To be specific, the first law of motion defines the force qualitatively, the second law of motion gives a quantitative measure of the force, and the third law of motion states that a single isolated force doesn’t exist.

What is Newton’s First Law of Motion?

Newton’s First Law of Motion is also known as Galileo’s law of inertia. A body continues to be in its state of rest or uniform motion in a straight line unless compelled by an external force to change its state. The law defines the force and states it as a factor, which can change the state of the object. Thus, Newton explains his first law of motion based on the inertia of rest, the inertia of motion, and the inertia of direction.

Inertia is the property of a body due to which it opposes any change in its state. The mass of a body is the measure of its inertia of translational motion. It is difficult to change the state of rest or uniform motion of a body of heavier mass and vice-versa. In simple words, inertia is a measure of the tendency of an object at rest to stay at rest or of an object in motion to stay in motion.

  • Mass of a body is a quantitative or numerical measure of a body’s inertia.

  • Larger the inertia of a body, the more will be its mass. 

The Inertia of Rest 

A body cannot change its state of rest by itself.

Examples:

  • When we shake a branch of a mango tree, the mangoes fall. 

  • When a bus or train starts suddenly, the passengers sitting inside tend to fall backward.

  • When a horse starts suddenly, the rider falls backwards.

  • The dust particles in a blanket fall off when it is beaten with a stick.

  • A coin is placed on cardboard, and this cardboard is placed over a tumbler, such that the coin is above the mouth of the tumbler. Now, if the cardboard is removed with a sudden jerk, the coin falls into the tumbler.

The Inertia of Motion 

A body cannot change its state of uniform motion by itself.

Examples:

  • When a bus or train stops suddenly, the passengers sitting lean forward.

  • A person who jumps out of a moving train may fall in the forward direction.

  • A bowler runs the ball before throwing it so that this speed of running gets added to the speed of the ball at the time of the throw.

  • An athlete runs through a certain distance before taking a long jump because the velocity acquired during the running gets added to the velocity of an athlete at the time of the jump, and hence he can jump over a longer distance.

  • A ball is thrown in the upward direction by a passenger sitting inside a moving train.

The ball will fall:-

  • back to the hands of the passenger, if the train is moving with constant velocity. 

  • ahead of the passenger, if the train is retarding (slowing down).

  • behind the passenger, if the train is accelerating (speeding up).

  

The Inertia of Direction 

A body cannot change its direction of motion by itself. The tendency of an object to oppose any change (unbalanced force) in its direction of motion and continue to stay in direction is called inertia of direction.

 Examples:

  • When a straight running car turns sharply, the person sitting inside feels a force radially outwards.

  • Rotating wheels of vehicles throw out mud, mudguards fitted over the wheels prevent this mud from spreading.

  • When a knife is pressed against a grinding stone, the sparks produced move in the tangential direction. 

What is an External Force?

According to Newton’s first law of motion, a push or a pull that either changes or tends to change the state of rest or uniform motion (constant velocity) of a body is known as a force. An external force is a force originating from outside an object rather than a force internal to an object. 

For instance, the force of gravity that Earth exerts on the moon is an external force on the moon. However, the force of gravity that the inner core of the moon exerts on the outer crust of the moon is an internal force on the moon. Internal forces within an object can’t cause a change in that object’s overall motion.

Effects of Resultant Force     

  1. It may change the speed of the body.     

  2. It may change the direction of motion.     

  3. It may change both the speed and direction of motion.     

  4.  It may change the size or/and the shape of the body.      

  5. It may start a motion in a stationary body or it may stop a moving body.

Units for Measurement of Force

Absolute units are-   

  

  1. N (M.K.S)     

  2. dyne (C.G.S)    

Other units are-    

  1. kg-wt or kg-f {kf-force}    

  2. g-wt or
    g-f

Newton’s First Law of Motion Examples in Daily Life

Some daily life examples are as below:

  • A small coin is put on a card and placed over a glass. When the card is flicked away with the finger, the coin drops into the glass.

  • Suppose we are sitting in a stationary bus. If it starts moving suddenly, we will feel a jerk in the backward direction. It is because our lower body is in contact with the seat of the bus that comes in motion as the bus starts moving, while the upper portion of our body remains at the rest due to inertia, and so we feel a jerk in the backward direction.

