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See, Coriolis Force is a force(inertia) felt by a body/system when it moves relative to a rotating frame ( it's formal def.)
Now, to understand this easily.. first you have to get an idea of inertia or frame.. Let's take a simple example, imagine you are deboarding a bus/train which is moving.. now when you put your foot on the road/platform you still keep moving in the direction of train ( cause you were in the train a moment earlier and acting as a system i.e. you+train was moving forward with same speed)! So, as Newton said you would keep moving until external force that is your foot's friction with the platform opposes the motion and then you stop after a while..
^from this, just remember when you change your frame, ie. from moving train to platform, you still have the speed of earlier frame until some force is applied to stop it...
Now, lets come to Earth.. Earth's every point is covering a full circle. But every point is not covering the same distance.. to understand this, imagine a basketball/orange which is rotating on its axis, now every point on this ball will cover a full circle in T (24hrs.) time... But on this ball, the point on equator will have maximum radius ( 6400kms) and any other point will have less radius, and pole will have zero radius.
Keep in mind two things, i) the axis around which the earth is rotating.. that is one passing from pole to pole.. ii) and the distance from this axis to any point on the ball.. At the exact middle of the ball (equator) this point is farthest from the pole, so in the given time T (24hrs) it will have to cover maximum distance that is 2*pi*r(6400km) , but other points on the ball has to cover less distance, as their distance from the axis of rotation will be lesser...
Lets now reconcile the train example with this ball... Suppose this ball is made of 7 discs, One is at centre and 3 gradually decreasing in diameter discs over and below this disc.. d1 d2 d3 D4 d5 d6 d7
d1 d 2 d 3 D 4 d 5 d 6 d7
D4 is ur equator wala disc which is covering maximum distance in 24hrs, so it will have maximum rotation speed, and gradually d3=d5 ; d2=d6; d1=d7 will have decreasing rotational speed.. Now lets move from D4 to d1, that is from equator to pole! You can make an analogy that first D4 is train d3 is the platform ( I hope it is not getting complicated, as d3 is moving in less speed than D4 so you can apply that train-platform concept here) I hope you got the point.!
One thing is clear now, when you move from D4 to d3, you will have some extra speed in the direction of rotation, as you just changed your frame (like from train to platform)
So if earth is moving from West towards East, in norther hemisphere, while moving from equator to polewards, you will get extra speed in the East direction.. as Equator was moving faster than upper latitudinal plane..
If you got the point till here, then only one query is remained,, Why coriolis is maximum towards pole and minimum i.e. ~0 at equator.. For this, you will have to understand how "Distance from Axis" is changing, cause this is what which gives you extra speed i.e. Coriolis effect...
See, in this circle ( centre at origin ) distance from the horizontal Y-axis to the point on equator is 'R' and that distance from the Axis to the point on pole is 0..
This distance is dependent on the angle from the centre... that is equator is at 0Degree and Pole is at 90degree, if you have read basic maths.. you could see that, this distance is R * Cosine of Degree that is R * cos θ ( I hope you got this point, this is most imp. if not then reply I could explain further.)
So you know, D4 is at 0 degree and lets say d3 was at 30 Degree, d2 at 60Degree d1 at 90 degree...and so on So the extra speed you get will depend upon how relatively faster was D4 moving than d3, ( that is how faster was the train moving decides how much further you will get dragged after deboarding the train..)
and for d3 to d2 also it will depend upon how much larger is cos 30 than cos 60 degree...
So in effect, coriolis force depends upon how fast is value of Cosine of Degree i.e. cos θ is changing...
as you know rate of change of cosine is Sine? (remember?) So, coriolis force ultimately depends upon Sine θ which is Rate of change of cos θ
Sine θ is MINIMUM at Equator.. Sin 0degree = 0 and Maximum at pole ie Sine 90Degree = 1
See, in this circle ( centre at origin ) distance from the horizontal Y-axis to the point on equator is 'R' and that distance from the Axis to the point on pole is 0..
