1. The document discusses vectors and tensors. It defines vectors as quantities with magnitude and direction, and provides examples like position, force, and velocity.
2. Tensors are quantities that have magnitude, direction, and a plane in which they act. Rank 0 tensors are scalars, rank 1 tensors are vectors, and rank 2 tensors can be represented by matrices.
3. The document covers various types of vectors like unit vectors and displacement vectors. It also discusses vector algebra operations and different ways vectors can be represented, such as in Cartesian form.
3-1 VECTORS AND THEIR COMPONENTS
After reading this module, you should be able to . . .
3.01 Add vectors by drawing them in head-to-tail arrangements, applying the commutative and associative laws.
3.02 Subtract a vector from a second one.
3.03 Calculate the components of a vector on a given coordinate system, showing them in a drawing.
3.04 Given the components of a vector, draw the vector
and determine its magnitude and orientation.
3.05 Convert angle measures between degrees and radians.
3-2 UNIT VECTORS, ADDING VECTORS BY COMPONENTS
After reading this module, you should be able to . . .
3.06 Convert a vector between magnitude-angle and unit vector notations.
3.07 Add and subtract vectors in magnitude-angle notation
and in unit-vector notation.
3.08 Identify that, for a given vector, rotating the coordinate
system about the origin can change the vector’s components but not the vector itself.
etc...
3-1 VECTORS AND THEIR COMPONENTS
After reading this module, you should be able to . . .
3.01 Add vectors by drawing them in head-to-tail arrangements, applying the commutative and associative laws.
3.02 Subtract a vector from a second one.
3.03 Calculate the components of a vector on a given coordinate system, showing them in a drawing.
3.04 Given the components of a vector, draw the vector
and determine its magnitude and orientation.
3.05 Convert angle measures between degrees and radians.
3-2 UNIT VECTORS, ADDING VECTORS BY COMPONENTS
After reading this module, you should be able to . . .
3.06 Convert a vector between magnitude-angle and unit vector notations.
3.07 Add and subtract vectors in magnitude-angle notation
and in unit-vector notation.
3.08 Identify that, for a given vector, rotating the coordinate
system about the origin can change the vector’s components but not the vector itself.
etc...
This presentation explains vectors and scalars, their methods of representation, their products and other basic things about vectors and scalars with examples and sample problems.
This presentation is as per the course of DAE Electronics ELECT-212.
Hello everyone! I am thrilled to present my latest portfolio on LinkedIn, marking the culmination of my architectural journey thus far. Over the span of five years, I've been fortunate to acquire a wealth of knowledge under the guidance of esteemed professors and industry mentors. From rigorous academic pursuits to practical engagements, each experience has contributed to my growth and refinement as an architecture student. This portfolio not only showcases my projects but also underscores my attention to detail and to innovative architecture as a profession.
7 Alternatives to Bullet Points in PowerPointAlvis Oh
So you tried all the ways to beautify your bullet points on your pitch deck but it just got way uglier. These points are supposed to be memorable and leave a lasting impression on your audience. With these tips, you'll no longer have to spend so much time thinking how you should present your pointers.
This presentation explains vectors and scalars, their methods of representation, their products and other basic things about vectors and scalars with examples and sample problems.
This presentation is as per the course of DAE Electronics ELECT-212.
Hello everyone! I am thrilled to present my latest portfolio on LinkedIn, marking the culmination of my architectural journey thus far. Over the span of five years, I've been fortunate to acquire a wealth of knowledge under the guidance of esteemed professors and industry mentors. From rigorous academic pursuits to practical engagements, each experience has contributed to my growth and refinement as an architecture student. This portfolio not only showcases my projects but also underscores my attention to detail and to innovative architecture as a profession.
7 Alternatives to Bullet Points in PowerPointAlvis Oh
So you tried all the ways to beautify your bullet points on your pitch deck but it just got way uglier. These points are supposed to be memorable and leave a lasting impression on your audience. With these tips, you'll no longer have to spend so much time thinking how you should present your pointers.
