1. Chapter 10 Center of Gravity
It doesn’t seem stable why doesn’t it fall?
Balanced Rock
Arches National Park
Moab, Utah

2. When a ball is spun in the air it spins around its center
& so does a block of wood
That is to say the axis of rotation is through the center of the object
A hammer behaves a little differently

3. center of mass center of gravity An object naturally spins around its:
which is very similar to (we will use these interchangeably)
center of gravity

4. Center of Gravity or Center of Mass
This is a location of the average position of mass in an object CM

5. If an object is symmetrical and
uniform (made of the same material throughout)
the center of mass is just the center CM

6. If an object has more mass at one end,
the center of mass if shifted that way CM
Lead
Plastic

7. Where is the center of mass?

8. Where is the center of mass?

9. Where would the CM of a large pot be?

10. But you can’t just say that there is the same amount of mass to the left and to the right
Where do you think this set of masses connected by a string would rotate about if swung in the air
At what point would there be the same mass to the left & right (assume the string is massless)
Equal mass L/R & U/D
Actual CM
1 kg
2 kg
Geometric center shown at line

11. Multiply the mass times its distance from the center of mass
Actual CM
1 kg
2 kg
1 m
1 m
1 m
2 m * 1 kg
1 m * 2 kg

12. A massive sun and 3 small planets.
Where is the center of mass?
Sun CM

13. The solar system does NOT rotate around the center of the sun.

14. The sun actually wobbles a bit because…

15. Does the center of mass of our solar system change or is it constant?
Sun

16. Compare the center of mass after the explosion?
If there are no outside forces, the center of mass is the same

17. What if the fragments are different sizes?

18. Why does a washing machine vibrate during the spin cycle sometimes but not others?
Where is the center of mass

19. If a puck is pushed across a frictionless table
It moves in a straight line at a constant speed

20. A motion graph for this is…

21. If a wrench is slid across a frictionless table
The wrench below spins about is CM
And its CM moves in a straight line at a constant speed

22. If a baseball is thrown into the air it follows a parabolic path

23. If a bat is tossed it looks a little more chaotic but….

24. But really just 2 things happen
1.) the object rotates around its CM
2.) the CM follows a parabolic path

25. If ball is thrown into the air, it follows a parabolic path (sorry can’t control the speed any better)

26. The hammer does 2 things when tossed
1.) rotates around the CM
2.) the CM follows the typical path

27. Now at the same time.

28. A hammer thrown into the air

30. The center of mass / center of gravity
is special for several reasons.

31. FOR EXAMPLE:
Gravity pulls down on an entire meter stick (each atom) Fg
BUT this would make calculations a bit tiresome

32. Fg = mg BUT you can PRETEND like the Force of gravity
FOR EXAMPLE:
Fg = mg
BUT you can PRETEND like the Force of gravity
is only pulling down on the CENTER OF MASS

33. FN = mg Fg = mg When a fulcrum is placed under the CM, It balances!!!
(the net force is zero)

34. This is an easy way to find the center of mass of an object
JUST BALANCE IT ON YOUR FINGER

35. If a weight is hung at one end, what happens to the CM

36. So the object isn’t balanced

37. In order to be balanced the pivot must be in line with the CM

38. What if the mass was dropped down by a string?
What would happen to the CM?
Would it still balance?

39. LET’s Try it

40. As long as the CM of mass and the pivot point
Are in line with gravity, it will balance

41. Another interesting fact about the CM, it that if an object is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.
A Gravity Vector drawn from the pivot point will always pass through the CM (when balanced)

42. Why doesn’t the leaning tower of pisa fall?

43. Would the object at the right fall over?

44. YES Would the object at the right fall overFg Fg
An object will topple if a vertical line through its CG is not under the support base

45. This block can’t be tilted anymore without fallingFg

46. DEMO- Tilting box

47. Still a little sinking left before TIMBER!!!
The CM is still under the base

50. A bus MUST withstand an angle of 28o without tipping
Some can withstand 40o
28o
Center line
40o

51. The CM must be lower for a greater tipping angle
Highest CM for 28o
Highest CM for 40o

52. How do the manufacturers get the CM well below the
halfway mark, even with passengers on the top deck?
Highest CM for 40o

54. Cargo in the back of truck should always be securedOK

55. If it isn’t secured or strapped in then…OK
UH OH

56. Activity: Place your feet on the floor in front of you chair.
Now stand up BUT notice what you do before standing!!!
Demos: balanced boards
hammer paint stick

57. Where is the book most stable
physics
physics
A system is most stable with the CM as low as possible.
There is a tendency towards this state.
Demo: rolling concrete

58. If a ping pong ball is pushed into the water in a glass what happens to the CM?

59. Which is more stable
This is more stable for 2 reasons
#1 a lower CG

60. The object at right must have its CM go UP before falling
The object at left does not

61. Unstable equilibrium Stable equilibrium Any movement lowers the CM
The CM must rise first

62. If the book is more stable here
physics
physics
physics
Why does it not fall when upright?

65. CM animation

66. Stable equilibrium The object is forced to pivot at the fulcrum.
Any rotation causes the CM to rise
Stable equilibrium

67. What about like this?
UNstable equilibrium

68. What about here?
This object is in neutral equilibrium..
The CM doesn’t rise or fall as it rotates

69. But you can’t just say that there is the same amount of mass to the left and to the right
Where do you think this set of masses connected by a string would rotate about if swung in the air
At what point would there be the same mass to the left & right (assume the string is massless)
Equal mass L/R & U/D
Actual CM
Geometric center shown at line

70. Book questions
page 147
9, 12, 14, 17, 18, 19, 23, 24, 26