UCM 4

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UCM 4

  1. 1. Uniform Circular Motion
  2. 2. What is UCM?
  3. 3. U C M niform
  4. 4. U C M niform same speed
  5. 5. U C M ircular
  6. 6. U C M otion
  7. 7. Centripetal Force
  8. 8. Centripetal Force F net making object move in UCM
  9. 10. F c =Tension
  10. 12. F c =Normal Force
  11. 14. F c =Gravity
  12. 16. F c =Friction
  13. 17. <ul><li>An object in UCM is </li></ul><ul><li>accelerating </li></ul>
  14. 18. <ul><li>An object in UCM is </li></ul><ul><li>accelerating </li></ul>always
  15. 19. <ul><li>An object in UCM is </li></ul><ul><li>accelerating </li></ul>toward the center of the circle always
  16. 20. How to Solve a UCM Problem
  17. 21. <ul><li>Write out the knowns </li></ul>
  18. 22. <ul><li>Identify force(s) causing the object to move in </li></ul><ul><li>UCM </li></ul>
  19. 23. An Example of How to Solve a UCM Problem
  20. 24. For the sake of this problem, we are going to assume that Glaz finally snaps and starts doing doughnuts in the parking lot. The radius of these doughnuts is 15m, and it takes her 5 seconds to do each. We are going to try and find her centripetal force.
  21. 25. You can tell this is a physics problem since the situation it presents is impossible; we all know Glaz snapped YEARS ago.
  22. 26. Oh, and we also won’t be taking into account silly little things like friction.
  23. 27. But forget about that, lets list our knowns. v=? T= 5secs a c =? r= 15m M=1100kg As you can see, we don’t know much.
  24. 28. In order to solve this problem we’re going to have to use three equations.
  25. 29. Velocity v=2πr/t Centripetal Acceleration A c =v^2/r Centripetal Force F c =ma c
  26. 30. Let’s start with velocity: Formula: v=2πr/t Formula with substitutions: 2π(15m)/5 secs Answer: 18.84955592m/s
  27. 31. Now we’ll move on to centripetal acceleration. Formula: A c =v^2/r Formula with substitutions: A c =(18.84955592m/s)^2/15m Answer: A c =23.68705056m/s^2
  28. 32. And finally we have enough data to calculate centripetal force. Formula: F c =ma c Formula with substitutions: 1100kg(23.68705056m/s^2) Answer: 26055.75561N
  29. 33. So as you can clearly see, UCM equations are quick, easy, and (generally) painless to do!

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