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

3. Direction of angular velocity: 1.Wrap right hand around the axis, fingers in direction of spin 2.Thumb is the “direction” of 

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

5. What direction is this  ?

10. Vector Cross Product: Torque is defined as  = r x F “x” in this case is the vector cross product: r F AxB = ABsin  in the Rt hand direction 1.Take your right hand, and put your index finger in the direction of the first vector. (r in this case) 2.Put your middle finger in the direction of the second. (F) 3.Your thumb is the direction of the cross product 4.Note that Vector x product is not commutative.

11. 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) r F AxB = ABsin  in the Rt hand direction 1.Take your right hand, and put your index finger in the direction of the first vector. 2.Put your middle finger in the direction of the second. 3.Your thumb is the direction of the cross product 4.Note that Vector x product is not commutative.

12. Find this cross product: x

13. x

14. x

15. x

16. x

17. x

18. x

19. x

20. x

21. x

22. x

23. 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! r F

24. Precession Concept 4 Direction of L F (gravity) L r 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

25. 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

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 x 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. Pivot Point

28. 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