  • Similarly, if we push a ball on the ground, it should continue its uniform motion indefinitely, but it stops after covering a certain distance. As soon as the ball starts moving, a force (force of friction) comes into play, which opposes the motion of the ball.

  • A book lying on a table can’t change its position by itself unless a force is applied to change its position.

[Physics Class Notes] on OTEC – Ocean Thermal Energy Conversion Pdf for Exam

OTEC full form is Ocean Thermal Energy Conversion and suggests a technology that creates a renewable source of energy. It mainly leverages the temperature differences among the different layers of seawater to generate thermal energy. 

This widely popular technology is instrumental in reducing the stress on conventional modes of energy, such as coal-driven energy. In 1881, French physicist Jacques-Arsene d’Arsonval proposed this alternative form of energy creation to battle the slow depletion of non-renewable sources of energy. 

 

What is Ocean Thermal Energy? 

As the name suggests, ocean thermal energy takes advantage of the fact that temperatures of each layer within a large water body differ. Consequently, a turbine generator exploits cold seawater at deeper layers. Also, the temperature difference arising from warm surfaces play a vital role in energy production. 

As per ocean thermal energy definition, the energy difference between such seawater layers is not just affordable but also predictable. Even though the surface of oceans and seas absorb solar energy, it falls short of temperature gradient. Therefore, scientists use liquids, such as ammonia, which have a low boiling point to produce thermal energy from the temperature difference. 

 

How Does Ocean Thermal Energy Conversion Work? 

The process of Ocean Thermal Energy Conversion mainly leverages the gap in the temperature gradient present at several layers of seawater. The larger the difference, the higher is the effectiveness of this method of producing renewable energy. 

For instance, let us suppose that the surface temperature of seawater is 300 C, which is sufficient for ammonia to boil. This heat at the surface vaporizes the working fluid, which in turn rotates a turbine. The turbine, therefore, generates electricity when it is attached to a generator. 

On the other hand, let us assume that the temperature of a deeper ocean layer is 50 C. The vapour thus produced at the surface further cools down from contact with deeper seawater. As a result, the vapour condenses back into a liquid, and one can reuse it again. 

OTEC becomes a part of a continuous process of sustainable energy generation which significantly reduces the impact of global warming. Also, this procedure can be instrumental for energy creation to the tune of 3-5 terawatts (where 1 terawatt = 1012 watts). 

 

Ocean Thermal Energy Conversion: Advantages and Disadvantages

The advantages and disadvantages of ocean thermal energy are widely discussed in several quarters of the globe which put special emphasis on an alternative source of usable energy. 

 

However, an in-depth analysis of the uses of this energy conversion process sheds light on the following Advantages of ocean thermal energy – 

 

Ocean thermal energy conversion is one of the most sustainable forms of energy. Besides, its availability at all times contributes to its success in providing energy irrespective of weather conditions. For instance, it is a vital mode of energy creation in such tropical islands which lack the conventional means of energy production. 

 

The by-products of this comprehensive process is desalinated freshwater which improves the scope of fish farming in several regions. Also, condensed greenhouse gases help in food production in dry landscapes. 

 

The cold water involved in this process plays an essential role in air conditioning at minimum costs. It also introduces an impressive extent of self-sufficiency in such regions which are behind in conventional sources of energy. 

 

Moreover, OTEC includes a few Disadvantages as well which are as follows – 

 

Thermal energy conversion through differences in temperatures of ocean layers is primarily a capital-intensive process. The machinery involved in this method, along with the working fluid, comes at high costs. 

 

The effectiveness of energy conversion in this process is significantly lower than other conventional counterparts. Besides, the cost of producing per kWh is substantially higher, which enhances its disadvantages. 

Therefore, ocean thermal energy is due to the exploitation of difference in surface and deeper level temperatures of seawater which give rise to a voluminous amount of alternative energy. 

Browse through our website for a detailed insight into this topic. Besides, you can also download our app to maximize your learning experience. 

