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Angular Mechanics - Vector cross product and precession Contents:

Angular Mechanics - Vector cross product and precession Contents: Direction of angular velocity vector Torque and direction of torque Vector cross product | Whiteboard Now for something really stupid Now for something really wierd. Direction of angular velocity:.

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Angular Mechanics - Vector cross product and precession Contents:

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  1. Angular Mechanics - Vector cross product and precession • Contents: • Direction of angular velocity vector • Torque and direction of torque • Vector cross product | Whiteboard • Now for something really stupid • Now for something really wierd

  2. Direction of angular velocity: • Wrap right hand around the axis, fingers in direction of spin • Thumb is the “direction” of 

  3. Direction of angular velocity: This  is in the .direction Conventions: . = Out of the page x = Into the page (Right hand threads)

  4. What direction is this  ?

  5. What direction is this  ?

  6. What direction is this  ?

  7. What direction is this  ?

  8. What direction is this  ?

  9. F r Vector Cross Product: Torque is defined as = rxF “x” in this case is the vector cross product: • AxB = ABsin in the Rt hand direction • Take your right hand, and put your index finger in the direction of the first vector. (r in this case) • Put your middle finger in the direction of the second. (F) • Your thumb is the direction of the cross product • Note that Vector x product is not commutative.

  10. F r Vector Cross Product: Note that this torque is in the . direction (out of the page) That means it will cause an angular acceleration in the . direction! (Duh) • AxB = ABsin in the Rt hand direction • Take your right hand, and put your index finger in the direction of the first vector. • Put your middle finger in the direction of the second. • Your thumb is the direction of the cross product • Note that Vector x product is not commutative.

  11. Find this cross product: x

  12. Find this cross product: x

  13. Find this cross product: x

  14. Find this cross product: x

  15. Find this cross product: x

  16. Find this cross product: x

  17. Find this cross product: x

  18. Find this cross product: x

  19. Find this cross product: x

  20. Find this cross product: x

  21. Find this cross product: x

  22. F r Precession • Concept 1 • Ft = p = Impulse • t = L • Concept 2 • p is in the direction of F • L is in the direction of  • Concept 3 • The direction of  is funky!

  23. F(gravity) r L Precession • Concept 4 • Direction of L • Concept 5 • Direction of rxF is x • Concept 6 • The tip of the L vector should change in direction of torque!!! • Concept 7 • This is precession! • Demo Pivot Point

  24. Direction of Precession? • 1. Find direction of L • 2. Find torque direction • (rxF) • 3. Tip of L vector will go in the direction of torque • 4. Simpler to apply force to tip of L vector. Tail moves in the opposite direction of torque. F Pivot Point

  25. Direction of Precession? 1. Find direction of L 2. Find torque direction 3. Tip of L vector will go in the direction of torque 4. Simpler to apply force to tip of L vector. Tail moves in the opposite direction of torque. F is x Pivot Point

  26. Direction of Precession? 1. Find direction of L 2. Find torque direction 3. Tip of L vector will go in the direction of torque 4. Simpler to apply force to tip of L vector. Tail moves in the opposite direction of torque. F is . Pivot Point

  27. Direction of Precession? 1. Find direction of L 2. Find torque direction 3. Tip of L vector will go in the direction of torque 4. Simpler to apply force to tip of L vector. Tail moves in the opposite direction of torque. F is x Pivot Point

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