1. Centripetal Force and Gravity 4/27/07

2. Recap  = s r  =     t  =     t s = r  v T = r  a T = r  a c = v2v2 r a c = r  2 F c = ma c = m v2v2 r F c = ma c = mr  2 = 22 T

3. Recap (UCM)Uniform Circular Motion UCM means that  is constant Which means that…  = 0 a T = 0 |v T | = constant BUT… v T is not constant because the direction changes

4. UCM

5. F SB

6. UCM F SB

7. UCM F SB

8. UCM F SB

9. UCM F SB

10. UCM F SB

11. UCM F SB

12. Vertical UCM

13. F SB

14. Vertical UCM F SB mg What’s keeping the ball pinned up against the top?

15. Vertical UCM F SB mg What’s keeping the ball pinned up against the top? Inertia

16. Vertical UCM F SB mg F c =  F = F SB + mg F c is the sum of the inward forces on the ball. FcFc

17. Vertical UCM F SB mg F c =  F = F SB + mg F c is the sum of the inward forces on the ball. FcFc F c = mr  2 = m v2v2 r

18. Vertical UCM F SB mg F c =  F = F SB + mg F c is the sum of the inward forces on the ball. FcFc m = F SB + mg F c = mr  2 = m v2v2 r v2v2 r

19. Vertical UCM

20. F SB mg F c is the sum of the inward forces on the ball.

21. Vertical UCM F SB mg F c is the sum of the inward forces on the ball. F c =  F = …

22. Vertical UCM F SB mg F c is the sum of the inward forces on the ball. F c =  F = F SB

23. Vertical UCM

24. F SB

25. Vertical UCM F SB mg

26. Vertical UCM F SB mg F c is the sum of the inward forces on the ball. F c =  F =

27. Vertical UCM F SB mg F c is the sum of the inward forces on the ball. F c =  F = F SB

28. Vertical UCM F SB mg F c is the sum of the inward forces on the ball. F c =  F = F SB - mg

29. Vertical UCM F SB mg F c is the sum of the inward forces on the ball. F c =  F = F SB - mg F c = mr  2 = m v2v2 r m = F SB - mg v2v2 r

30. Vertical UCM Is the force of the string on the ball greater at the top or at the bottom?

31. Vertical UCM F SB mg F SB mg Is the force of the string on the ball greater at the top or at the bottom?

32. Vertical UCM What is the slowest v T the ball can have if it doesn’t fall when it reaches the top?

33. Vertical UCM What is the slowest v T the ball can have if it doesn’t fall when it reaches the top? Happens when F c just counters mg (I.e. F SB = 0)

34. Vertical UCM What is the slowest v T the ball can have if it doesn’t fall when it reaches the top? m = mg v2v2 r Happens when F c just counters mg (I.e. F SB = 0)

35. Vertical UCM What is the slowest v T the ball can have if it doesn’t fall when it reaches the top? m = mg v2v2 r Happens when F c just counters mg (I.e. F SB = 0) = g v2v2 r

36. Vertical UCM What is the slowest v T the ball can have if it doesn’t fall when it reaches the top? m = mg v2v2 r Happens when F c just counters mg (I.e. F SB = 0) = g v2v2 r v 2 = rg

37. Vertical UCM What is the slowest v T the ball can have if it doesn’t fall when it reaches the top? m = mg v2v2 r Happens when F c just counters mg (I.e. F SB = 0) = g v2v2 r v 2 = rg v = rg