This distance is dependent on the angle from the centre... that is equator is at 0Degree and Pole is at 90degree, if you have read basic maths.. you could see that, this distance is R * Cosine of Degree that is R * cos θ ( I hope you got this point, this is most imp. if not then reply I could explain further.)
So you know, D4 is at 0 degree and lets say d3 was at 30 Degree, d2 at 60Degree d1 at 90 degree...and so on So the extra speed you get will depend upon how relatively faster was D4 moving than d3, ( that is how faster was the train moving decides how much further you will get dragged after deboarding the train..)
and for d3 to d2 also it will depend upon how much larger is cos 30 than cos 60 degree...
So in effect, coriolis force depends upon how fast is value of Cosine of Degree i.e. cos θ is changing...
as you know rate of change of cosine is Sine? (remember?) So, coriolis force ultimately depends upon Sine θ which is Rate of change of cos θ
Sine θ is MINIMUM at Equator.. Sin 0degree = 0 and Maximum at pole ie Sine 90Degree = 1
See, in this circle ( centre at origin ) distance from the horizontal Y-axis to the point on equator is 'R' and that distance from the Axis to the point on pole is 0..
This distance is dependent on the angle from the centre... that is equator is at 0Degree and Pole is at 90degree, if you have read basic maths.. you could see that, this distance is R * Cosine of Degree that is R * cos θ ( I hope you got this point, this is most imp. if not then reply I could explain further.)
So you know, D4 is at 0 degree and lets say d3 was at 30 Degree, d2 at 60Degree d1 at 90 degree...and so on So the extra speed you get will depend upon how relatively faster was D4 moving than d3, ( that is how faster was the train moving decides how much further you will get dragged after deboarding the train..)
and for d3 to d2 also it will depend upon how much larger is cos 30 than cos 60 degree...
So in effect, coriolis force depends upon how fast is value of Cosine of Degree i.e. cos θ is changing...
as you know rate of change of cosine is Sine? (remember?) So, coriolis force ultimately depends upon Sine θ which is Rate of change of cos θ
Sine θ is MINIMUM at Equator.. Sin 0degree = 0 and Maximum at pole ie Sine 90Degree = 1
Gotcha?
I have still some confusion regarding 2nd part especially maths formula wala part
Bhai, Equator is not a point... it is a zone... now, around equator ie. at Zero degree (say at point A) , you/wind system tries to move just a little bit towards pole ( say at point B ) then we have to see how much the rotations speed of these two points have been changed...
Since point A is at R * cos 0 degree and Point B is at R* cos 0+little bit degree... now, we have to see change around Cos 0 to cos 0 + little bit rate of change around cos 0 would be sin 0... which is very very less...
The point is, around equator RATE OF CHANGE IN ROTATION SPEED IS VERY VERY LESS... so coriolis effect is negligible... and it is simply said Coriolis is ZERO..
Theoretically, around equator rotational speeds of the points change very very slowly... but as you move upper latitude this change is larger...
Take an orange,, touch at equator :P you will find that around equator when you move finger it is quite like vertical motion... but at upper latitude, it changes sharply, feels like you are getting closer to the axis.. Feel aayi?? :P
I will explain it in a simple language...compare half of earth ie from equator to south pole to dhoni's bat ,now handle of the bat is equator and end of the bat is south pole. Now u imagine kahaane par gendh lagne se six hoga.
In real sense farther u are from equator more will the force.
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Comments
See, Coriolis Force is a force(inertia) felt by a body/system when it moves relative to a rotating frame ( it's formal def.)
Now, to understand this easily.. first you have to get an idea of inertia or frame.. Let's take a simple example, imagine you are deboarding a bus/train which is moving.. now when you put your foot on the road/platform you still keep moving in the direction of train ( cause you were in the train a moment earlier and acting as a system i.e. you+train was moving forward with same speed)! So, as Newton said you would keep moving until external force that is your foot's friction with the platform opposes the motion and then you stop after a while..
