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A Physicists Approach to Springboard Diving

A Physicists Approach to Springboard Diving. Edward N. Roberts University of the South, Sewanee March 6 th 2002. A Question Posed to Physicists:.

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A Physicists Approach to Springboard Diving

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  1. A Physicists Approach to Springboard Diving Edward N. Roberts University of the South, Sewanee March 6th 2002

  2. A Question Posed to Physicists: • Is it possible for a somersaulting springboard diver to initiate a twisting motion without any torque being applied to their body? That is, can a diver begin to twist after having left the diving board?

  3. Answer: • Yes • Physics Department at Cornell University: • Interestingly 56%* of those asked the question answered incorrectly. *Frohlich, Cliff “Do springboard divers ...”, Am.J.Phys.47(7), July 1979.

  4. Laws of Physics applicable to the sport of Diving • Center of Mass • Angular Velocity • Moments of Inertia • Principle of Acceleration • Many more...

  5. Why even talk about the physics of Diving? Laws of Physics applicable to the sport of Diving

  6. Terminology used in Diving: • The Approach • The Hurdle • Categories of dives: • Forward • Back • Reverse • Inward • Twister

  7. Terminology used in Diving: • Four positions of dives: • Straight • Pike • Tuck • Free

  8. Flight of a Dive • Rotation around Center of Mass • Parabolic Flight of Dives • What can be determined from this?

  9. Flight of a Dive • Equations of Motion:

  10. Parabolic flight of a dive

  11. Parabolic flight of a dive

  12. Conservation of Angular Momentum • Conservation of Angular Momentum Equation: • Angular Velocity Equation is:

  13. Moments of Inertia: • Moments of Inertia must be determined: • Assumptions: • Rigid Body • Density Distribution equally • 14 Separate parts • Represent simple Geometric shapes

  14. Calculation of the Inertia: Thin Rod Cylinder: Sphere: Solid Cylinder:

  15. Calculation of the Mass Chart: Stanley Plagenhoef, Patterns of Human Motion (Englewood Cliffs, NJ:Prentice-Hall, 1971), chapter 3

  16. Calculation of the Mass:

  17. Calculation of the Inertia: • The Parallel-Axis Theorem: • “Relates the moment of inertia about an axis through the center of mass of an object to the moment of inertia about a second parallel axis.”

  18. 14 Separate parts diagramExample Calculation

  19. 14 Separate parts diagramExample Calculation

  20. Calculation of distance from Axis of Rotation

  21. Calculation of distance from Axis of Rotation

  22. Videopoint Calculation of  • Center of Mass used as the origin • Plotted the rotation of the head around the center of mass

  23. Example of Tuck  calculation

  24. Calculated moment of Inertia for the tuck position: I = 5.30 kgm2  = 560 °/s = 9.60 rad/s L = 50.9 kgm2/s Conservation of Angular Momentum Calculated moment of Inertia for the straight position: I = 15.7 kgm2  = 115 °/s = 2.01 rad/s L = 31.5 kgm2/s • 31.5 kgm2/s = 50.9 kgm2/s

  25. Mechanics of Somersaults • Angular Velocity: • “Throwing” of arms • “Leaning” • Equal and opposite forces

  26. Mechanics of a Twist • Three types of Twists: • Torque Twist • “Cat Twists” or Zero Angular Momentum Twist • Torque-free Twist

  27. Torque Twist • The simplest form of a twist • Equal and opposite force • Unable to be controlled

  28. “Cat Twists” • Why does a cat when dropped land on it’s feet? • Conservation of Angular Momentum • How does a cat perform this? • How a diver can do the same twist.

  29. Torque-free Twist • Type of twist which divers perform • How a torque-free twist occurs • Possession of Angular Momentum • Not on the board and can twist • Can be controlled

  30. Tilt of a Torque-free Twist

  31. My Experiments • Three Camera Angles • Timing of each camera Angle.

  32. Picture of the Overhead Camera

  33. Results of Torque-free Twist

  34. Torque-free Twist

  35. Torque-free Twist

  36. My experiments • Diving Board considered a cantilever: • -lever arm the distance from the fulcrum to the end of board • Setup for how this was done • Results

  37. Lever Arm changing Data

  38. Conclusion • Divers are able to twist without the diving board • Increasing relationship between the Lever Arm and height received • Questions???

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