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Circular Thinking

Circular Thinking. Ken McGregor. 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. A hollow world Frames of reference

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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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