PENDULUM SUMMARY NOTES

🎯 Objectives: TO GET OVERVIEW IDEA ON PENDULUM

The Complete Theory of Pendulum

The Complete Theory of Pendulum (Physics Made Fun!)

🌍 History of the Pendulum

The pendulum was first studied by Galileo Galilei in the late 1500s. He discovered that the time it takes for a pendulum to swing does not depend on how far it swings — this was the first step in using pendulums to measure time!

Later, Christiaan Huygens used pendulums to make the first precise clocks. Pendulums became a key part of science, engineering, and education.

🔍 What is a Pendulum?

A pendulum is a weight (called a bob) hanging from a string that swings back and forth due to gravity.

Simple Pendulum: A string and a small bob swinging from a fixed point without air resistance or friction.

⚙️ Parts of a Pendulum

  • Point of Suspension: Where the pendulum is attached.
  • String: The length from suspension point to the center of the bob.
  • Bob: The mass that swings.
  • Equilibrium Position: The rest position of the pendulum.

🧪 Working Principle

When the pendulum bob is lifted and released, it converts potential energy into kinetic energy. It moves in a regular rhythm (called oscillation).

📏 Formula and Calculations

The time period (T) of a pendulum is the time it takes to complete one swing (to and fro).

Formula: \[ T = 2\pi \sqrt{\frac{L}{g}} \] Where:
  • T = Time period (seconds)
  • L = Length of the pendulum (meters)
  • g = Acceleration due to gravity (9.8 m/s²)

📊 Graph of T² vs L

🧠 Fun Facts About Pendulums

  • Pendulums were used in ancient seismographs to measure earthquakes.
  • Pendulum clocks ruled the world before digital watches!
  • The Eiffel Tower can act like a giant pendulum when strong winds blow.

📈 Example Problem:

A student swings a 0.5 m long pendulum and finds the time for 10 swings is 14.2 seconds. What is the value of g?

Solution: T = 14.2 / 10 = 1.42 s
T² = (1.42)² = 2.0164
Use T² = (4π²/g)L → g = 4π²L / T²
g = (4 × 9.8696 × 0.5) / 2.0164 ≈ 9.75 m/s²

📽️ Interactive Video:

Enjoy learning physics and explore the magic of how nature works in rhythmic beauty. 🌟

📖 Reference Book: Tanzania Institute of Education. (2009–2013). *Physics Book 1–4*. Dar es Salaam: TIE. Ngoma, D. K. (2012). *Practical Physics for Secondary Schools Book 3 & 4*. Oxford University Press. Mussa, I. E. (2015). *Physics Made Simple for Secondary Schools*. Nyambari Nyangwine Publishers. National Examinations Council of Tanzania. (2010–2023). *NECTA O-Level Physics Past Papers*. Retrieved from https://www.necta.go.tz Anyakoha, M. W. (2002). *New School Physics for Senior Secondary Schools*. Africana-FEP Publishers. Nelkon, M., & Parker, P. (1995). *Advanced Level Physics*. Heinemann Educational Books.

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