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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)
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)

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ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2\(\large \omega = \frac{2 \pi}{T}\)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2earth is taking 1 day to to rotate around itself. \(\large \omega = \frac{2 \pi~radians}{1~ day}\)

artemisxrpg
 2 years ago
Best ResponseYou've already chosen the best response.0it's 2 pi because that how much one revolution is?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2Yup ! to go around circle once, it takes 2pi radians

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1380369147272:dw

artemisxrpg
 2 years ago
Best ResponseYou've already chosen the best response.0so angular speed in 24 hrs would be pi/12

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2Yes, pi/12 radians per hour

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.22 pi radians per day us same as saying, pi/12 radians per hour

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2its just the unit conversion

artemisxrpg
 2 years ago
Best ResponseYou've already chosen the best response.0v = r*theta/t, so in this case it would be 6400*2pi/1 day or 24 hr?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2theta/t is the angular speed \(\omega \)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2linear speed v = r\(\omega \)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2simply multiply radius wid \(\omega\)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2whats the radius of earth at north pole ?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2let me put it this way : whats the distance from axis of rotation to you, when you are at north pole ?

artemisxrpg
 2 years ago
Best ResponseYou've already chosen the best response.0I'm still confuseddw:1380370272714:dw

artemisxrpg
 2 years ago
Best ResponseYou've already chosen the best response.0this is where the north pole would be?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1380370352008:dw

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1380370410225:dw

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2thats the axis of rotation, straight line from North pole to Sounth pole wats the distance ? :)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2'point on North pole' , is right 'next to axis of rotation'

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2so, distance between them = r = 0

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2for a person on North / South poles : linear velocity \(v = r \omega = 0\times \omega = 0 \)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2see if that makes more/less sense

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1380370749167:dw

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2starting from equator, as you move towards the poles, the linear velocity decreases and becomes 0 at poles

artemisxrpg
 2 years ago
Best ResponseYou've already chosen the best response.0so this is where the equator is?dw:1380371306773:dw

artemisxrpg
 2 years ago
Best ResponseYou've already chosen the best response.0not at the center of the graph?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2yup ! thats the equator, and since distance from axis is maximim, equals radius of earth, the speed wud be maximum at equator

artemisxrpg
 2 years ago
Best ResponseYou've already chosen the best response.0so then radius would be 6400 at the equator?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2lets call it, distance from axis. at equator, distance from axis = radius of earth = 6400

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2in ur speed formula, \(v = r \omega\) , \(r\) is distance form axis

artemisxrpg
 2 years ago
Best ResponseYou've already chosen the best response.0then if the linear speed is halfway from the equator to north pole, radius would be 3200?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2nopes, use trig to find r, the distance from axis

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1380372161083:dw

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1380372288001:dw

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1380372490038:dw

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2thats the distance from axis, \(r\) you can find it using proper trig ratio

artemisxrpg
 2 years ago
Best ResponseYou've already chosen the best response.018045= 135  90= 45. since it's a special triangle, both side are 6400 so use pythagorean theorem and the answer should be 9050.97?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2Nope, careful 6400 is the hypotenuse

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1380442777970:dw

artemisxrpg
 2 years ago
Best ResponseYou've already chosen the best response.0sin45 = x/6400 = 4525.48?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.2Yup ! thats the \(r\)
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