[Physics Class Notes] on P-N Junction Pdf for Exam

A junction known as the p-n junction is an interface or a boundary that is present between two semiconductor material types. These material types are namely the p-type and the n-type inside a semiconductor.

 

The side which is known as the p-side or the positive side of the semiconductor has an excess of holes and the n-side or the negative side has an excess of electrons. In a semiconductor, we can say that the p-n junction is created by the method of doping. The process that is basically doping is explained in further detail in the next section.

What is PN Junction Doping?

As we already know that if we use different semiconductors or the different materials to make a p-n junction then there will be a grain boundary that would inhibit the movement of electrons from one side to the other by scattering the electrons and holes.  Thus, here we use the process that is known as doping. 

 

We will understand the process of doping with the help of this example. Let us now further consider a thin p-type silicon semiconductor sheet. Now, again If we add a small amount that is of pentavalent impurity to this thing, we can see that a part of the p-type Si will get converted to n-type silicon. This sheet which we are talking about will now contain both p-type region and n-type region and a junction which is between these two regions. The processes that we have talked about we need to follow after the formation of a p-n junction are of two types – diffusion and drift.  

Depletion Region

As we already have this thing in our mind that there is a difference in the concentration of holes and electrons at the two sides of a junction,  the holes from the p-side diffuse to the n-side, and the electrons from the n-side diffuse to the p-side. Now we can notice that these give rise to a diffusion current across the junction. Also, we will notice that when an electron diffuses from the n-side to the p-side then at that moment an ionized donor is left behind on the n-side that is immobile.

 

As this whole process goes on we can see a layer of positive charge is developed on the n-side of the junction. Similarly, we can say that when a hole goes that too from the p-side to the n-side then we can say that an ionized acceptor is left behind in the p-side which then results in the formation of a layer of negative charges in the p-side of the junction. This region which we have seen here is of positive charge and negative charge on either side of the junction is termed as the depletion region. 

 

Drift

These all things are due to this positive space charge region on either side of the junction. An electric field direction from a positive charge towards the negative charge is developed.  Now again we can see that due to this electric field that an electron on the p-side of the junction moves to the n-side of the junction. This motion which we have already seen is termed the drift. Here we can easily notice that the direction of the drift current is opposite to that of the diffusion current.

Application of PN Junction Diode

  • The junction which is the p-n junction diode can be used as a photodiode, the diode which is sensitive to the light when the configuration of the diode is reverse-biased.

  • It can be used as a solar cell.

  • When the diode is forward-biased, it can be used in LED lighting applications.

  • We can see that it is also used as a rectifier in many electric circuits and as a voltage-controlled oscillator in varactors.

There are two operating regions in the p-n junction diode:

  • The P-type

  • Then the N-type

There are also three biasing conditions which are generally for the junction which is the p-n junction diode and this is based on the voltage applied:

  • Zero Bias: there is no external voltage applied to the p-n junction diode.

  • Forward Bias: which is the positive terminal that is of the voltage potential is connected to the p-type while the negative terminal is connected to the n-type.

  • Reverse Bias: that is we can say that the negative terminal which is of the voltage potential is connected to the p-type and the positive is connected to the n-type.

 

Reverse Bias of P-N Junction

The p-n junction is said to be reverse-biased when the p-type is linked to the negative terminal of the battery and the n-type is attached to the positive side. The applied electric field and the built-in electric field are both in the same direction in this scenario. Because the generated electric field is in the same direction as the built-in electric field, the depletion area becomes more resistive and thicker. If the applied voltage is increased, the depletion region gets more resistant and thicker.

V-I Characteristics of PN Junction Diode

A curve between the voltage and current through the circuit defines the VI properties of PN junction diodes. Voltage is represented on the x-axis, and current is represented on the y-axis.

 

With the help of the curve, we can see that the diode works in three different zones, which are:

  • Zero bias 

  • Forward bias

  • Reverse bias

 

If the PN junction diode is zero biased, no external voltage will be supplied. This means that the junction potential barrier is blocking the flow of current.

[Physics Class Notes] on Permeability Pdf for Exam

What is Permeability?

Permeability is the ability of a material to allow the magnetic flux when the object is placed inside the magnetic field where magnetic flux is the measure of the number of magnetic lines of forces that can pass via a given surface.

