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Balanced Rock Arches National Park Moab, Utah

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

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Balanced Rock Arches National Park Moab, Utah

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  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. An object naturally spins around its: center of mass 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. Equal mass L/R & U/D Actual CM 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) 1 kg 2 kg Geometric center shown at line

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

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

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

  14. Sun 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

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

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

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

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

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

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

  35. So the object isn’t balanced

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

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

  38. LET’s Try it

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

  40. 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)

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

  42. Would the object at the right fall over ?

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

  44. This block can’t be tilted anymore without falling Fg

  45. DEMO- Tilting box

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

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

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