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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
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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ganeshie8Best ResponseYou've already chosen the best response.2
\(\large \omega = \frac{2 \pi}{T}\)
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
earth is taking 1 day to to rotate around itself. \(\large \omega = \frac{2 \pi~radians}{1~ day}\)
 6 months ago

artemisxrpgBest ResponseYou've already chosen the best response.0
it's 2 pi because that how much one revolution is?
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
Yup ! to go around circle once, it takes 2pi radians
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
dw:1380369147272:dw
 6 months ago

artemisxrpgBest ResponseYou've already chosen the best response.0
so angular speed in 24 hrs would be pi/12
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
Yes, pi/12 radians per hour
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
2 pi radians per day us same as saying, pi/12 radians per hour
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
its just the unit conversion
 6 months ago

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

ganeshie8Best ResponseYou've already chosen the best response.2
theta/t is the angular speed \(\omega \)
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
linear speed v = r\(\omega \)
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
simply multiply radius wid \(\omega\)
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
whats the radius of earth at north pole ?
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
let me put it this way : whats the distance from axis of rotation to you, when you are at north pole ?
 6 months ago

artemisxrpgBest ResponseYou've already chosen the best response.0
I'm still confuseddw:1380370272714:dw
 6 months ago

artemisxrpgBest ResponseYou've already chosen the best response.0
this is where the north pole would be?
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
dw:1380370352008:dw
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
dw:1380370410225:dw
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
thats the axis of rotation, straight line from North pole to Sounth pole wats the distance ? :)
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
'point on North pole' , is right 'next to axis of rotation'
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
so, distance between them = r = 0
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
for a person on North / South poles : linear velocity \(v = r \omega = 0\times \omega = 0 \)
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
see if that makes more/less sense
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
dw:1380370749167:dw
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
starting from equator, as you move towards the poles, the linear velocity decreases and becomes 0 at poles
 6 months ago

artemisxrpgBest ResponseYou've already chosen the best response.0
so this is where the equator is?dw:1380371306773:dw
 6 months ago

artemisxrpgBest ResponseYou've already chosen the best response.0
not at the center of the graph?
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
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

artemisxrpgBest ResponseYou've already chosen the best response.0
so then radius would be 6400 at the equator?
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
lets call it, distance from axis. at equator, distance from axis = radius of earth = 6400
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
in ur speed formula, \(v = r \omega\) , \(r\) is distance form axis
 6 months ago

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

ganeshie8Best ResponseYou've already chosen the best response.2
nopes, use trig to find r, the distance from axis
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
dw:1380372161083:dw
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
dw:1380372288001:dw
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
dw:1380372490038:dw
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
thats the distance from axis, \(r\) you can find it using proper trig ratio
 6 months ago

artemisxrpgBest ResponseYou've already chosen the best response.0
18045= 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

ganeshie8Best ResponseYou've already chosen the best response.2
Nope, careful 6400 is the hypotenuse
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
dw:1380442777970:dw
 6 months ago

artemisxrpgBest ResponseYou've already chosen the best response.0
sin45 = x/6400 = 4525.48?
 6 months ago

ganeshie8Best ResponseYou've already chosen the best response.2
Yup ! thats the \(r\)
 6 months ago
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