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anonymous

  • 3 years ago

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)

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  1. ganeshie8
    • 3 years ago
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    \(\large \omega = \frac{2 \pi}{T}\)

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

  3. anonymous
    • 3 years ago
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    it's 2 pi because that how much one revolution is?

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

  5. ganeshie8
    • 3 years ago
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    |dw:1380369147272:dw|

  6. anonymous
    • 3 years ago
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    so angular speed in 24 hrs would be pi/12

  7. ganeshie8
    • 3 years ago
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    Yes, pi/12 radians per hour

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

  9. ganeshie8
    • 3 years ago
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    its just the unit conversion

  10. ganeshie8
    • 3 years ago
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    *is

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

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

  13. ganeshie8
    • 3 years ago
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    linear speed v = r\(\omega \)

  14. ganeshie8
    • 3 years ago
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    simply multiply radius wid \(\omega\)

  15. ganeshie8
    • 3 years ago
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    whats the radius of earth at north pole ?

  16. anonymous
    • 3 years ago
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    6400?

  17. ganeshie8
    • 3 years ago
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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 ?

  18. anonymous
    • 3 years ago
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    I'm still confused|dw:1380370272714:dw|

  19. anonymous
    • 3 years ago
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    this is where the north pole would be?

  20. ganeshie8
    • 3 years ago
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    |dw:1380370352008:dw|

  21. ganeshie8
    • 3 years ago
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    |dw:1380370410225:dw|

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

  23. anonymous
    • 3 years ago
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    12800?

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

  25. ganeshie8
    • 3 years ago
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    so, distance between them = r = 0

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

  27. ganeshie8
    • 3 years ago
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    see if that makes more/less sense

  28. ganeshie8
    • 3 years ago
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    |dw:1380370749167:dw|

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

  30. anonymous
    • 3 years ago
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    so this is where the equator is?|dw:1380371306773:dw|

  31. anonymous
    • 3 years ago
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    not at the center of the graph?

  32. ganeshie8
    • 3 years ago
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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

  33. anonymous
    • 3 years ago
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    so then radius would be 6400 at the equator?

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

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

  36. anonymous
    • 3 years ago
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    then if the linear speed is halfway from the equator to north pole, radius would be 3200?

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

  38. ganeshie8
    • 3 years ago
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    |dw:1380372161083:dw|

  39. ganeshie8
    • 3 years ago
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    |dw:1380372288001:dw|

  40. ganeshie8
    • 3 years ago
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    |dw:1380372490038:dw|

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

  42. anonymous
    • 3 years ago
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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?

  43. ganeshie8
    • 3 years ago
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    Nope, careful 6400 is the hypotenuse

  44. ganeshie8
    • 3 years ago
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    |dw:1380442777970:dw|

  45. anonymous
    • 3 years ago
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    sin45 = x/6400 = 4525.48?

  46. ganeshie8
    • 3 years ago
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    Yup ! thats the \(r\)

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