^from this, just remember when you change your frame, ie. from moving train to platform, you still have the speed of earlier frame until some force is applied to stop it...
Now, lets come to Earth..
Earth's every point is covering a full circle. But every point is not covering the same distance.. to understand this, imagine a basketball/orange which is rotating on its axis, now every point on this ball will cover a full circle in T (24hrs.) time... But on this ball, the point on equator will have maximum radius ( 6400kms) and any other point will have less radius, and pole will have zero radius.
Keep in mind two things,
i) the axis around which the earth is rotating.. that is one passing from pole to pole..
ii) and the distance from this axis to any point on the ball..
At the exact middle of the ball (equator) this point is farthest from the pole, so in the given time T (24hrs) it will have to cover maximum distance that is 2*pi*r(6400km) , but other points on the ball has to cover less distance, as their distance from the axis of rotation will be lesser...
Lets now reconcile the train example with this ball... Suppose this ball is made of 7 discs, One is at centre and 3 gradually decreasing in diameter discs over and below this disc.. d1 d2 d3 D4 d5 d6 d7
d1
d 2
d 3
D 4
d 5
d 6
d7
D4 is ur equator wala disc which is covering maximum distance in 24hrs, so it will have maximum rotation speed, and gradually d3=d5 ; d2=d6; d1=d7 will have decreasing rotational speed.. Now lets move from D4 to d1, that is from equator to pole!
You can make an analogy that first D4 is train d3 is the platform ( I hope it is not getting complicated, as d3 is moving in less speed than D4 so you can apply that train-platform concept here)
I hope you got the point.!
One thing is clear now, when you move from D4 to d3, you will have some extra speed in the direction of rotation, as you just changed your frame (like from train to platform)
So if earth is moving from West towards East, in norther hemisphere, while moving from equator to polewards, you will get extra speed in the East direction.. as Equator was moving faster than upper latitudinal plane..
If you got the point till here, then only one query is remained,, Why coriolis is maximum towards pole and minimum i.e. ~0 at equator..
For this, you will have to understand how "Distance from Axis" is changing, cause this is what which gives you extra speed i.e. Coriolis effect...
continued...
This distance is dependent on the angle from the centre... that is equator is at 0Degree and Pole is at 90degree, if you have read basic maths.. you could see that, this distance is R * Cosine of Degree that is
R * cos θ ( I hope you got this point, this is most imp. if not then reply I could explain further.)
So you know, D4 is at 0 degree and lets say d3 was at 30 Degree, d2 at 60Degree d1 at 90 degree...and so on
So the extra speed you get will depend upon how relatively faster was D4 moving than d3, ( that is how faster was the train moving decides how much further you will get dragged after deboarding the train..)
and for d3 to d2 also it will depend upon how much larger is cos 30 than cos 60 degree...
So in effect, coriolis force depends upon how fast is value of Cosine of Degree i.e. cos θ is changing...
as you know rate of change of cosine is Sine? (remember?)
So, coriolis force ultimately depends upon Sine θ which is Rate of change of cos θ
Sine θ is MINIMUM at Equator.. Sin 0degree = 0
and Maximum at pole ie Sine 90Degree = 1
Gotcha?
Since point A is at R * cos 0 degree and Point B is at R* cos 0+little bit degree...
now, we have to see change around Cos 0 to cos 0 + little bit
rate of change around cos 0 would be sin 0... which is very very less...
The point is, around equator RATE OF CHANGE IN ROTATION SPEED IS VERY VERY LESS... so coriolis effect is negligible... and it is simply said Coriolis is ZERO..
Take an orange,, touch at equator :P you will find that around equator when you move finger it is quite like vertical motion... but at upper latitude, it changes sharply, feels like you are getting closer to the axis.. Feel aayi?? :P
Now u imagine kahaane par gendh lagne se six hoga.
In real sense farther u are from equator more will the force.