On this page, we will learn about the following topics:

  1. Electromagnetism

  2. Magnetomotive force, and the strength of the magnetic field.

  3. Types of material: Ferromagnetic, Paramagnetic, and Diamagnetic

  4. Permeability: Absolute and Relative

  5. Reluctivity.

Let’s take any straight current-carrying conductor or a coil when kept inside the magnetic field allows the magnetic field lines to pass through, which we can find out by Fleming’s left-hand rule.

Fleming’s Left-Hand Rule:

Fleming’s left – hand rule states that if we stretch the thumb, middle finger and the

The index finger of the left hand in such a way that they make an angle of 90 degrees       (Perpendicular to each other) and the conductor placed in the magnetic field 

 experiences Magnetic force.

    Such that:

  1.  Thumb: It points towards the direction of force (F)  

  2. Middle finger: It represents the direction of the current (I)

  3. Index finger:  It represents the direction of the magnetic field (B)

Here, in this image, we can see that the magnetic flux is concentrated more at the center than in the exteriors, which infers that magnetic field strength is directly proportional to the current ‘I’ flowing through the conductor and inversely proportional to the distance.

For a Straight Wire, the Strength of a Magnetic Field can be Calculated as:

H (magnetic field strength) = I (current)/ 2* pi * r

And for a coil, it is proportional to the number of turns of wire (N) and the current ’I’ flowing through it, but inversely proportional to the length, ‘L’ of the wire:

H= I × N/ L

Just have a look at the table shown below with the different Relative permeability (mr) values of various types of materials kept in the magnetic field.

Table 1.1: Value of Relative Permeability (mr) for Some Objects:

S.No.

Object

Relative permeability (mr)

1.

Wood

1.00000043

2.

Aluminium

1.000022

3.

Cobalt

250

4.

Nickel

600

5.

Iron

2, 00, 000

Here, Relative permeability (mr)  computes the efficient permeability of any substance.

Magnetic field intensity of an electromagnet depends upon the material being used, so a medium or a material plays a major role here because the main purpose is to concentrate the magnetic flux inside the field in a particular path.

There are three types of materials: Paramagnetism, Ferromagnetism, and Diamagnetism.

1. Paramagnetism:

The paramagnetic property of an element depends on the electronic configuration, and they are weakly attracted to the magnet, and they don’t retain their magnetism after an external magnetic field is removed. The materials such as Magnesium, Molybdenum, Lithium, possess Paramagnetism.

2. Diamagnetism:

The electrons in the outer shell of an element are paired in their orbitals that’s why they don’t possess magnetism in themselves as we see in table  1.1 above that the value wool and aluminium as compared to Co, Ni, and Fe are negligible.

3. Ferromagnetism:

Any element which has unpaired electrons in its outermost shell such that when it is placed in the magnetic field, possess high magnetic field strength, and retains this attribute even if an external magnetic field is removed.

Table 1.1, shows the strength of the magnetic field of elements like Co, Ni, and Fe.

The element Fe has the highest value, because of its high ability to concentrate a dense magnetic flux around itself.

One thing can be observed that the element, “Fe” behaves as both Paramagnetic and a ferromagnetic as well, why is there a difference?

It all depends upon the composition and the temperature, on the basis on which the electrons are polarized.

At high temperatures, Iron behaves as a paramagnetic material while at low, it behaves as a ferromagnetic material.

The type of material we use decides the amount of work being done, which in turn means the strength of the magnetic field created around the material.

Permeability:

Any material let’s say Iron when placed inside the magnetic field possesses magnetism in itself.

Here, Iron has an ability to allow magnetic fields with high strength in itself, and that’s why it has high permeability.

While the material like Wood, Aluminium doesn’t allow the magnetic fields to pass via and, they are reluctant to permit magnetism in itself, that’s why they also are calculated regarding permeability of free space or permeability constant.

In simple terms, permeability is an ability of any material to permit the density of the magnetic flux.

Magnetic Intensity and Intensity of Magnetization:

Magnetic Intensity defines the degree of magnetism (created by a magnetic field) a material can hold in itself.