Between Filth and Fortune- Urban Cattle Foraging Realities by Devi S Nair, An...Mansi Shah
This study examines cattle rearing in urban and rural settings, focusing on milk production and consumption. By exploring a case in Ahmedabad, it highlights the challenges and processes in dairy farming across different environments, emphasising the need for sustainable practices and the essential role of milk in daily consumption.
Transforming Brand Perception and Boosting Profitabilityaaryangarg12
In today's digital era, the dynamics of brand perception, consumer behavior, and profitability have been profoundly reshaped by the synergy of branding, social media, and website design. This research paper investigates the transformative power of these elements in influencing how individuals perceive brands and products and how this transformation can be harnessed to drive sales and profitability for businesses.
Through an exploration of brand psychology and consumer behavior, this study sheds light on the intricate ways in which effective branding strategies, strategic social media engagement, and user-centric website design contribute to altering consumers' perceptions. We delve into the principles that underlie successful brand transformations, examining how visual identity, messaging, and storytelling can captivate and resonate with target audiences.
Methodologically, this research employs a comprehensive approach, combining qualitative and quantitative analyses. Real-world case studies illustrate the impact of branding, social media campaigns, and website redesigns on consumer perception, sales figures, and profitability. We assess the various metrics, including brand awareness, customer engagement, conversion rates, and revenue growth, to measure the effectiveness of these strategies.
The results underscore the pivotal role of cohesive branding, social media influence, and website usability in shaping positive brand perceptions, influencing consumer decisions, and ultimately bolstering sales and profitability. This paper provides actionable insights and strategic recommendations for businesses seeking to leverage branding, social media, and website design as potent tools to enhance their market position and financial success.
White wonder, Work developed by Eva TschoppMansi Shah
White Wonder by Eva Tschopp
A tale about our culture around the use of fertilizers and pesticides visiting small farms around Ahmedabad in Matar and Shilaj.
You could be a professional graphic designer and still make mistakes. There is always the possibility of human error. On the other hand if you’re not a designer, the chances of making some common graphic design mistakes are even higher. Because you don’t know what you don’t know. That’s where this blog comes in. To make your job easier and help you create better designs, we have put together a list of common graphic design mistakes that you need to avoid.
Can AI do good? at 'offtheCanvas' India HCI preludeAlan Dix
Invited talk at 'offtheCanvas' IndiaHCI prelude, 29th June 2024.
https://www.alandix.com/academic/talks/offtheCanvas-IndiaHCI2024/
The world is being changed fundamentally by AI and we are constantly faced with newspaper headlines about its harmful effects. However, there is also the potential to both ameliorate theses harms and use the new abilities of AI to transform society for the good. Can you make the difference?
Unleash Your Inner Demon with the "Let's Summon Demons" T-Shirt. Calling all fans of dark humor and edgy fashion! The "Let's Summon Demons" t-shirt is a unique way to express yourself and turn heads.
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1. Budge Budge Institute Of Technology
Name - Manish Kumar
Department-Mechanical Engineering
Sem-5th
University Roll No-2760072003
Paper Name - Solid Mechanics
Paper Code - (PC-ME 502)
Faculty Name-SKM
Topic- Introduction To Cartesian Tensors
2. A vector is a bookkeeping tool to keep track of two pieces of information (typically
magnitude and direction) for a physical quantity. Examples are position, force and velocity.
The vector has three components.
Vector qualities include:
1. displacement
2. 2. velocity
3. 3. acceleration
4. 4. force
5. 5. weight
6. 6. momentum
3. Types of Vectors
1. Zero Vector.
2. Unit Vector.
3. Position Vector.
4. Co-initial Vector.
5. Like and Unlike Vectors.
6. Co-planar Vector.
7. Collinear Vector.
8. Equal Vector.
Unit Vector:
A vector having unit magnitude is called a unit vector. A
unit vector in the direction of vector A is given by A unit
vector is unit less and dimensionless vector and
represents direction only
Unit Vector= Vector/vector’s magnitude
4. VV
Vector quantities change when:
their magnitude changes
their direction changes
their magnitude and direction both
Vector Algebra
Vectors algebra involves algebraic operations across vectors. The algebraic operations
involving the magnitude and direction of vectors is performed in vector algebra. Vector
algebra helps for numerous applications in physics, and engineering to perform addition
and multiplication operations across physical quantities, represented as vectors in three-
dimensional space.
