this is class 12 Maharashtra board physics subject content. this is complete content with notes with easily explaination.
for buying or neet attractive ppt in any subject contact me 8879919898. go to my site akchem.tk
blog akchem.blogspot.com
This PPT is based on Physics on Chapter Motion. In this you will find every thing of that chapter with great images. in this PPT their are many animation and images .
thank you
this is class 12 Maharashtra board physics subject content. this is complete content with notes with easily explaination.
for buying or neet attractive ppt in any subject contact me 8879919898. go to my site akchem.tk
blog akchem.blogspot.com
This PPT is based on Physics on Chapter Motion. In this you will find every thing of that chapter with great images. in this PPT their are many animation and images .
thank you
Elasticity, Plasticity and elastic plastic analysisJAGARANCHAKMA2
It is actually the basis of structural engineering to study elasticity and plasticity analysis. So people who are also studying in various fields of structure and need to analyze finite element analysis also need to study this basis.
This presentation covers scalar quantity, vector quantity, addition of vectors & multiplication of vector. I hope this PPT will be helpful for Instructors as well as students.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
2. • Distance = 20cm
• Speed =20m/s
• Time= 60s
• Temperature = 200K
• Displacement = 20cm east
• velocity =40 m/s north
• Acceleration = 30m/s south
• Force = 20N east
• Numerical value (magnitude)
• Unit
• Numerical value (magnitude)
• Unit
• Direction
Scalar Quantities Vector Quantities
3. Scalars and Vectors
Scalars Vectors
1. Scalars have only magnitude. 1. Vectors have both magnitude and
direction.
1. They change if their magnitude
changes.
2. They change if either their magnitude,
direction or both change.
2. They can be added according to
ordinary laws of algebra.
ex: Distance, speed, work, mass,
density, etc
3. They can be added only by using laws
of vector addition.
ex: Displacement, velocity, force, etc
4. Vectors:
Those physical quantities which require magnitude as well as direction for
their complete representation and follows vector laws are called vectors
or vector quantities. A vector quantity is specified by a number with a unit
and its direction.
Representation of a vector:
A vector quantity is represented by a straight line arrowhead over it.
ex: i) force vector is represented as 𝐹 or F.
5. Position and Displacement vectors:
Position vector: a vector which gives position of an object with reference
to the origin of a co-ordinate system.
Displacement vector:
it is that vector which tells how much and in which direction an object has
changed its position in a given time interval.
6. Different Types of Vectors:
Equal Vectors:
Two vectors are said to be equal if
they have same magnitude and
same direction.
𝐴 and 𝐵 are
equal vectors.
Negative of a Vector:
The negative of a vector is defined as
another vector having the same magnitude
but having an opposite direction.
𝐵 is a negative equal
vector of 𝐴 or vice
versa
𝐴
𝐴
𝐵
𝐵
7. Modulus of a Vector:
The modulus of a vector means the length or the magnitude of the
vector.
It is the scalar quantity.
| 𝐴| = 𝐴
Unit Vector:
A unit vector is a vector of unit magnitude drawn in the direction of a given
vector.
𝑨 =
𝑨
|𝑨|
=
𝑨
𝑨
8. Collinear Vectors:
Vectors having equal or unequal magnitudes but acting along the same
or parallel lines.
Co-initial Vectors:
Vectors having a common initial point.
Co-terminus Vectors:
Vectors having a common terminal point.
Zero/ null Vector:
Vectors having zero magnitude and arbitrary direction.
represented as 0
9. Properties of Zero/ null Vector:
when a vector is added to a zero vector, we get the same
vector.
𝐴 + 0 = 𝐴
when a vector is multiplied to a zero vector, we get the
zero vector.
𝐴 0 = 0
10. Laws of Addition of Vectors:
1. Triangle Law of Vector Addition
If two vectors acting at a point are represented in
magnitude and direction by the two sides of a
triangle taken in one order, then their resultant is
represented by the third side of the triangle taken
in the opposite order.
