FISIKA VEKTOR KELAS XI [FASE F] PART 1 - KURIKULUM MERDEKA

Summary

This educational script introduces the fundamental concepts of vectors and scalars, emphasizing the importance of understanding their differences. It explains that scalars have magnitude without direction, exemplified by mass, while vectors have both magnitude and direction, illustrated with potential energy. The script delves into vector description, showing how to represent them with arrows and points, and discusses methods for vector addition and subtraction, including the triangle and parallelogram methods. It also covers the cosine formula for determining the magnitude of the resultant vector, providing an example problem to solidify the concepts.

Takeaways

• 📚 The first objective of the lesson is to understand vector calculation operations using various methods.
• 🔍 The second objective is to identify vector components and describe vectors in detail.
• 📏 Scalars are quantities with magnitude but no direction, such as mass, which is exemplified by 10 kg of rice.
• 🧭 Vectors are quantities with both magnitude and direction, differing from scalars by having directional properties.
• 🦏 An example of a vector is potential energy, demonstrated by an elephant moving from top to bottom, indicating a directional movement.
• 📐 Vectors are described by their starting point (anchor point), ending point (tip), magnitude, and direction, often represented with an arrow.
• 📉 The magnitude of a vector is its length, and the direction is usually given in degrees, like a vector AB with a magnitude of 50 meters and a direction of 30°.
• ✍️ Vectors are written with a symbol and a size, where the symbol is marked with an arrow, such as acceleration or force vectors.
• 🔄 Vectors can be added or subtracted using methods like the triangle method, parallelogram method, and polygon method to find the resultant vector.
• ➡️ The triangle method involves arranging vectors head-to-tail to form a triangle and finding the resultant as the diagonal.
• 🟪 The parallelogram method involves placing vectors tail-to-head to form a parallelogram, with the resultant being the diagonal.
• 🔢 The cosine formula is used to determine the magnitude of the resultant vector, expressed as \( r = \sqrt{a^2 + b^2 + 2ab \cdot \cos(\alpha)} \), where \( a \) and \( b \) are vector magnitudes and \( \alpha \) is the angle between them.
• 📌 Understanding the cosine formula and special angle trigonometric values is essential for solving vector problems.

Q & A

What is the fundamental difference between scalar and vector quantities?

Scalar quantities have only magnitude without direction, such as mass. Vector quantities have both magnitude and direction, such as velocity.

Can you provide an example of a scalar quantity mentioned in the script?

An example of a scalar quantity given in the script is the mass of rice weighing 10 kg, which has magnitude but no direction.

How is a vector quantity described in the script?

A vector quantity is described by its magnitude and direction. For instance, the script describes the movement of an elephant from top to bottom as a vector quantity because it has a direction.

What are the two main components of a vector mentioned in the script?

The two main components of a vector are its magnitude and direction. The script uses the example of vector OB where OB represents both the magnitude and the direction of the vector.

How can the magnitude and direction of a vector be represented?

The magnitude of a vector can be represented by the length of the vector, and the direction can be represented by an angle, as shown in the script with vector AB having a magnitude of 50 meters and a direction of 30°.

What is the significance of the anchor point and the tip of the vector in describing vectors?

The anchor point is the starting point of the vector, and the tip is the endpoint, usually marked with an arrow to indicate direction. Knowing these helps in the correct depiction and understanding of vector directionality.

According to the script, how can two vectors be considered the same?

Two vectors are considered the same if they have the same magnitude and direction, as explained in the script with the example of two vectors both having a magnitude of 50 and a direction of 30°.

What is the triangle method for adding vectors as described in the script?

The triangle method for adding vectors involves placing the vectors head-to-tail to form a triangle, with the resultant vector being the third side of the triangle, as demonstrated with vectors A and B in the script.

What is the parallelogram method for adding vectors, and how does it differ from the triangle method?

The parallelogram method for adding vectors involves placing the vectors tail-to-tail to form a parallelogram, with the resultant vector being the diagonal of the parallelogram. It differs from the triangle method in the arrangement of the vectors and the shape formed.

How does the script explain the concept of vector subtraction?

The script explains vector subtraction by considering one vector as having a negative value, effectively reversing its direction, and then adding it to the other vector using the parallelogram method to find the resultant vector.

What is the cosine formula used for in the context of vector addition, and how is it applied?

