## artemisxrpg 2 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)

1. ganeshie8

$$\large \omega = \frac{2 \pi}{T}$$

2. ganeshie8

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

3. artemisxrpg

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

4. ganeshie8

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

5. ganeshie8

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6. artemisxrpg

so angular speed in 24 hrs would be pi/12

7. ganeshie8

8. ganeshie8

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

9. ganeshie8

its just the unit conversion

10. ganeshie8

*is

11. artemisxrpg

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

12. ganeshie8

theta/t is the angular speed $$\omega$$

13. ganeshie8

linear speed v = r$$\omega$$

14. ganeshie8

simply multiply radius wid $$\omega$$

15. ganeshie8

whats the radius of earth at north pole ?

16. artemisxrpg

6400?

17. ganeshie8

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

18. artemisxrpg

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

19. artemisxrpg

this is where the north pole would be?

20. ganeshie8

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21. ganeshie8

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22. ganeshie8

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

23. artemisxrpg

12800?

24. ganeshie8

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

25. ganeshie8

so, distance between them = r = 0

26. ganeshie8

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

27. ganeshie8

see if that makes more/less sense

28. ganeshie8

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29. ganeshie8

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

30. artemisxrpg

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

31. artemisxrpg

not at the center of the graph?

32. ganeshie8

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

33. artemisxrpg

so then radius would be 6400 at the equator?

34. ganeshie8

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

35. ganeshie8

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

36. artemisxrpg

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

37. ganeshie8

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

38. ganeshie8

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39. ganeshie8

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40. ganeshie8

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41. ganeshie8

thats the distance from axis, $$r$$ you can find it using proper trig ratio

42. artemisxrpg

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

Nope, careful 6400 is the hypotenuse

44. ganeshie8

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45. artemisxrpg

sin45 = x/6400 = 4525.48?

46. ganeshie8

Yup ! thats the $$r$$