What Causes a Particle to Move in a Circular Trajectory Due to Coriolis Force?

[ATY]

Hello,
I got a question about the coriolis force. It is probably super simple, but I am still not getting it:
The coriolis force, forces my particle onto a circle trajectory, but I am not sure why (yes, I can show it mathematically, but I want to understand what is happening).
When I am moving a particle to the north, I get my coriolis force because the Earth is moving underneath me. So it is obious, why my particle is moving eastwards, but how do I get a circle ?
If I really move from the equator towards north, my particle will move to the right, but for a circle movement, I would have to move my particle somehow south (because otherwise I would still move to the north)
So, where is my mistake ?

 

[A.T.]

Hello,
I got a question about the coriolis force. It is probably super simple, but I am still not getting it:

Try this:

The coriolis force, forces my particle onto a circle trajectory, but I am not sure why

A net force acting perpendicularly to velocity will tend to do that, in general:

https://en.wikipedia.org/wiki/Centripetal_force

But note that in the rotating frame you also have the centrifugal force:

https://en.wikipedia.org/wiki/Centrifugal_force

 

[256bits]

So, where is my mistake ?

You have two cases to think about.
A satellite with a planar ( wrt to some distant observer removed from the Earth ) polar orbit will pass by the north and south pole.
The ground in this case moves under the satellite to the right.
To people on the ground, the satellite is moving to the left.

An object attached to the Earth at the equator and then moving north will move to the right, or eastward, as seen by people on the earth.

Say the object started out moving north at the same speed as the Earth at the equator - ie it is moving eastward at 1000 mph as and 1000 mph as seen by a distance observer. The object would have an eastward velocity vector V_Eand a northward velocity vector V_N, so an actual velocity at a 45 degree angle NE as seen by the observer. Taking a short distance of movement to Point P of only of say 100 miles north of the equator, does the vector V_N now still point north or just a little but to the right of north.
In other words, can one can think of the V_N vector having a tilt to the east imposed upon it, and not always pointing north as would be "intuitively" the thing for it to do.

Question for you is:
Does the tilt ever shift southward and/or westward to verify the "movement in a circle claim"?

Ad that's all that I know about Coriollis movement , and with good grace I didn't botch it.

 

[ATY]

Try this:

A net force acting perpendicularly to velocity will tend to do that, in general:

https://en.wikipedia.org/wiki/Centripetal_force

But note that in the rotating frame you also have the centrifugal force:

https://en.wikipedia.org/wiki/Centrifugal_force

so, but how do I explain this:

So the circular movement in your video happens, because the pendulum is moving forwoard and backward, but in a case like this the particle does not move forwoard and backward on such large scales

 

[A.T.]

but in a case like this the particle does not move forwoard and backward on such large scales

And you have more forces acting, than just Coriolis.

 

[A.T.]

So, where is my mistake ?

I think it's the common misconception of considering only the tangential component of the Coriolis force, due to the radial movement (changing circumference, while maintaining tangential speed). But there is also a radial Coriolis component, due to tangential movement (changing the required centripetal force).