Calculated as: H (Magnetic field strength) = n * I

Where n = no of turns in the wire

             I = The current flowing through the conductor.

and, Intensity of Magnetization of a magnetic material is defined as a magnetic moment per unit volume of the material, which is calculated as:

I = Magnetic moment (A)/ Volume (V).

Which is high for Ferromagnetic material and low for a diamagnetic material.

Permeability solely depends upon the medium being used, so, ‘type of medium’ plays a major role here.

Permeability working can be observed in transformers.

There are Certain Points to Understand How Permeability Depends upon Various Factors Given Below:

1. Temperature:

If the temperature of the medium is high, then the strength of the magnetic field will also become low
, which means work done will be less.

Temperature  = k/ work  = k/ m  (m is permeability.)         

2. Field Strength:

Field strength is one of the fundamental physical quantities that measure the intensity of magnetic fields.

If the material isn’t good, then the field strength won’t be good too.

3. Field frequency:

If the frequency of supply varies, then, harmonics will develop, which would create a humming sound, which usually happens in the Transformer.

4. Humidity:

During summer, when the temperature keeps on changing which in turn creates some variations in the properties of a material, it overall makes changes in the work being done and creates an impact on the permeability as well.

Simply, to increase the strength of the magnetism of the medium that we call it as permeability, m. The material should be of good quality.

If the medium is good, then the work done will also be more, because work done is directly proportional to the strength of the magnetic field and the permeability as well.

Permeability and its Types: Absolute and Relative.

Iron provides a low reluctance path and helps in the formation of magnetic fields which means, ‘High Permeability.’ It is because the molecular structure on the inside is easily able to induce these magnetic field lines.

Thus, permeability represents how much it would be helpful in energy conservation.Permeability is two types: Absolute and Relative

Magnetic Permeability is the ratio of Magnetic flux density to the field strength.

m= B/ H = Henries/ meter.

Fig. A  shows the direction of the magnetic field around the dipole, which shows that the density of magnetic flux is more at the center than on the exteriors.

In this case, if we put the compass in the magnetic field, then the South Pole of the magnetic needle of the compass would get attracted to the North Pole of the magnet and vice-versa.                                                                                                 

         

But, if there is a case that the medium such as Wood, Aluminium is kept in the place of a dipole, then the needle would show no deflection because there wouldn’t be any change in the magnetic field, which we refer to as the permeability of free space or simply, a permeability constant denoted by m-naught or m-zero.

.

The relative permeability of a magnetic material, designated mr, is the ratio of its absolute permeability m to that of air m-zero.

The absolute permeability (m) of a soft iron core is given as 80 milli-henries/meter. Though the value of m for Iron may have values from 100 to 5000, depending upon the grade of the material.

mr of magnetic materials such as cobalt, nickel, iron, steel, and their alloys are far greater than unity and are not constant, as you can see in Fig. B(2) and Fig. B(3).

The mr of a non-magnetic material, such as air, copper, wood glass, and plastic are, for all practical purposes, equal to unity.

mr = m / m-zero

The value of m-zero = 4 * pi * 10^-7

             = 1.257 * 10^-  7.

[Physics Class Notes] on Physics Symbols Pdf for Exam

In physics, there are a large number of physical quantities we include while performing calculations. To make it more convenient for users and easier to use and remember, we often use notations/symbols to represent these physical quantities. These notations/symbols we use to represent physical quantities when solving problems related to them or for other purposes are symbols.

In physics, we symbolise everything with an English/Greek alphabet, such as for the speed of light, wavelength, velocity, and so on.

Let us assume that a lady drives her car at a speed of 30 kmph and reaches her hometown in 2 hrs and if she drives at 50 kmph, she reaches in 1.5 hr. So, if we have to represent these units as symbols, how can we do that?

In this article,  you will find the most popular physics symbols and also those we commonly use in physics with their names, the type of quantities along with their respective units in tabular format. 

Examples of Physical Symbols

Also, the symbols used for physical quantities are vastly different. Sometimes, the symbol may be the first letter of the physical quantities they represent, like ‘d’, which stands for distance. Other times, they may be completely unrelated to the name of the physical quantities, such as c symbolises the speed of light. They may also be in the form of Greek characters, like λ, which stands for wavelength.

