Gerak Melingkar • Part 1: Sudut Radian & Gerak Melingkar Beraturan (GMB)

Introduction

This tutorial is designed to explain the concepts of circular motion, specifically focusing on radians and uniform circular motion (Gerak Melingkar Beraturan, GMB). It will guide you through key definitions, relationships, and formulas necessary for understanding these concepts, as presented in the video by Jendela Sains.

Step 1: Understanding Radian Measure

• Definition of Radian: Radian is a unit of angle measurement where one radian is the angle subtended at the center of a circle by an arc whose length is equal to the radius of that circle.
• Conversion Between Units:
  • To convert degrees to radians:
    • Use the formula:

      Radians = Degrees × (π / 180)
      

  • To convert radians to degrees:
    • Use the formula:

      Degrees = Radians × (180 / π)
      

  • To convert between full rotations and radians:
    • 1 full rotation = 2π radians.

Step 2: Positioning in Mechanics

• Application of Circular Motion: Understand that circular motion is a fundamental concept in mechanics, where an object moves along a circular path.
• Key Concepts:
  • Circular motion can be uniform (constant speed) or non-uniform (changing speed).

Step 3: Key Quantities in Uniform Circular Motion

• Frequency (f): The number of complete rotations per unit time (e.g., revolutions per second).
• Period (T): The time taken for one complete rotation.
  • Relationship:

    T = 1 / f
    

• Angular Velocity (ω): The rate of change of angular displacement, measured in radians per second.
  • Given by:

    ω = 2πf
    

• Linear Velocity (v): The tangential speed of an object in circular motion, calculated as:

  v = r × ω
  

  where r is the radius of the circular path.

Step 4: Centripetal Acceleration and Force

• Centripetal Acceleration (a_c): The acceleration directed towards the center of the circular path, calculated using:

  a_c = v² / r
  

• Centripetal Force (F_c): The net force required to keep an object moving in a circular path, directed towards the center. It can be calculated using:

  F_c = m × a_c
  

  where m is the mass of the object.

Conclusion

In this tutorial, we covered the essential concepts of radians and uniform circular motion, including key formulas for frequency, period, angular velocity, linear velocity, centripetal acceleration, and centripetal force. These principles are foundational for further studies in physics, particularly in mechanics. For a deeper understanding, consider watching the subsequent parts of the Gerak Melingkar series on the Jendela Sains channel.