Vectors carry a point A to point B. The length of the line between the two points A and B is
called the magnitude of the vector and the direction or the displacement of point A to
point B is called the direction of the vector AB. Vectors are also called Euclidean vectors or
Spatial vectors. Vectors have many applications in mathematics, physics, engineering, and
various other fields.
Vectors have an initial point at the point where they start and a terminal point that tells
the final position of the point. Various algebraic operations such as addition, subtraction,
and multiplication can be performed in vector algebra.
5. Representation of Vectors
Vectors are usually represented in bold lowercase such as a or using an arrow
over the letter as . can also be denoted by their initial and terminal points with
an arrow above them,
for example, vector AB can be denoted as . The standard form of representation
of a vectors is Here, a, b, c are real numbers and i, j, k are the unit vectors
along the x-axis, y-axis, and z-axis respectively. ai+bj +ck
Since the three components of A act in the positive i, j, and k directions, we can
write A in Cartesian vector form as
6. Co-Initial Vectors
A vector is said to be a co-initial vector when two or more
vectors have the same starting point, for example, Vectors AB
and AC are called co-initial vectors because they have the same
starting point A.
Like and Unlike Vectors
The vectors having the same directions are said to be
like vectors whereas vectors having opposite directions are said
to be unlike vectors.
Coplanar Vectors
Three or more vectors lying in the same plane are known as
coplanar vector
Collinear Vectors
Vectors that lie in the parallel line or the same line concerning
their magnitude and direction are known to be collinear vectors,
also known as parallel vectors.
Equal Vectors
Two vectors are said to be equal vectors when they have both
direction and magnitude equal, even if they have different initial
points. Displacement Vector
The vector AB represents a displacement vector if a point is
displaced from position A to B.
7. Negative of a Vector
Suppose a vector is given with the same magnitude and direction, now if
any vector with the same magnitude but the opposite direction is given
then this vector is said to be negative of that vector. Consider two vectors a
and b, such that they have the same magnitude but opposite in direction
then these vectors can be written as a = – b
Orthogonal Vectors:
Two or more vectors in space are said to be orthogonal if the angle
between them is 90 degrees. In other words, the dot product of orthogonal
vectors is always 0.
Free vector
A vector that can be displaced parallel to itself and applied at any point is
called a free vector.
Null vector
A vector whose magnitude is zero and has no direction, it may have all
directions is said to be a null vector.
A null vector can be obtained by adding two or more vectors
8. Intoduction To Cartisian Tensor
Tensor
A tensor is a quantity, for example a stress or a strain, which has magnitude,
direction and a plane in which it acts.
Stress and strain are both tensor quantities.In real engineering components,
stress and strain are 3-D tensors.
Whenever we want to represent some physical quantity mathematically, wneed
to see how much information is needed to specify the value of that quantity.
▶ The rank (or order) of a tensor is defined by the number of directions (and
hence the dimensionality of the array) required to describe it
▶ The need for second rank tensors comes when we need to consider more than
one direction to describe one of these physical properties.
9. ▶ 1. Rank 0 Tensor:
The familiar scalar is the simplest tensor and is a rank 0 tensor. Scalars are just
single real numbers like ½, 99 or -1002 that are used to measure magnitude (size).
Scalars can technically be written as a one-unit array: [½], [99] or [-1002], but it’s
not usual practice to do so. •
Scalar:
Tensor of rank 0. (magnitude only – 1 component)
2. Rank 1 Tensor:
Vectors are rank 1 tensors. There are many ways to write vectors, including as an
array:
3. Rank 2 Tensor:
The next level up is a Rank 2 tensor, which can be represented by a matrix.
Matrices are rectangular arrays of numbers arranged into columns and rows (similar
to a spreadsheet). They have a rank of 2 because of the two-dimensional array •
Vector: Tensor of rank 1. (magnitude and one direction – 3 components) •
Dyad:
Tensor of rank 2. (magnitude and two directions – 3 2 = 9 components) •
Triad:
Tensor of rank 3. (magnitude and three directions – 3 3 = 27 components)