Below is an elaborated list of the most commonly used list of symbols in physics with their SI units. Please note that a particular symbol might relate to more than one quantity.

Symbols for Physical Quantities Related to Space and Time

Symbols

Quantity/ Coefficients

S.I. Unit

Physical Quantity (Scalar/Vector)

r

Radius, the radius of curvature

Metre

Functions as both scalar and vector

s

Displacement

Metre

Vector

d

Distance

Metre

Scalar

θ

Angular displacement, 

Radian

Vector

φ

The rotational angle

Radian

A uniquely-defined magnitude and direction, but is not a vector quantity.

(Does Not obey commutative law)

x, y, z

Cartesian Coordinates

Unitless

Scalar

î, ĵ, k̂

Cartesian unit vectors

Unitless

Vector

r, θ, φ

Spherical coordinates

Metre/Radian

Vector

r̂, θ̂, φ̂

Spherical vectors

Unitless

Vector

r, θ, z

Cylindrical coordinates

Metre/Radian

Scalar

r̂, θ̂, ẑ

Cylindrical vectors

Unitless

Vector

Normal vector

Unitless

Vector

Tangential unit vector

Unitless

Vector

h

Height, Depth

Metre

Scalar

ℓ, L

Length

Metre

Scalar 

t

Time

Second 

Scalar

D (= 2 r)

Diameter

Metre

Scalar

C

Circumference

Metre

Scalar 

A

Area

Square Metre

Functions as both scalar and vector (like Area vector in a magnetic flux formula)

V

Volume 

Cubic Metre (m3)

Scalar

τ

Time Constant

Second (s)

Scalar

T

Periodic time

Second (s)

Scalar 

f

Frequency 

1/second or (1/s)

Scalar 

ω

Angular frequency

Rad/s

Scalar

Below are some symbols that are used frequently in physics with their names, the type of quantities and their respective SI units in tabular format.

Physics Symbols Related to Mechanics

Symbols

Quantity/ Coefficients

S.I. Unit

Physical Quantity (Scalar/Vector)

v

Velocity, speed

metre/second (m/s)

Speed = Scalar

Velocity = vector

a

Acceleration

metre/square second (m/s2)

Vector 

g

Acceleration due to gravity

metre/square second 

Vector 

ac

Centripetal/Centrifugal acceleration

metre/square second

Vector 

m

Mass

Kilogram (kg)

Scalar 

F

Force

Newton (N)

Vector

W/Fg

Force due to gravity/Weight

Newton

Vector

Fg/ N

Normal force

N

Vector

Ff

Force of friction

N

Vector

µ

Coefficient of friction

Unitless

Scalar

p

Momentum

Kg.m/s

Vector

J

Impulse

N/s

Vector

E

Energy

Joule  (J)

Scalar

Kinetic energy

J

Scalar

U

Potential Energy

J

Scalar

Vg

Gravitational potential

J/kg

Scalar

η

Efficiency

Unitless

Scalar

P

Power

Watt

Scalar

α

Rotational acceleration

Radian per second squared (Rad/s2)

Vector

ω

Rotational velocity 

Rad/s

Vector

τ

Torque

N/m

Vector

L

Angular momentum

Kilogram meter squared per second

Kg.m2/s

Vector

ρ

Density

Volume 

Mass density

Kilogram per cubic meter

Scalar 

I

Moment of inertia

Kg.m2

Scalar

Physical Symbols Related to Fluid Mechanics

Symbols

Quantity/ Coefficients

S.I. Unit

Physical Quantity (Scalar/Vector)

λ

Linear mass density

kg/m

Scalar

σ

Area mass density

Kilogram per square meter (kg/m2)

Scalar 

FB, B

Buoyancy

N

Vector

qm

Mass flow rate

kg/s

Scalar

qV

Volume flow rate

m3/s

Scalar

FD, R

Drag or air resistance

N

Vector

CD

Drag Coefficient

Unitless

Scalar 

η

Viscosity

Pascal-second

Scalar

v

Kinematic Viscosity

m2/s

Scalar 

σ

Area mass density

kg/m2

Scalar

Re

Reynolds number

Unitless

Scalar

Fr

Froude number

Unitless

Scalar 

Ma

Mach number

Unitless

Scalar

Symbols Related to Solid Mechanics

Symbols

Quantity/ Coefficients

S.I. Unit

Physical Quantity (Scalar/Vector)