The cosine formula is used to determine the magnitude of the resultant vector when adding two vectors. It is applied using the formula R = √(A² + B² + 2ABcos(α)), where A and B are the magnitudes of the vectors and α is the angle between them, as demonstrated in the script with an example problem.

Outlines

00:00

📚 Introduction to Scalars and Vectors

This paragraph introduces the fundamental concepts of scalar and vector quantities. Scalars are quantities with magnitude but no direction, exemplified by mass, which has a value like 10 kg but no directional component. Vectors, in contrast, have both magnitude and direction, such as potential energy, which can be demonstrated by an elephant moving from top to bottom, indicating a directional movement. The paragraph emphasizes the importance of understanding the difference between these two types of quantities and encourages learners to explore more examples of scalar and vector quantities.

05:07

📝 Describing Vectors and Their Components

The second paragraph delves into the description of vectors, using a simple conceptual model where a vector is represented as a line with an arrow. The anchor point is labeled 'O' and the tip 'B', with 'OB' representing both the magnitude and direction of the vector. An example is given with vector 'AB' having a magnitude of 50 meters and a direction of 30°. The paragraph explains the importance of knowing the anchor and tip of a vector and how to denote vectors with symbols and their magnitudes.

10:09

🔍 Vector Equality, Addition, and Subtraction Methods

This paragraph discusses the criteria for vector equality, which is based on both magnitude and direction being the same. It contrasts this with vectors that differ either in magnitude or direction. The concept of vector addition and subtraction is introduced, with the triangle method being the first technique explained, where vectors A and B are placed head-to-tail to form a triangle, and the resultant is the third side. The paragraph also touches on the parallelogram method and the polygon method for adding multiple vectors, highlighting the importance of understanding positive and negative vector values.

15:16

📐 Advanced Vector Operations: Parallelogram and Polygon Methods

The fourth paragraph expands on vector addition methods, focusing on the parallelogram method and the polygon method for adding more than two vectors. It provides a step-by-step explanation of how to graphically represent the addition of vectors using these methods, emphasizing the concept of positive and negative values and their impact on the direction of the resultant vector. The paragraph also explains vector subtraction using the parallelogram method, illustrating how a negative vector value affects the outcome.

20:22

🧮 Calculating Resultant Vectors Using the Cosine Formula

The final paragraph introduces the cosine formula as a method for determining the magnitude of the resultant vector when adding two vectors. It presents the formula R = √(A² + B² + 2ABcosα) and explains its components, where 'A' and 'B' are the magnitudes of the vectors, and 'α' is the angle between them. An example problem is provided where two vectors of magnitudes 5 and 3 units form a 60° angle, and the formula is used to calculate the resultant vector's magnitude, which is found to be 7 units. The paragraph concludes with a reminder of the importance of knowing trigonometric values for special angles in solving vector problems.

🗣️ Closing Remarks and Invitation for Feedback

In the concluding paragraph, the script invites viewers to understand the concepts discussed and encourages those who have difficulties to leave comments for further clarification. The speaker offers to close the session and ends the video, expressing gratitude for the viewers' attention.

Keywords

💡Vector

A vector is a mathematical object that has both magnitude (size) and direction. In the context of the video, vectors are fundamental to understanding physical quantities that have directional properties, such as force or velocity. The script uses the concept of vectors to explain their difference from scalars and how they can be described and manipulated through operations like addition and subtraction.

💡Scalar

A scalar is a quantity that has magnitude but no direction. In the video, the concept of scalars is introduced to contrast with vectors. An example given is mass, which has a measurable value but does not inherently have a direction, unlike vectors.

💡Magnitude

The magnitude of a vector represents its size or length. In the script, the magnitude is discussed in the context of vector addition and subtraction, where it is one of the key components that determine the resultant vector's size, along with direction.

💡Direction

Direction refers to the orientation of a vector in space. The script emphasizes the importance of direction in distinguishing vectors from scalars and in calculating the resultant of vector operations, often represented by angles in the context of the video.

💡Resultant

The resultant is the outcome of adding or subtracting vectors, which can be found using various methods like the triangle rule or the parallelogram rule. The script explains how to determine the magnitude and direction of the resultant vector from the given vectors.

💡Triangle Method

The triangle method is a technique for adding vectors by placing them head-to-tail to form a triangle, with the resultant vector being the closing side of the triangle. The script uses this method to illustrate the addition of vectors with different directions.

