1. Bell Ringer In terms of energy, what happens to the energy of an object in free-fall?

2. Bell Ringer Identify one station from yesterday’s lab. –How did you change the object’s center of mass? –What did this do to the object?

3. Center of Mass

4. Center of Gravity (CG) The point at the center of an object’s weight distribution –The force of gravity can be considered to act on an object at this one point Located in the geometric center of a symmetrical object Located in the heavier end of an asymmetrical object May be located where there is no actual material –i.e. A donut

5. Center of Gravity (CG) An object which rotates/revolves about its CG moves smoothly An object which rotates/revolves about a point other than its CG tends to wobble

6. Center of Mass (CM) The average position of all of the particles making up an object Usually located very close to the center of gravity –Not the case with very tall objects –Gravity pulls harder on the bottom of the object making the bottom “heavier”

7. Stability An object will topple if its CG is tipped beyond its support base An object is most stable when its CG lie below their support points –Extra work is required to lift the CG to the point of toppling

8. Stability

9. Three types of equilibrium: –Stable: Object balanced so that any motion will raise its CG

10. Stability Three types of equilibrium: –Unstable: Object balanced so that any motion will lower its CG

11. Stability Three types of equilibrium: –Neutral: Object balanced so that any motion will not change location of CG

12. CG of People Men tend to have slightly higher centers of gravity than women

13. Bell Ringer This is a view of the tennis ball from above. Write down the letter of the correct path of travel as the string is cut. DO NOT DISUSS WITH THOSE AROUND YOU

14. Bell Ringer Why, when carrying a large object, do you tend to learn back?

15. Rotational Mechanics

16. Rotational Motion Axis: The straight line around which circular motion takes place Rotation: When an object turns about an internal axis –The Earth rotates on its axis Revolution: When an object turns about an external axis –The Earth revolves around the Sun

17. Rotational Motion Period (T): The time it takes for an object to complete one full circle –Units: seconds

18. Two Types of Velocity –Tangential Velocity (v): The speed of an object moving along a circular path Units: m/s Direction of motion: –Always changing –Always tangent to the circle

19. Two Types of Velocity v = (2  r)/T T = period of motion (s) r = radius of circular path (m)  = 3.14

20. Two Types of Velocity v = (2  r)/T T = period of motion (s) r = radius of circular path (m)  = 3.14

21. Two Types of Velocity –Rotational Velocity (  ): The number of rotations or revolutions per unit time Units: –radians per second –revolutions per minute (rpm) i.e.) All parts of a turntable have the same rotational velocity

22. Relating Tangential and Rotational Velocity v = r  Therefore, for any rigidly rotating system: –All parts have the same rotational speed –Tangential speed depends on rotational speed,  and radius, r

23. Bell Ringer If a car does doughnuts with a radius of 6 m and completes one full circle every 3s, what is the car’s tangential velocity? What is the car’s rotational velocity?

25. Which is the right path? This is a view of the tennis ball from above. Write down the letter of the correct path of travel as the string is cut.

28. Why does a CD case slide across the dashboard on a turn?

29. What really happens…

30. What is the right answer?

31. What is a piece of equipment that use centripetal force for a mechanical advantage?

32. Centripetal Force The force that causes an object to follow a curved path –“Center-seeking” force –Always directed at a right angle to the direction of motion F c = (mv 2 )/r

33. Centripetal Force If the centripetal force stops acting, the object will fly off in a straight line path, tangent to the circle

34. Centripetal Acceleration The change in velocity of an object in rotational motion, caused by the centripetal force a c = v 2 /r –Occurs even if tangential speed remains constant –Object is still changing direction to maintain its circular path

35. CentriFUGal Force “Fictional” center-fleeing force Only felt by an object within a rotating reference frame –Simply a reaction to the centripetal force ACTION REACTION

36. CentriFUGal Force

37. Action: Centripetal force pushes object into the circle Reaction: Object exerts centrifugal force back on the surface away from the circle

38. Simulated Gravity Comes from the centrifugal force acting on rotating object Simulated gravity will feel stronger when: –The capsule spins faster –The object sits farther from the axis of rotation of the capsule If sitting on the axis of rotation, the object will feel no “gravity”

39. Bell Ringer A friend pushes you out of his car as you go around a turn. In what direction will you travel?

40. Bell Ringer What provides the centripetal force for a tetherball? What is the only way to measure the centrifugal force?

41. Bell Ringer In order for there to be a “simulated gravity” effect, what must happen? (in other words what must something equal to)

42. Examining G Forces

43. Torque Recall: Forces tend to make objects accelerate Torque makes an object rotate Torques occur when a force is applied with leverage –Note: A perpendicular push or pull gives more rotation with less effort

44. Torque When the applied force is perpendicular: –Force is represented by F  –Lever arm ( l ): the distance from the axis to the point of contact

45. Torque Therefore, torque (  ) is:  = F  l –Units: Newton meters (N. m) The same torque can be produced with: –Large force & small lever arm –Small force & large lever arm

46. Torque If a force is applied directly to the CG ( l = 0), no rotation will occur –Kicking a football directly in its CG (no rotation) vs. off its CG (rotation)

47. Balanced Torques In order for an object to remain balanced the torques on either end must balance each other Therefore:  ccw =  cw –ccw = counter-clockwise –cw = clockwise

48. Balanced Torques

49. Bell Ringer What are three things that you can do to increase the amount of torque on a stubborn rusted bolt?

50. Rotational Inertia Recall: Newton’s Law of Inertia There is a similar Law of Rotational Inertia: An object rotating about an axis tends to keep rotating about that axis unless acted upon by a net torque.

51. Rotational Inertia Rotational inertia ( I ) depends on the distribution of mass of an object –Objects with mass far from their CGs will have more rotational inertia

52. Rotational Inertia

53. Which has less rotational inertia: –A short pendulum or a long pendulum of the same mass? Short pendulum –A hoop or a solid disk of the same mass? Solid disk

54. Rotational Inertia

55. Bell Ringer What are three things that you can do to increase the amount of torque on a stubborn rusted bolt?

56. Rotational Inertia

57. Angular Momentum Recall: Any moving object has momentum Similarly, any rotating object has angular momentum Angular Momentum = I  The more angular momentum an object has, the more torque required to change it –i.e. moving bicycle vs. stationary bicycle

58. Angular Momentum

60. Conservation of Angular Momentum Law of Conservation of Angular Momentum: Without a balanced, external torque, the angular momentum of a system will remain constant In an isolated system: –If I increases,  will decrease –If I decreases,  will increase

61. Conservation of Angular Momentum