Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

artemisxrpg

  • one year 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)

  • This Question is Closed
  1. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  2. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  3. artemisxrpg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it's 2 pi because that how much one revolution is?

  4. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yup ! to go around circle once, it takes 2pi radians

  5. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1380369147272:dw|

  6. artemisxrpg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so angular speed in 24 hrs would be pi/12

  7. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yes, pi/12 radians per hour

  8. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    2 pi radians per day us same as saying, pi/12 radians per hour

  9. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    its just the unit conversion

  10. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    *is

  11. artemisxrpg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    v = r*theta/t, so in this case it would be 6400*2pi/1 day or 24 hr?

  12. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    theta/t is the angular speed \(\omega \)

  13. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    linear speed v = r\(\omega \)

  14. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    simply multiply radius wid \(\omega\)

  15. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    whats the radius of earth at north pole ?

  16. artemisxrpg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    6400?

  17. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    let me put it this way :- whats the distance from axis of rotation to you, when you are at north pole ?

  18. artemisxrpg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm still confused|dw:1380370272714:dw|

  19. artemisxrpg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    this is where the north pole would be?

  20. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1380370352008:dw|

  21. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1380370410225:dw|

  22. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    thats the axis of rotation, straight line from North pole to Sounth pole wats the distance ? :)

  23. artemisxrpg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    12800?

  24. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    'point on North pole' , is right 'next to axis of rotation'

  25. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so, distance between them = r = 0

  26. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    for a person on North / South poles :- linear velocity \(v = r \omega = 0\times \omega = 0 \)

  27. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    see if that makes more/less sense

  28. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1380370749167:dw|

  29. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    starting from equator, as you move towards the poles, the linear velocity decreases and becomes 0 at poles

  30. artemisxrpg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so this is where the equator is?|dw:1380371306773:dw|

  31. artemisxrpg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    not at the center of the graph?

  32. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yup ! thats the equator, and since distance from axis is maximim, equals radius of earth, the speed wud be maximum at equator

  33. artemisxrpg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so then radius would be 6400 at the equator?

  34. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    lets call it, distance from axis. at equator, distance from axis = radius of earth = 6400

  35. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    in ur speed formula, \(v = r \omega\) , \(r\) is distance form axis

  36. artemisxrpg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then if the linear speed is halfway from the equator to north pole, radius would be 3200?

  37. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    nopes, use trig to find r, the distance from axis

  38. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1380372161083:dw|

  39. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1380372288001:dw|

  40. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1380372490038:dw|

  41. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    thats the distance from axis, \(r\) you can find it using proper trig ratio

  42. artemisxrpg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Nope, careful 6400 is the hypotenuse

  44. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1380442777970:dw|

  45. artemisxrpg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sin45 = x/6400 = 4525.48?

  46. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yup ! thats the \(r\)

  47. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.