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Balanced Rock Arches National Park Moab, Utah

It doesn’t seem stable why doesn’t it fall?. Center of Mass. 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. It doesn’t seem stable why doesn’t it fall? Center of Mass 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 based on conservation of momentum

  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. Complex motion like the hammer can be simplified 1.) The CM moves (translates) in a straight line or parabola 2.) The object rotates around the CM APPLET

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

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

  28. Now at the same time.

  29. 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. 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. A Force causes acceleration A Torque causes angular acceleration (rotation) Torque Force

  37. Anytime you rotate an object you apply a torque

  38. When you open door, it rotates. Where is the pivot point / axis of rotation?

  39. A B To open a heavy door where would you push on the door to make it easiest? C

  40. The distance from the pivot point to the location of the force is called the LEVER ARM (distance) A B C The longer the lever arm the greater the torque

  41. This force has no lever arm and produces no torque or rotation

  42. The direction of the force matters too, how well will these two forces work for opening the door? B A

  43. To Rotate an object the force must be applied perpendicular to the lever arm (the door in this case) B A A is perpendicular to the lever

  44. TORQUE t = F d lever arm length (m) NOT distance traveled Force perpendicular to lever arm (N)

  45. Torque MORE Torque Where should you push the wrench in order to loosen a stubborn bolt? t = F d Force Force

  46. A wrench is all about TORQUE You create the most torque by holding the wrench at the end and by exerting a large force. If you can’t loosen the bolt with all your strength, what do you do?

  47. Force Force Get a longer wrench!! lever arm Even with the same force, twice the lever arm gives twice the TORQUE

  48. Torque MORE Torque The greater the force,the greater the torque t = F d Force Force

  49. only the blue part counts The more perpendicular the force the greater the torque t = F d Force Torque Force MORE Torque

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