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artemisxrpg

Earth revolves on its axis once every 24 hr. Assuming that Earth's radius is 6400 km, find the following. a. angular speed of earth in radians per day and radian per hours b. linear speed at the north pole or south pole c. linear speed at quito,ecuador, a city on the equator d. linear speed at salem, oregon (halfway from the equator to the north pole)

  • 6 months ago
  • 6 months ago

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  1. ganeshie8
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    \(\large \omega = \frac{2 \pi}{T}\)

    • 6 months ago
  2. ganeshie8
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    earth is taking 1 day to to rotate around itself. \(\large \omega = \frac{2 \pi~radians}{1~ day}\)

    • 6 months ago
  3. artemisxrpg
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    it's 2 pi because that how much one revolution is?

    • 6 months ago
  4. ganeshie8
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    Yup ! to go around circle once, it takes 2pi radians

    • 6 months ago
  5. ganeshie8
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    |dw:1380369147272:dw|

    • 6 months ago
  6. artemisxrpg
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    so angular speed in 24 hrs would be pi/12

    • 6 months ago
  7. ganeshie8
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    Yes, pi/12 radians per hour

    • 6 months ago
  8. ganeshie8
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    2 pi radians per day us same as saying, pi/12 radians per hour

    • 6 months ago
  9. ganeshie8
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    its just the unit conversion

    • 6 months ago
  10. ganeshie8
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    *is

    • 6 months ago
  11. artemisxrpg
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    v = r*theta/t, so in this case it would be 6400*2pi/1 day or 24 hr?

    • 6 months ago
  12. ganeshie8
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    theta/t is the angular speed \(\omega \)

    • 6 months ago
  13. ganeshie8
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    linear speed v = r\(\omega \)

    • 6 months ago
  14. ganeshie8
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    simply multiply radius wid \(\omega\)

    • 6 months ago
  15. ganeshie8
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    whats the radius of earth at north pole ?

    • 6 months ago
  16. artemisxrpg
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    6400?

    • 6 months ago
  17. ganeshie8
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    let me put it this way :- whats the distance from axis of rotation to you, when you are at north pole ?

    • 6 months ago
  18. artemisxrpg
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    I'm still confused|dw:1380370272714:dw|

    • 6 months ago
  19. artemisxrpg
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    this is where the north pole would be?

    • 6 months ago
  20. ganeshie8
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    |dw:1380370352008:dw|

    • 6 months ago
  21. ganeshie8
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    |dw:1380370410225:dw|

    • 6 months ago
  22. ganeshie8
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    thats the axis of rotation, straight line from North pole to Sounth pole wats the distance ? :)

    • 6 months ago
  23. artemisxrpg
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    12800?

    • 6 months ago
  24. ganeshie8
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    'point on North pole' , is right 'next to axis of rotation'

    • 6 months ago
  25. ganeshie8
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    so, distance between them = r = 0

    • 6 months ago
  26. ganeshie8
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    for a person on North / South poles :- linear velocity \(v = r \omega = 0\times \omega = 0 \)

    • 6 months ago
  27. ganeshie8
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    see if that makes more/less sense

    • 6 months ago
  28. ganeshie8
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    |dw:1380370749167:dw|

    • 6 months ago
  29. ganeshie8
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    starting from equator, as you move towards the poles, the linear velocity decreases and becomes 0 at poles

    • 6 months ago
  30. artemisxrpg
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    so this is where the equator is?|dw:1380371306773:dw|

    • 6 months ago
  31. artemisxrpg
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    not at the center of the graph?

    • 6 months ago
  32. ganeshie8
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    yup ! thats the equator, and since distance from axis is maximim, equals radius of earth, the speed wud be maximum at equator

    • 6 months ago
  33. artemisxrpg
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    so then radius would be 6400 at the equator?

    • 6 months ago
  34. ganeshie8
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    lets call it, distance from axis. at equator, distance from axis = radius of earth = 6400

    • 6 months ago
  35. ganeshie8
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    in ur speed formula, \(v = r \omega\) , \(r\) is distance form axis

    • 6 months ago
  36. artemisxrpg
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    then if the linear speed is halfway from the equator to north pole, radius would be 3200?

    • 6 months ago
  37. ganeshie8
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    nopes, use trig to find r, the distance from axis

    • 6 months ago
  38. ganeshie8
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    |dw:1380372161083:dw|

    • 6 months ago
  39. ganeshie8
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    |dw:1380372288001:dw|

    • 6 months ago
  40. ganeshie8
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    |dw:1380372490038:dw|

    • 6 months ago
  41. ganeshie8
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    thats the distance from axis, \(r\) you can find it using proper trig ratio

    • 6 months ago
  42. artemisxrpg
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    180-45= 135 - 90= 45. since it's a special triangle, both side are 6400 so use pythagorean theorem and the answer should be 9050.97?

    • 6 months ago
  43. ganeshie8
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    Nope, careful 6400 is the hypotenuse

    • 6 months ago
  44. ganeshie8
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    |dw:1380442777970:dw|

    • 6 months ago
  45. artemisxrpg
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    sin45 = x/6400 = 4525.48?

    • 6 months ago
  46. ganeshie8
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    Yup ! thats the \(r\)

    • 6 months ago
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