P

Pressure 

Pascal

Or

N/m2

Scalar 

σ

Stress

Pascal

Scalar 

τ

Shear stress

Pascal

Scalar

k

Spring constant

N/m

Scalar

E

Young’s modulus of elasticity

Pascal

Scalar 

G

Shear modulus of rigidity

Pascal

Scalar

ε

Linear strain

Unitless 

Scalar 

γ

Shear strain

Unitless

Scalar 

θ

Volume strain

Unitless 

Scalar 

S

Surface Tension 

N/m

Scalar 

K

Bulk modulus of compression

Pascal

Scalar 

Physical Quantities Related to Thermal Physics

Symbols

Quantity/ Coefficients

S.I. Unit

Physical Quantity (Scalar/Vector)

k

Thermal conductivity

W/m.K

Scalar 

P

Heat flow rate

Watt

Scalar

N

Number of particles

Unitless 

Scalar 

n

Amount of substance

Mole

Scalar

L

Latent heat/specific latent heat

J/kg

Scalar 

c

Specific heat capacity

J/kg. K

Scalar 

Q

Heat

J

Scalar 

Volume expansivity, coefficient of volume thermal expansion

1/K (inverse Kelvin)

Scalar 

α

Linear expansivity, coefficient of thermal expansion

1/K (inverse Kelvin)

Scalar 

T

Temperature 

Kelvin

Scalar 

Physical Symbol Related to Wave and Optics

Symbol

Quantity/Coefficients

S.I Unit

Physical Quantity (Scalar/Vector)

M

Magnification

Untiless 

Scalar 

f

Focal length

Metre 

Scalar 

n

Index of refraction

Unitless 

Scalar 

L

Level

Decibel (dB), decineper

Scalar 

I

Intensity

W/m2

Scalar

v, c

Wave speed

m/s

Scalar 

λ

Wavelength

Metre (m)

Scalar 

P

Power of a lens

Dioptre (D)

Scalar 

Physics Symbols Related to Electricity and Magnetism

Symbol

Quantity/Coefficients

S.I Unit

Physical Quantity (Scalar/Vector)

Poynting vector, intensity

W/m2

Vector 

η

Energy density

J/m3

Scalar 

n

Turns per unit length

1/m

Scalar 

N

Number of turns

Unitless 

Scalar

φB

Magnetic flux 

Weber

Vector

Magnetic field

Tesla

Vector 

FB

Magnetic force

N

Vector 

σ

Conductivity

Siemens/m 

(S/m)

Scalar 

G

Conductance 

Siemens

Scalar 

ρ

Resistivity

Ohm-m

Scalar 

R, r

Electric resistance/internal resistance

Ohm 

Scalar 

I

Electric current

Ampere (A)

Scalar 

ϵ

Dielectric constant

Unitless

Scalar 

Electromotive Force

Volt (V)

Scalar

C

Capacitance

Farad (F)

Scalar 

V

Voltage, electric potential

V

Scalar 

UE

Electric potential energy

J

Scalar 

φE

Electric flux 

Newton meter squared per coulomb (N/m2.C)

Vector 

E

Electric field 

N/C or V/m

Vector 

FE

Electrostatic force

N

Vector 

λ

Linear charge density

kg/m

Scalar 

σ

Area charge density

kg/m2

Scalar 

ρ

Volume charge density

kg/m3

Scalar 

q, Q

Electric charge

Coulomb (C)

Scalar 

Symbols Used in Modern Physics

Symbol

Quantity/Coefficients

S.I Unit

Physical Quantity (Scalar/Vector)

D

Dose/ dose absorbed

Gray (Gy)

Scalar

t1⁄2

Half-life

Second

Vector

ψ(r,t), ψ(r)φ(t)

Wave function 

Unitless 

Scalar

Work function

J

Scalar

H

Effective Dose

Sievert

Scalar

Γ

Lorentz factor/Lorentz gamma

Unitless

Scalar

From the above text on physics symbols, we understand that in Physics, we use various symbols or notations to denote different quantities. The denotations make the representation of the quantities easier.

