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Circular Thinking

Dive into the world of circular motion and forces, from rolling balls to trebuchets and boomerangs. Explore concepts like speed, acceleration, and inertia through creative and critical thinking. Join Ken McGregor on this exciting journey!

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Circular Thinking

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  1. Circular Thinking Ken McGregor

  2. Why? • It’s a challenge. • Can see & feel what’s going on. Instinctive gut reaction that might be right or wrong, but probably needs explanation. • Allows for creative & critical thinking – perhaps not so comfortable.

  3. A hollow world Frames of reference Rolling, sliding and spinning balls Snooker Collisions Trebuchet Circus see-saw A bola Half pipe Rolling Coin Why does a boomerang come back? Examples

  4. Building Blocks • Speed, acceleration, force & inertia • Having cycled on a bike or on a skateboard • Spinning a bucket of water.

  5. Hollow Planet

  6. ‘Forces’ on the surfaceThe world inside

  7. Letting a ball drop & Launching a ‘satellite’

  8. Coriolis Effect

  9. Frame of Reference

  10. Transit time 1 hr 20mins Same time no matter what arc is chosen.

  11. Can show the radial acceleration is And the transverse acceleration is Bug moving at steady speed along radial spoke of a wheel rotating at constant angular speed

  12. Rolling, sliding & Spinning Balls

  13. Slowing down while Rolling

  14. Questions • What would the rolling curve be like if you were inside a light rubber tyre that was rolling on the flat? • And if you were at the edge of a Yo-yo that was falling under gravity? • What would it feel like in both cases?

  15. Collisions

  16. Usually no spin given to the target ball Snooker Collisions

  17. Height of Rebounding Edge

  18. Circus See Saw – Teeterboard

  19. The angular acceleration on both sides must the same: • The work done on m must equal the work expended by M : • Combining these we get • So the moments on inertia must the same. • And not -

  20. A Bola

  21. No gain or loss of energy, until the balls strike • But angular momentum of the balls decreases as it’s imparted to the earth. • Balls strike post radially.

  22. R1 R2 m1 m2 Trebuchet

  23. If both arms have the same length: Without wheels, we get With wheels, we get

  24. Half Pipe – pumping for speed

  25. Rolling Coin

  26. Balance in the vertical gives • ‘Balance’ in the horizontal • This gives • If the basin is the bottom part of a shell: • then

  27. If the basin has a log shape i.e. • Then • We then get • And so • i.e. a constant

  28. Boomerang

  29. Concepts • Stimulates 3D visualisation, through not essential • Doesn’t need to be mathematical – simple algebra is enough • Don’t need to specify moment of inertia • Experience with a bucket of water • Don’t need to specify torque • Just the example of a spanner and nut

  30. THANK YOU FOR YOUR ATTENTION • Questions, comments, other experiences? • kwmcgregor@optusnet.com.au

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