🚀 Main Idea: The oscillation of a pendulum can be compared and linked to the concept of circular motion, leading us to the idea of angular frequency.

🌈 Fun Real-world Analogy: Imagine two synchronized dancers. One dances in a circle (like whirling dervishes) while the other sways back and forth. When viewed from the side, their motions look the same. This is like our pendulum and the rotating sphere!

• Two metal spheres.
  • Sphere A: Acts as the pendulum's mass.
  • Sphere B: Mounted on a rotating turntable.
• Adjust the string's length so that pendulum's time period (T) matches the turntable's rotation time.

🎥 Visual Magic: If you illuminate this setup from the side and project it, the two spheres move in sync. Sphere B’s circular motion on the screen resembles Sphere A's pendulum movement!

Angular Speed (of the rotating sphere): Angular Speed = \(\frac {Angular\ Displacement\ (in radians)}{Time\ for\ one rotation}\)Time for one rotationAngular Speed=Time for one rotationAngular Displacement (in radians)​ Which is - =\(\frac {2π}{T}\)​

• From previous topics (A.2 and A.4), Angular Speed is denoted by ω = \(\frac {2π}{T}\)
• The relationship between T and ω: T= \(\frac 1f\)​ =\(\frac {2π}{w}\)

• It's like the "beat" of the pendulum!
• Uses the same symbol as angular speed, ω.
• It has the unit s⁻¹, similar to Hertz (Hz).
• Even though it's in rad×s⁻¹, we drop the radian because it’s unitless.