If two vectors 𝐴 and 𝐵 acting at a point are
inclined at an angle θ, then their resultant 𝑅
𝑹 = 𝑨 + 𝑩
Magnitude, 𝑹 = 𝑨 𝟐 + 𝟐𝑨𝑩𝒄𝒐𝒔𝜽 + 𝑩 𝟐
𝒕𝒂𝒏𝜷 =
𝑩𝒔𝒊𝒏𝜽
(𝑨 + 𝑩𝒄𝒐𝒔𝜽)
𝑨
𝑩
𝑹
11. 2. Parallelogram Law of Vector Addition
If two vectors acting at a point are represented
in magnitude and direction by the two adjacent
sides of a parallelogram draw from a point, then
their resultant is represented in magnitude and
direction by the diagonal of the parallelogram
draw from the same point.
If two vectors 𝐴 and 𝐵 acting at a point are
inclined at an angle θ, then their resultant 𝑅
𝑹 = 𝑨 + 𝑩
Magnitude, 𝑹 = 𝑨 𝟐 + 𝟐𝑨𝑩𝒄𝒐𝒔𝜽 + 𝑩 𝟐
𝒕𝒂𝒏𝜷 =
𝑩𝒔𝒊𝒏𝜽
(𝑨+𝑩𝒄𝒐𝒔𝜽)
𝑨
𝑩
𝑹
12. 3.Polygon Law of Vector Addition
It states that if number of vectors acting on a particle
at a time are represented in magnitude and direction
by the various sides of an open polygon taken in
same order, their resultant vector E is represented
in magnitude and direction by the closing side of
polygon taken in opposite order, polygon law of
vectors is the outcome of triangle law of vectors.
𝑅 = 𝐴 + 𝐵 + 𝐶 + 𝐷 + 𝐸
𝑂𝐸= 𝑂𝐴 + 𝐴𝐵 + 𝐵𝐶 + 𝐶𝐷 + 𝐷𝐸
13. Properties of Vector Addition
(i) Vector addition is commutative,
i.e., 𝑨 + 𝑩 = 𝑩 + 𝑨
In fig side OP and OQ of a parallelogram OPSQ
represents vector 𝐴 and 𝐵 respectively.
Using triangle law of vector addition,
In OPS, 𝑂𝑆 = 𝑂𝑃 + 𝑃𝑆
𝑅 = 𝐴 + 𝐵
In OQS, 𝑂𝑆 = 𝑂𝑄 + 𝑄𝑆
𝑅 = 𝐵 + 𝐴
From above equations,
𝐴 + 𝐵 = 𝐵 + 𝐴
𝑨
𝑩
𝑹
O
P
S Q
14. (ii) Vector addition is associative,
i.e., 𝑨 +( 𝑩 + 𝑪 )= (𝑨 + 𝑩 )+ 𝑪
(iii) Vector addition is distributive,
i.e., m (𝑨 + 𝑩 ) = m 𝑨 + m 𝑩
15. Analytical method of vector addition:
(by using parallelogram law of vector addition)
Consider two vectors A and B making an angle θ with each other, let OP
and OQ are the sides of OPSQ represents vectors A and B respectively,
To find the magnitude of the resultant:
from point S, draw SN perpendicular to extended OP
In ONS,
OS2 =ON2 +NS2
= (OP+PN)2 +NS2
=OP2 +(2 OP* PN) +PN2 +NS2
𝑶𝑷 = 𝑨 OP= A,
𝑷𝑺 = 𝑩 PS=B,
𝑶𝑺 = 𝑹 OS=R
17. To find the direction of the resultant:
let the resultant R make an angle β with the
direction of A.