It was also interesting to see that some physics symbols were very relatable (like “d” for distance) while some were unrelatable (like “c” for the speed of light or “λ” for wavelength). Also, we noticed that a particular symbol was related to more than one quantity.

[Physics Class Notes] on Polestar Pdf for Exam

The Pole Star meaning is the North Star or Polaris that lies closely in line with the axis of the Earth’s rotation “above” the North Pole, i.e., the north celestial pole. 

The pole star or Polaris stands almost motionless or static in the sky, and all the stars of the northern sky surrounding this star appear to rotate around it. Therefore, it makes an excellent fixed point from which scientists draw measurements for celestial navigation and astrometry.

In this article, we will understand the polestar definition, how to find the pole star in detail.

Define Pole Star

The Pole star or polar star is the name of Polaris lies in the constellation of Ursa minor, as it is the star nearest to the earth’s celestial north pole that we can in the image below:

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So, basically, the Polaris is a multiple star system including Polaris A, a yellow supergiant in orbit with a smaller star Polaris Ab and they both lie in the orbit of Polaris B.

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Where is Pole Star Located?

When the earth rotates about its axis, the pole star ‘appears’ to remain stationary because the position of the earth remains unchanged with respect to the pole star. Pole stars are also known as Polaris or North Star.

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So no matter wherever we are residing on the earth and no matter what the time is, the position of the pole star remains on this axis. However, this is not the case with the other stars in the galaxy. Only, the pole star is visible from the northern hemisphere.

However, the Pole star will not last forever. For the last thousands of years, the earth’s axis has been rotating slightly. This is called ‘precession’ and this results in the pole star shifting from the axis. A time will come, the present pole star will vanish and some other star, which is lying on the axis of the earth at that time will become our new pole star.

Now, let’s understand how to find pole star:

How to Identify Pole Star?

To understand how to identify pole star or how to find pole star, we have a scenario to understand where the pole star is located.

Imagine a Blackball as Earth and the marked blue dot on the Ball represent the North Pole. Now, draw the Equator along with the circumference of the ball.

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Mark a black dot somewhere on the white wall that will represent the Pole Star.

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Now, hold the ball in your right hand in such a way that the blue dot on the blackball points directly towards the black dot on the wall. This pertains to the current position of how Earth and Pole stars are aligned in the universe.

Now, we will rotate the blue ball along with the North-pole (its marked axis).

We notice that the relative position of the dot on the wall, i.e., Pole star remains invariant with respect to the dot on the ball, i.e., North Pole.

Now, as we move a certain distance away from the blue dot on the Ball, i.e., the North Pole or head towards the Equator, still the relative position remains unchanged.

Fun Fact

Do you know that the distance between the Earth and the Pole star is 433 Light Years? So, in the actual situation, this relative position is difficult to signify. This is the sole reason why the pole star remains stationary in the sky. 

Now, after crossing the Equator, what we do is, move towards the Southern Hemisphere,  a straight line that joins the two points breaks directly.

At this moment, the pole star indicates the direction to the place where it becomes invisible. Therefore, it becomes difficult to say where the pole star is located.

What is Polaris?

Polaris is also known as the North star. It appears static in the sky because it is located near the line of the axis of the Earth that is projected into space.

It is only a bright star whose position relative to the rotating Earth remains unchanged, while all other stars appear to move in an opposite direction to that of Earth’s rotation under them.

At the North Pole, Polaris appears directly above with the other stars circling around it during the entire night. As we move south, i.e.,  away from the pole, Polaris appears further descended in the Northern sky but still remains at the center of daily stellar motions around it. 

Below is the figure of the Polaris a.k.a the North star with other stars circling around it.

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Since there is no bright star in the South pole, the South Star exists in the universe. However, this is also true that the North star or the Polaris, or the Pole Star direction would always be towards the North because the Earth wobbles (moves unsteadily) like a top in its orbit. 

Do You Know?

Polaris will eventually appear to move away from the pole and won’t be remaining a North Star after a period of 26,000 years.