💡Parallelogram Method

The parallelogram method involves adding vectors by placing them tail-to-head to form a parallelogram, with the diagonal representing the resultant vector. The script explains this method and contrasts it with the triangle method for visualizing vector addition.

💡Polygon Method

The polygon method is a generalization of the parallelogram method for adding more than two vectors. The script briefly mentions this method as a way to add multiple vectors, starting from the first vector and sequentially adding the others to find the overall resultant.

💡Cosine Formula

The cosine formula is used to calculate the magnitude of the resultant vector when vectors are known to form a specific angle with each other. The script provides an example using this formula to find the resultant of two vectors that form a 60-degree angle.

💡Special Angles

Special angles, such as 30°, 45°, 60°, and 90°, have predefined trigonometric values that are essential for solving vector problems. The script mentions the need to memorize the cosine values for these angles to simplify calculations in vector operations.

Highlights

Introduction to the concept of scalar and vector quantities, emphasizing their fundamental differences in having or lacking direction.

Explanation of scalar quantities with the example of mass, illustrating how they have magnitude but no direction.

Introduction to vector quantities, characterized by having both magnitude and direction, using potential energy as an example.

Description of how to represent vectors graphically, including the notation and components such as the anchor point and the tip marked with an arrow.

Illustration of vector magnitude and direction through a simulation, showing the movement of an elephant to explain directional values.

Discussion on the importance of understanding the anchor point and tip of a vector for correct vector description.

Introduction to the concept of vector addition and subtraction, and the resultant vector produced from these operations.

Explanation of vector addition using the triangle method, showing how to combine vectors in different directions to form a triangle.

Clarification on the concept of negative vectors and their representation in the context of addition and subtraction.

Practical example of adding vectors using the triangle method, with vectors A and B having magnitudes of 12 and 5 Newtons respectively.

Introduction to the parallelogram method for vector addition, explaining how to form a parallelogram to find the resultant vector.

Description of the polygon method for adding multiple vectors, outlining the steps to find the resultant of more than two vectors.

Discussion on the concept of vector subtraction using the parallelogram method, illustrating how to handle negative vector values.

Introduction to the cosine formula for determining the magnitude of the resultant vector, providing a mathematical approach to vector operations.

Presentation of two equations related to the angle and magnitude of vectors, essential for understanding the relationship between vector components.

Example problem solving using the cosine formula, demonstrating how to calculate the resultant of two vectors forming a 60° angle with magnitudes of 5 and 3 units.

Emphasis on the importance of memorizing the values of trigonometric functions for special angles in vector calculations.

Conclusion summarizing the key concepts covered in the video, encouraging viewers to ask questions for further clarification.

Transcripts

Our first title this time is about vectors, okay, firstly,

there are two objectives for our learning. Firstly, identify vector calculation operations using various

methods. Then secondly, identify vector components and describe vectors.

Okay, the first thing we will discuss is about scalar quantities and quantities.

vector so this is fundamental for all friends to understand

what a vector is okay the first thing we will discuss is what is the meaning of a scalar quantity

a scalar quantity is a quantity that has a value

but has no direction okay so here friends have to understand what is the difference between

values and there is no direction here I have given an example, the example is mass.

Okay, for example here we have rice which weighs 10 kg, which means this rice

has a value, namely a weight value, yes, the weight value is 10 kg, then we weigh it,

resulting in a value of 10 KG, but the rice has 10 This kg has no direction

or we automatically make it immobile or static so the definition of a

scalar quantity is a quantity that has value but has no direction. There are still many examples of

scalar quantities, friends, please share your own search in books or on the internet, then

we will discuss Regarding vector quantities,

vector quantities are quantities that have a value and have a direction,

so we can see the difference between a scalar and a vector,

the difference is whether they have a direction or not, whereas the scalar quantity has a value

but no direction, but a vector quantity is a quantity that has a value and has a direction.

direction, for example, is potential energy, we can see here here I made a simulation that

this elephant has a weight value or mass value, then this elephant moves from top to bottom. This

means there is a direction value, the direction value is from top to bottom

, so there is a movement process that happens and that is the value of a vector quantity

and there are still many examples of vector quantities, friends, please look for them yourself so that you

understand everything thoroughly, what are the examples of scalar quantities and

vector quantities? Here I am just running in general, so here we add the first physics concept

in our material, the first to recognize vectors, is that scalar quantities are quantities that

only have value but no direction, meanwhile vector quantities are quantities

that have value and direction. This is one of the concepts in our first chapter of material.