Then from right angled triangle ONS, we get
tan β =
SN
𝑂𝑁
=
SN
𝑂𝑃+𝑃𝑁
tan β =
Bsinθ
𝐴+𝐵𝑐𝑜𝑠θ
18. Special cases:
i) if two vectors A and B are acting along the same
direction, 𝜃=0◦
R = 𝐴2 + 2𝐴𝐵𝑐𝑜𝑠𝜃 + 𝐵2
R = 𝐴2 + 2𝐴𝐵𝑐𝑜𝑠0 + 𝐵2
R = 𝐴2 + 2𝐴𝐵 + 𝐵2
R = 𝐴 + 𝐵
tan β =
Bsinθ
𝐴+𝐵𝑐𝑜𝑠θ
=
Bsin0
𝐴+𝐵𝑐𝑜𝑠0
=0
19. ii) if two vectors A and B are acting along the opposite direction, 𝜃=180◦
R = 𝐴2 + 2𝐴𝐵𝑐𝑜𝑠180 + 𝐵2
R = 𝐴2 − 2𝐴𝐵 + 𝐵2
R = 𝐴 − 𝐵
tan β =
Bsinθ
𝐴+𝐵𝑐𝑜𝑠θ
=
Bsin180
𝐴+𝐵𝑐𝑜𝑠180
=0
20. i) when the two vectors A and B are acting at right angle to each other,
𝜃=90◦
R = 𝐴2 + 2𝐴𝐵𝑐𝑜𝑠90 + 𝐵2
R = 𝐴2 + 𝐵2
tan β =
Bsinθ
𝐴+𝐵𝑐𝑜𝑠θ
=
Bsin90
𝐴+𝐵𝑐𝑜𝑠90
=
𝐵
𝐴
𝛽 = tan−1 𝐵
𝐴
21. The flight of a bird is an example of
composition of vectors.
Working of a sling is based on law of
vector addition
22. 1. The two forces of 5N and 7N acts on a particle with an angle of 60
between them. Find the resultant force.
𝐹1= 5𝑁
𝐹2= 7𝑁
= 60
R = 𝐴2 + 2𝐴𝐵𝑐𝑜𝑠𝜃 + 𝐵2
F = 𝐹1
2
+ 2 𝐹1 𝐹2 𝑐𝑜𝑠𝜃 + 𝐹2
2
F = 52 + (2𝑋5𝑋7𝑐𝑜𝑠60) + 72
F = 109𝑁
23. 2. Two vectors both equal in magnitude have their resultant equal in
magnitude of the either. Find the angle between the two vectors.
A=B=R
= ?
R = 𝐴2 + 2𝐴𝐵𝑐𝑜𝑠𝜃 + 𝐵2
A = 𝐴2 + 2𝐴2 𝑐𝑜𝑠𝜃 + 𝐴2
A = 2𝐴2 + 2𝐴2 𝑐𝑜𝑠𝜃
A = 2𝐴2(1 + 𝑐𝑜𝑠𝜃)
1 + 𝑐𝑜𝑠𝜃 =
1
2
𝑐𝑜𝑠𝜃 =
1
2
− 1
𝑐𝑜𝑠𝜃 = −
1
2
𝜃=120
28. Multiplication of a Vector:
By a Real Number
When a vector A is multiplied by a real number n, then its magnitude
becomes n times but direction and unit remains unchanged.
𝑩 = n 𝑨
29. Multiplication of Two Vectors
1.Scalar or Dot Product of Two Vectors
2.Vector or Cross Product of Two Vectors
30. 1. Scalar or Dot Product of Two Vectors
The scalar product of two vectors is equal to the product of their
magnitudes and the cosine of the smaller angle between them.
It is denoted by ٠ (dot).
𝑨 ٠ 𝑩 = |𝑨 ||𝑩 | cos θ = AB cos θ
cos θ =
𝑨 ٠ 𝑩
𝐴𝐵
The scalar or dot product of two vectors is a scalar.
Physical quantities such as
• W= 𝑭 ٠ 𝒔
• Power= 𝑭 ٠ 𝒗
31. Properties of Scalar Product
(i) Scalar product is commutative, i.e., A ٠ B= B ٠ A
(ii) Scalar product is distributive, i.e., A ٠ (B + C) = A ٠B + A ٠ C
(iii) Scalar product of two perpendicular vectors is zero.
A ٠ B = AB cos 90° = O
(iv) Scalar product of two parallel vectors is equal to the product of their
magnitudes,
i.e., A ٠B = AB cos 0° = AB
(v) Scalar product of a vector with itself is equal to the square of its magnitude,
i.e.,A ٠ A = AA cos 0° = A2
35. 3. A force F = (7i + 6k )N makes a body move with a velocity of
v = (3j + 4k )m/s, calculate power in watt.
F = (7i + 0j + 6k )N
v = (0i + 3j + 4k )m/s
Power = F ٠ v = (7i + 0j + 6k )٠ (0i + 3j + 4k )
= (7x0) + (0x3) + (6x4)
= 0 + 0 + 24
Power = 24watt
36. 4. Calculate the work done by a force F = (−i + 2j + 3k )N in displacing
an object through a distance of 4m along the z-axis.
