1. Universal Force of Gravity and Circular Motion Unit 5

2. Law of Universal Gravitation

7. Let’s calculate your weight 1 Earth’s radius above Earth’s surface. r r 2r

12. Uniform Circular Motion Uniform Circular Motion- An object that is moving in a circle with a constant radius and a constant speed.

13. Describing Velocity Let’s picture an object traveling in a circle in a clockwise direction: Direction of Motion

14. Describing Velocity How would you draw the velocity vector at this point?

15. Describing Velocity The velocity vector is tangent to the circle V

16. Describing Velocity Tangent means that the vector only touches the circle at one point. V

17. Describing Velocity The velocity of an object in circular motion is sometimes referred to as the “tangential” velocity. V

18. Describing Velocity If this object were being spun in a circle on the end of a string and the string broke, what direction would the object travel in? V

19. Describing Velocity In the direction of it’s velocity, straight down. V

20. Describing Velocity How would you draw the velocity vector at this point?

21. Describing Velocity Also tangent to the circle and in the direction of travel V

22. Describing Velocity Also tangent to the circle and in the direction of travel V

23. Describing Velocity Also tangent to the circle and in the direction of travel V

24. Calculating Velocity V= d/t For objects traveling in circular motion, the distance they travel is the circumference of the circle. r = 5m

25. Calculating Velocity V= d/t For objects traveling in circular motion, the distance they travel is the circumference of the circle. circumference = 2πr r = 5m

26. Calculating Velocity So we can say v = 2πr / t t is the time it takes the object to complete 1 full rotation. r = 5m

27. Calculating Velocity If it takes an object 10s to complete this circle, calculate the tangential velocity of the object. r = 5m

28. Calculating Velocity If it takes an object 10s to complete this circle, calculate the tangential velocity of the object. v = 2πr/t r = 5m

29. Calculating Velocity If it takes an object 10s to complete this circle, calculate the tangential velocity of the object. v = 2πr/t v = (2π 5m) / 10s r = 5m

30. Calculating Velocity If it takes an object 10s to complete this circle, calculate the tangential velocity of the object. v = 2πr/t v = (2π 5m) / 10s v = 3.14 m/s r = 5m

31. Calculating Velocity If it takes an object 10s to complete 10 rotations, calculate the tangential velocity of the object. v = 2πr/t r = 5m

32. Calculating Velocity If it takes an object 10s to complete 10 rotations, calculate the tangential velocity of the object. v = 2πr/t v = 10(2π 5m) / 10s r = 5m

33. Calculating Velocity If it takes an object 10s to complete 10 rotations, calculate the tangential velocity of the object. v = 2πr/t v = 10(2π 5m) / 10s v = 31.4m/s r = 5m

34. Describing Acceleration Does the velocity change as the object rotates? V

35. Describing Acceleration Yes! How is the velocity changing? V

36. Describing Acceleration What do we call a change in velocity? V

37. Describing Acceleration What do we call a change in velocity? Acceleration V

38. Describing Centripetal Acceleration What is the direction of this acceleration? v

39. Describing Centripetal Acceleration The acceleration vector is always drawn from the object towards the center of the circle. acac v

40. Centripetal Acceleration

41. Find the centripetal acceleration of a rubber stopper being spun around on the end of a.9m string with a tangential velocity of 3 m/s..9m

42. Find the centripetal acceleration of a rubber stopper being spun around on the end of a.9m string with a tangential velocity of 3 m/s..9m

43. Find the centripetal acceleration of a rubber stopper being spun around on the end of a.9m string with a tangential velocity of 3 m/s. r =.9m v = 3 m/s

44. r =.9m v = 3 m/s

45. Find the velocity of an object if it is being spun in uniform circular motion with a radius of.9m and a centripetal acceleration of 30 m/s 2.

50. Centripetal Force Centripetal Force- The force required to keep an object moving in a circular path. It is NOT centrifugal (fictional)

51. Centripetal Force Centripetal Force- The force required to keep an object moving in a circular path. It is NOT centrifugal (fictional) F c = ma c

52. Centripetal Force

53. Based on what you know about centripetal acceleration, what do you think is the direction of centripetal force?

54. Centripetal Force

55. v acac

56. v acac FcFc F c is also always directed towards the center of the circle

57. Why Does it Feel Like You’re Pulled Outward When You Travel in a Circle? You’re actually feeling the acceleration toward the center of the circle.

58. Why Does it Feel Like You’re Pulled Outward When You Travel in a Circle? You’re actually feeling the acceleration toward the center of the circle. Don’t believe me?

59. Why Does it Feel Like You’re Pulled Outward When You Travel in a Circle? When you’re in the car and the driver slams on the brakes, which direction do you accelerate in? What direction does it feel like you’re accelerating in?

62. A 5kg cart travels clockwise in a horizontal circle of radius 2 meters at a constant speed of 4 m/s. What is the magnitude of the centripetal force acting on the cart?

66. An unbalanced force of 40N keeps a 5kg object traveling in a circle of radius 2m. What is the speed of the object?

72. Satellites Find the velocity required for a satellite to orbit the Earth one Earth’s radius about Earth’s surface.

73. Satellites Find the velocity required for a satellite to orbit the Earth one Earth’s radius above Earth’s surface. FgFg

76. Satellites Geosynchronous orbit- When a satellite orbits a body in the same amount of time it takes that body to rotate. Think about communication satellites (like GPS). Why is this important? What would happen if the satellite that served your cell phone was not in geosynchronous orbit?

77. The Law of Ellipses What does Kepler’s 1 st Law State? The paths of the planets are elliptical in shape, with the center of the sun being located at one of the foci.

78. The Law of Equal Areas What does Kepler’s 2nd Law State? “When a planet is closer to the sun it moves faster, and when it is further away it moves slower.” (An imaginary line drawn from the center of the planet to the sun will sweep out equal areas in equal time intervals.) http://www.walter-fendt.de/ph11e/keplerlaw2.htm

80. The Law of Harmonies What does Kepler’s 3rd Law State? “Planets further from the sun take longer to complete one orbit.” (More distant planets take longer to orbit the Sun (travel at slower average speeds), obeying a precise mathematical relationship.)