OK, let's continue. to the next sub-chapter How to describe vectors

OK vector here I have created a simple concept How to describe vectors vector

is a long line yes and this long line requires an arrow clearly

like this here we have an arrow Oh is the vector capture point while B

is the tip of the vector OB is the magnitude of the vector and OB is also the direction of the vector. OK, let's try to simulate it

in the form of a value here, AB, yes, the length is 50 meters. This length means the magnitude of Ab is

50 meters. The direction of the vector AB here already has a value, right, 30°, which means direction vector AB 30°

so this is an important component. How do we understand how to describe

vectors? We have to know which is the anchor point of the vector and which is the tip of the vector. Yes, the tip of the vector

is usually marked with an arrow and the vector capture point does not have an arrow,

so it is still in the middle. In describing vectors here we also need to know

how to write vectors correctly, so writing vectors here consists of two, yes,

there is a vector symbol and there is a vector size. Usually the vector symbol is marked with

an arrow on it. Yes, the notation looks like this. This is an example of

acceleration . and this is a force means this is a vector quantity

okay vector quantity but this is one of the symbols then How to

determine the size of a vector to determine the size of a vector is depicted like this so

this is to determine the vector symbol and

this is to determine the size of a vector to write the actual vector

then here we make the first comparison, two vectors are said to be the same if their

magnitude and direction are the same. Okay, if two vectors are said to be the same, then their magnitude and direction are the same.

for example like this the magnitude is the same as 50 50 But the direction of the vector is also the same yes 3030

this is if two vectors are said to be the same then if for example we make 2 vectors they are said to be different

meaning perhaps the magnitude is the same but the direction is not the same here the magnitude is the same

as 50 but the direction is different this one is equal to 30° and this is 120

degrees, which means these two vectors are not the same even though the magnitude is the same.

OK, so friends, you have to understand what the difference is between the magnitude of a vector and the direction of the vector.

The direction of the vector is usually in the form of an angle, while the magnitude of the vector is. What is the value of the vector?

OK, we Entering the addition and subtraction of vectors, so the properties of vectors can be added

or subtracted to produce a result where this result is said to be the resultant of

a vector. So there are several methods that we use to determine the addition and subtraction

of vectors. OK, the first thing we will discuss is adding vectors using the method. triangle,

okay, here we already have vector A and vector B in different directions, then

we have to draw it, we have to draw vector A and vector B so that it forms a

triangle, vector A goes to the right, then vector B goes upwards, OK? And this is the

catch point, then what this is the tip of the vector then we pull it so that this is

the resultant value which means the sum of the resultants is a plus B then we need to understand that for

negative B values ​​it is in the opposite direction of vector B if the direction of vector B upwards is positive

meaning the negative value is in the opposite direction meaning this is a negative vector B value

the same as vector a, if vector a is to the right, the value is positive, meaning for vector a

the negative value is opposite to the direction of vector a, meaning the direction is to the left,

yes. And this is conditional, depending on the type of problem, which means the direction of vector a is negative,

yes, depending on the type of problem, then in here we make it into an example of

two vectors A and B where vector a has a magnitude of 12 newtons to the right

and vector B has a magnitude of 5 n to the right as in the following picture,

this is vector A and this is vector B. Determine the magnitude of the two vectors If

we add them using the triangle method, okay, here it's easier, just sort them

alphabetically, A and B, we start from vector A, this is vector A and

this is the capture point, then we start again from vector B, vector B in the downward direction.

Okay, so the shape is like this, this is vector A and this is vector B, we give the notation sign which

states that this is a vector, then we draw the resultant line and this is the resultant line

, meaning the resultant is the magnitude of vector a + the magnitude of vector B. The value of vector a

is 12 12 plus vector B, the value is 5 means that the sum of the resultant between vector

A and vector B is 17 Newtons, so this is actually still quite easy for

all of you to do, so here we have to understand how to describe vectors

and here we haven't found the size of the resultant, so we just looking for the result of adding vectors,

we will discuss later how to find the result or size of the resultant.

OK, then we enter the second method of adding vectors using the parallelogram method.

Here we have vector A and vector B, then we draw it to produce

a method whose image looks like a parallelogram. Then, to draw the resultant value right

from point O, we pull it upwards so that a parallelogram is formed

and the sum of the resultants, so vector A remains the same, vector A plus vector B,

this is the parallelogram method, then adding vectors using the polygon or polygon method,

so in here there are vectors that are more than one or more than 2, that's called the polygon

or polygon method, here I made an example, there are 3, there is vector a, there is vector B and vector c.

