# Why Coriolis Acceleration Matters for Vertical Projection

• ehrenfest
In summary: The centrifugal force is caused by the rotating platform or the playground toy, but the coriolis force is caused by the Earth's motion.The centrifugal force is caused by the rotating platform or the playground toy, but the coriolis force is caused by the Earth's motion.
ehrenfest

## Homework Statement

If you project a particle vertically upward, and you neglect everything except gravity and the Coriolis acceleration, my book says that it will not land on the point where you projected it. Why does this make any sense since the Coriolis force should be antisymmetric on the ascent and on the descent and should thus cancel?

## The Attempt at a Solution

Why not? - (w cross v) = w cross -v, right?

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I think you might actually have to look at a solution to get the full story. That v -> -v reverses the coriolis acceleration is a valid observation IF you are treating the acceleration as an infinitesimal perturbation to the w=0 trajectory. But that just means that the displacement of the landing position is a higher order effect.

It's easiest to understand using angular momentum.
To keep angular momentum constant, the angular velocity has to decrease as the altitude
increases.

pam said:
It's easiest to understand using angular momentum.
To keep angular momentum constant, the angular velocity has to decrease as the altitude
increases.
I don't see how that explains the lack of symmetry in the ascent and the descent.

This is very sensible if you can manage to try it. Do you live somewhere where you can get on a rotating platform (a Merry-go-round) or one of those kid's spinners at the playground (if it's not covered by snow). In a pinch find a rotating stool which is fastened to the floor. Get a tennis ball. While spinning, toss it in the air. Watch what happens going up. Watch what happens coming down.

TVP45 said:
This is very sensible if you can manage to try it. Do you live somewhere where you can get on a rotating platform (a Merry-go-round) or one of those kid's spinners at the playground (if it's not covered by snow). In a pinch find a rotating stool which is fastened to the floor. Get a tennis ball. While spinning, toss it in the air. Watch what happens going up. Watch what happens coming down.
That is a different effect.

Well, you're partly right. The movement outward is centrifugal force, but the movement CW or CCW is the coriolis force.

## 1. What is Coriolis acceleration and why does it matter for vertical projection?

Coriolis acceleration is the apparent deflection of an object's path due to the rotation of the Earth. It matters for vertical projection because it affects the trajectory and speed of objects launched in the vertical direction.

## 2. How does Coriolis acceleration affect objects projected vertically?

Coriolis acceleration causes objects that are launched vertically to appear to deflect to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This is because the Earth's rotation causes the ground to rotate beneath the object as it travels, altering its trajectory.

## 3. Can Coriolis acceleration be ignored when launching objects vertically?

No, Coriolis acceleration cannot be ignored when launching objects vertically. It is a fundamental force that affects all objects on Earth and must be taken into account for accurate projections and calculations.

## 4. How does the strength of Coriolis acceleration vary with latitude?

The strength of Coriolis acceleration increases with latitude. This is because the Earth's rotation is faster at the equator and slower at the poles, resulting in a larger deflection of objects at higher latitudes.

## 5. Are there any practical applications of understanding Coriolis acceleration for vertical projection?

Yes, understanding Coriolis acceleration is important for a variety of practical applications, such as predicting the trajectory of missiles, launching satellites into orbit, and understanding weather patterns. It is also crucial for navigation and surveying, as it affects the accuracy of measurements taken on a rotating Earth.

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