Coriolis acceleration and magnitude question

[P-Jay1]

Q. An aeroplane flies at constant altitude due south over London. Its speed is 320 km/h and the latitude of London is 51 degrees North. What is the magnitude and direction of the Coriolis acceleration on the aeroplane?


Do I use Coriolis acceleration = 2ω x v to find acc? Is ω = 2π / 24 x60 x60 ??
What is the direction?

 

[tiny-tim]

hi P-Jay1 !

Do I use Coriolis acceleration = 2ω x v to find acc? Is ω = 2π / 24 x60 x60 ??
What is the direction?

actually it's minus 2ω x v

(and yes, = |ω| = 2π / 24 x60 x60)

to find the direction of https://www.physicsforums.com/library.php?do=view_item&itemid=86", remember that velocity (of a fixed point on the Eartth) = ω x r, so that'll help you to work out the direction!

 

[P-Jay1]

Hey Tim!

That's cleared up a few things.. still a bit confused about the direction though. I'm not sure where the latitude of London comes in.

Do I use ω x r = ωrsinθ ? Do I use the right hand rule? The plane is in the Northern hemisphere, but traveling south, so is direction of Coriolis acceleration east to west?

 

[tiny-tim]

I'm not sure where the latitude of London comes in.

That helps you find θ.

Do I use ω x r = ωrsinθ ? Do I use the right hand rule? The plane is in the Northern hemisphere, but traveling south, so is direction of Coriolis acceleration east to west?

|ω x v| = ωvsinθ.

As to the rest, you're on your own … I don't want to muddle my brain up trying to work it out!

 

[paranormal]

I would like to clarify that Coriolis acceleration is not a constant value that can be calculated using a single formula. It is a force that acts on objects in motion due to the Earth's rotation. In this scenario, the aeroplane is flying at a constant speed and altitude, so there is no change in its velocity and thus no Coriolis acceleration. However, if the aeroplane were to change its direction or speed, the Coriolis acceleration would come into play.

To answer the question about magnitude and direction, we need to understand the factors that affect the Coriolis acceleration. These include the velocity of the object, the latitude of the location, and the rotation rate of the Earth. In this case, the aeroplane is flying due south, which means it is moving in a direction perpendicular to the Earth's axis of rotation. The latitude of London is 51 degrees North, which means the rotation rate of the Earth at this location is 2π/24 x 60 x 60 = 0.0000727 radians per second. However, since the aeroplane is not changing its direction or speed, the Coriolis acceleration on it would be negligible.

In conclusion, the Coriolis acceleration on the aeroplane in this scenario is very small and can be considered to be zero. Its direction would be towards the east, but it is not significant enough to have any noticeable effect on the aeroplane's flight. I hope this explanation helps to clarify any confusion.