How to describe it is simple, we just start from the letters, letters a,

b and c. We adjust here we make the resultant value the sum of everything, yes, at the beginning

it was explained that this has positive and negative values, yes, the positive value is to the right,

which means the negative value is to the left, yes, that means, for example, if the value B is positive, it is upwards, which means

the negative value is downwards. If the positive value of c is upwards, it means it seems to be downwards.

Now we just take the sum, vector a, this is vector a, the arrow

then we start again from vector B, which is the capture point, we enter it

here to produce vector B and this is the tip of vector B then we enter vector C if we drag it.

Now this is the value of the resultant addition using the polygon method. Yes, that means this is the resultant

vector a + vector B plus vector C. This is the addition of vectors using the polygon method.

The concept is the same as at the beginning. We have to know how to do it. depicting vectors,

then earlier we discussed selling vectors using the parallelogram method

and now to understand how the subtraction is the same, if for example

we make a subtraction, it means that the value of B, we already considered the value to be positive,

yes, the value of a is already positive, then if we draw it using the parallelogram method

produces a subtraction value, meaning vector B has a negative value downwards,

meaning this is a negative vector B value,

vector B value is negative, while a has a negative vector value to the left, so friends, you have to

understand how vectors have positive values ​​and negative values ​​if we draw them

between Vector A is positive with vector B negative using the parallelogram method, meaning the direction is like

this, vector A is to the right, then this vector B is negative, downwards, yes, this means that here

the tip of the vector is the tip of the vector, we pull it between the two vectors from point O, which is the

capture point and produces The value of the resultant value is positive, vector A and vector B are negative

, so subtracting the vector is the size of vector A minus the size of vector B,

so this is the concept of reducing vectors using the parallelogram method.

OK, then now we go in. How to determine the size of the resultant vector using

the cosine formula, so it's easy for us to determine how big it is. The resultant

uses the cosine formula because it is easier to understand and it is quicker for us

to solve the equation. For example, here, from the parallelogram method,

the resultant value is here, but here we do not discuss the addition and subtraction

of vectors, but we discuss how the resultant value is to determine the result

of The resultant value of the equation is a squared plus b squared plus 2 ab cos Alfa

yes this is the first equation then the second equation which is related to the angle yes

and the angle and the magnitude of the vector the equation is r/sin Alfa = B per Sin Theta = Al per Sin

Alpha minus Teta, so here are two equations that all of you have to understand,

a is the size of vector a, which means the size of vector a, here

this is the size of the vector, ab is the size of vector B, which is the size of the vector,

then

the size of the resultant between vectors a and b is vector A and vector B and this is

the resultant value for simplicity. Let's discuss the following example problem. Two vectors a

and b each form an angle of 60° with each other. Vector A and vector B, for example, let's make this one

a vector A and this one is vector B, this is vector B, this one is vector A and forms an angle of 60°

if the lengths of the two vectors are 5 and 3 units, this is in order, yes, that

means this one is a, this one is B, this means that a, this is 5 units, that B is

3 units, that means if it's like that, it's too long, so let's

shorten it first

, the length is 3 units

, this is the length of the resultant of the two vectors, we want to find

what the resultant value is, if we want to use the parallelogram method, that means

we draw it between the two vectors A and vector B. so that it produces

an image like a parallelogram. Let's say the image is like this. Yes,

the image is not very good, but the result is like this.

Okay, then we immediately enter the equation. That means r = root of a squared plus b squared

plus 2 ab cos. Alpha value of a is 5. Yes, that means root of 5 quadrant plus

B the value is 33 squared plus 2 multiplied by 5 multiplied by 3 multiplied by cos 60

then we solve for 5 squared this is 25 then 3² 9 plus 2 times 5 10 10 * 3 30

yes, 30 multiplied by cos 60 is 1/2, so you all have to memorize the value of sine cosine Tangent

of special angles is a prerequisite for all friends to be able to solve

problems on vectors then here we solve it here 30 divided by 25

then if we solve it means the result here is 49 roots of

49 what the result is 7 means the resultant of the two vectors a and b is 7 units

OK OK, this first part of the video, hopefully all of you can understand it conceptually

and in terms of So, for friends who still don't understand, please

write in the comments column, I will close it and I will end it, thank you