Fisika kelas X - Vektor part 1 - Cara Menggambar dan Menghitung Vektor

Main ideas & lessons (Physics: Vectors in Grade X)

Vectors vs. scalars

• Vector: has magnitude (value) and direction.
• In physics, priority is often the direction because quantities like:
  • force (F)
  • acceleration
  • velocity / speed
  • displacement

behave as vectors.

• If a quantity has no direction, it is treated as a scalar.

Cardinal / compass directions

• Directions such as North, East, South, West are emphasized.
• Also intermediate directions:
  • NE (between North & East)
  • SE (between East & South)
  • SW (between South & West)
  • NW (between West & North)
• These are used to interpret where a motion/force points.

Trigonometry as prerequisites for vector problems

The video stresses that vector components and resultant calculations require memorizing core trig values.

• Special angles to memorize: 0°, 30°, 45°, 60°, 90° (and also commonly 37° and 53°)

• Common relationships:

  • Often illustrated with sine–cosine symmetry
  • tangent as opposite/adjacent in right triangles

• Pythagorean (right-triangle) relationships used repeatedly:

  • [ \tan \alpha = \frac{\text{front}}{\text{side}} ]

  • [ \sin \alpha = \frac{\text{front}}{\text{diagonal}} ]

  • [ \cos \alpha = \frac{\text{side}}{\text{diagonal}} ]

• Angle naming:

  • Angle can be (\alpha) or (\theta) depending on the question.
  • Trig definitions use the angle relative to a chosen reference (commonly the positive x-axis).

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Methodology / step-by-step instructions

A) How to draw and add vectors (resultant vectors)

1) Choose a scale and drawing approach

• Use a ruler/scale so the vector length on the drawing matches its magnitude.
• Drawing errors affect the resultant length, so keep the scale accurate.

2) Understand vector notation

• A vector quantity is shown with an arrow above the symbol (e.g., (\overrightarrow{A}), and expressions like (\overrightarrow{A+B})).
• The arrow indicates the quantity has direction.

3) Add vectors using two main geometric methods

(i) Polygon (head-to-tail) method

• Goal: construct the resultant (\vec{A}+\vec{B}) (and extend to more vectors).
• Steps:
  • Draw vector A.
  • From the end of A, draw vector B in its direction.
  • The vector from the start of A to the end of B is the resultant.
• Terms:
  • The final vector is the resultant of (\vec{A}+\vec{B}).

(ii) Parallelogram method

• Goal: get the resultant of (\vec{A}+\vec{B}) as the diagonal of a parallelogram.
• Steps:
  • Place vectors A and B starting from the same origin point.
  • Complete the parallelogram using parallel lines.
  • The resultant is the diagonal from the origin to the opposite corner.
• For multiple vectors (like (\vec{A}+\vec{B}+\vec{C})):
  • Add two vectors first (get an intermediate resultant),
  • then add the next vector using the same idea.

4) Handling subtraction: (\vec{A}-\vec{B})

• Subtracting a vector means adding the opposite direction: [ \vec{A}-\vec{B}=\vec{A}+(-\vec{B}) ]

• If (\vec{B}) points one way, (-\vec{B}) points exactly opposite.

5) Resultant meaning (important)

The resultant must include:

• the length (magnitude) and
• an arrow direction (where it points).
• When computing from drawings, the resultant length comes from the scale-drawn vector.

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B) Calculating vector components (1 vector split into x- and y-components)

Key definitions used

The vector is split into:

• x-axis component (often (F_x))
• y-axis component (often (F_y))

“Near vs far” triangle logic:

• Component adjacent to the angle → uses cos
• Component opposite to the angle → uses sin

Procedure

• Draw the vector with angle (\alpha) relative to the positive x-axis.
• Construct a right triangle (using parallelogram/axes logic).

• Compute:

  • [ F_x = F\cos(\alpha) ]

  • [ F_y = F\sin(\alpha) ]

• Determine sign (+/−) using quadrant/axis direction:

  • Right (positive x) → (+) for x-component
  • Left (negative x) → (−) for x-component
  • Up (positive y) → (+) for y-component
  • Down (negative y) → (−) for y-component

Special case

• If the vector lies exactly along the x-axis, one component becomes 0 (no perpendicular “height”).

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C) Calculating resultant of 2 vectors (magnitude)

Case 1: Vectors form a right angle (perpendicular)

• Use Pythagoras:
  • resultant magnitude = hypotenuse: [ \sqrt{F_1^2 + F_2^2} ]

Case 2: Vectors form an angle (\alpha) (not necessarily 90°)

• Use the cosine rule:

For addition: [ |\vec{A}+\vec{B}|=\sqrt{F_1^2+F_2^2+2F_1F_2\cos\alpha} ]

For subtraction (difference magnitude): [ |\vec{A}-\vec{B}|=\sqrt{F_1^2+F_2^2-2F_1F_2\cos\alpha} ]

• Plus version → addition
• Minus version → subtraction

Interpretation tip

The formulas depend on the angle between the vectors, not just their individual directions.

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D) Finding the direction (angles) of the resultant using the Sine Rule

When it’s used

• When asked for the angle between:
  • the resultant and one given vector, or
  • the direction of the resultant in a triangle formed by two vectors.

Method (conceptual)

• Use the vector triangle and the sine rule:

  • The video describes it as: “Resultant divided by sine of its opposite angle equals the other sides divided by their sines.”

• Steps implied:

  1. Compute the resultant magnitude first (via cosine rule / Pythagoras).
  2. Use the sine rule to determine angle(s).
  3. Use special values when possible; otherwise use arc-sin.

Arc-sin note

• If (\sin(\beta)) doesn’t match a memorized special angle: [ \beta=\arcsin(\text{value}) ]

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Speaker(s) / sources featured

• Primary speaker/host: the YouTube narrator (referred to in subtitles as “little brother” / “koko” / “Koko”).
• Other voices: none clearly identifiable (instructional narration and music only).
• Source material: no separate external documentary/source is cited—this is the video’s physics explanation.