Besaran Vektor | Vektor | Part 1 | Fisika Dasar

Introduction

This tutorial is designed to help you understand the fundamental concepts of vectors in basic physics. By following these steps, you'll gain a clearer understanding of what vectors are, their properties, and how they apply to various physical scenarios.

Step 1: Understand the Definition of Vectors

• What is a Vector?

  • A vector is a physical quantity that has both magnitude and direction.
  • Examples include displacement, velocity, acceleration, and force.

• Difference from Scalars

  • Scalars only have magnitude (e.g., temperature, mass).
  • Vectors require both magnitude and direction for their complete representation.

Step 2: Identify Vector Components

• Breaking Down Vectors

  • Any vector can be resolved into components, typically along the X and Y axes.
  • For a vector ( A ):
    • ( A_x = A \cdot \cos(\theta) )
    • ( A_y = A \cdot \sin(\theta) )

• Practical Tip

  • Always sketch the vector and label its components to visualize the direction and magnitude better.

Step 3: Vector Addition

• How to Add Vectors

  • Use the head-to-tail method: Place the tail of one vector at the head of another.
  • The resultant vector is drawn from the tail of the first vector to the head of the last vector.

• Mathematical Addition

  • For two vectors ( A ) and ( B ):
    • ( R_x = A_x + B_x )
    • ( R_y = A_y + B_y )
    • Resultant vector ( R = \sqrt{R_x^2 + R_y^2} )

Step 4: Vector Subtraction

• Understanding Vector Subtraction

  • To subtract vector ( B ) from vector ( A ), reverse the direction of ( B ) and then apply the vector addition method.

• Mathematical Subtraction

  • For vectors ( A ) and ( B ):
    • ( R_x = A_x - B_x )
    • ( R_y = A_y - B_y )

Step 5: Scalar Multiplication of Vectors

• What is Scalar Multiplication?

  • When you multiply a vector by a scalar, you change its magnitude but not its direction.
  • For a vector ( A ) and a scalar ( k ):
    • ( B = k \cdot A )

• Example

  • If ( A = 5 ) units in the positive x-direction and ( k = 2 ), then ( B = 10 ) units in the positive x-direction.

Step 6: Understanding Unit Vectors

• What are Unit Vectors?

  • A unit vector has a magnitude of one and indicates direction.
  • Commonly represented as ( \hat{i} ) (for x-direction) and ( \hat{j} ) (for y-direction).

• Creating Unit Vectors

  • For any vector ( A ):
    • ( \hat{A} = \frac{A}{|A|} )

Conclusion

Understanding vectors is fundamental in physics as they describe a wide range of physical phenomena. Remember to:

• Differentiate between vectors and scalars.
• Break down vectors into components for simpler calculations.
• Use vector addition and subtraction techniques to analyze physical situations.

Following these steps will enhance your grasp of vectors and prepare you for more advanced topics in physics. Continue practicing with vector problems to solidify your understanding!