F = (−i + 2j + 3k )N
s = (0i + 0j + 4k )m
Work = F ٠ s = (−i + 2j + 3k) ٠(0i + 0j + 4k )
= 0 + 0 + 12
Work = 12 joule
37. 5. Prove that the vector A = i + 2j + 3k and B = 2i − j are
perpendicular to each other.
A = i + 2j + 3k
B = 2i − j + 0k
A ٠ B = 0
A ٠ B = (i + 2j + 3k) ٠(2i − j + 0k)
= 2 - 2 + 0
= 0
A and B 𝑎𝑟𝑒 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝑡𝑜 𝑒𝑎𝑐ℎ 𝑜𝑡ℎ𝑒𝑟
38. 6. Find the value of n, so that the vectors A = 2i + nj + k
and B = 4i − 2j −2k are perpendicular to each other.
A = 2i + nj + k
B = 4i − 2j −2k
A ٠ B = 0
A ٠ B = (2i + nj + k) ٠(4i − 2j − 2k)
0= 8 – 2n + 2
2n =6
n= 3
39. Vector or Cross Product of Two Vectors
The vector product of two vectors is equal to the product of their magnitudes and the sine
of the smaller angle between them.
It is denoted by x (cross).
𝑨 x 𝑩 = AB sin θ n
sin θ =
𝑨 x 𝑩
𝐴𝐵
n =
𝑨 x 𝑩
|𝑨 x 𝑩|
The direction of unit vector n can be obtained from right hand thumb rule.
If fingers of right hand are curled from A to B through smaller angle
between them, then thumb will represent the direction of vector (A x B).
40. Properties of Vector Product
(i) Vector product is not commutative, i.e.,
𝑨 x 𝑩 ≠ 𝑩 x 𝑨
(𝑨 x 𝑩 ) = - (𝑩 x 𝑨 )
(ii) Vector product is distributive,
𝑨 x (𝑩 + 𝑪 ) = (𝑨 x 𝑩) + (𝑨 x 𝑪 )
(iii) Vector product of two parallel vectors is zero, i.e.,
𝑨 x 𝑩 = AB sin O° = 𝟎
41. (iv) Vector product of any vector with itself is zero.
𝑨 x 𝑨 = AA sin O° = 𝟎
(v) The vector or cross product of two vectors is also a vector.
Physical quantities such as
Torque = 𝒓 x 𝑭
Angular momentum 𝑳 = 𝒓 x 𝒑
48. Projectile Motion
A body thrown with some initial velocity and then allowed to
move under the action of gravity alone, is known as a
projectile.
If we observe the path of the projectile, we find that the
projectile moves in a path, which can be considered as a
part of parabola. Such a motion is known as projectile
motion.
49. Examples of projectiles are
(i) a object thrown from an aeroplane
(ii)a javelin or a shot-put thrown by an athlete
(iii)motion of a ball hit by a cricket bat
(iv)an arrow released from bow, etc.
Assumptions of Projectile Motion:
(1) There is no resistance due to air.
(2) The effect due to curvature of earth is negligible.
(3) The effect due to rotation of earth is negligible.
(4) For all points of the trajectory, the acceleration due to gravity ‘g’ is constant in
magnitude and direction.
50. Angle of projection:
The angle between the initial direction of projection and the horizontal
direction through the point of projection is called the angle of projection.
Velocity of projection:
The velocity with which the body is projected is known as velocity of
projection.
51. Trajectory:
The path described by the projectile is called the trajectory.
Range:
Range of a projectile is the horizontal distance between the point of
projection and the point where the projectile hits the ground.
Time of flight:
Time of flight is the total time taken by the projectile from the instant of
projection till it strikes the ground.
Maximum height reached by the projectile:
The maximum vertical displacement produced by the projectile is known
as the maximum height reached by the projectile.
52. Types of Projectile Motion
Projectile fired at an angle with the horizontal (oblique projection):
For maximum range Rmax
sin 2θ = 1, (i.e) θ = 45°
Therefore the range is maximum when the angle of projection
is 45°.