Coriolis from our orbit around the Sun

[D H]

I mean inertia as described by the second law: in order to accelerate an object a force is required.

That is usually called force, not inertia. The second law, strictly speaking, applies only in inertial frames. Those fictitious forces arise only in the mind of someone who is force-fitting Newton's second law to a non-inertial frame -- a frame in which the law of inertia does not apply.

The reference for acceleration is the equivalence class of inertial coordinate systems, with the members of the class related by Galilean transformations. The equivalence class of inertial coordinate systems is singled out by the laws of motion. The laws of motion hold good if and only if the motion is mapped in an inertial coordinate system. If motion is mapped in any non-inertial coordinate system then additional terms, such as a centrifugal term, are necessary.

Exactly. That mapping is an act of a human mind, not an act of nature.

Inertial forces, such as the centrifugal force, coriolis force, and ahem, gravity, are not measurable.

Coriolis force is measurable.

The coriolis force is not measurable from the perspective of a windowless elevator car. From the perspective of an inertial observer, this thing that you are calling coriolis force can always be attributed to plain old linear momentum.

 

[Cleonis]

Sliding down the pole that cleonis described, [...] it's just the pole trying to keep your intantaneous velocity equal to it's own at that radial distance from the centre.

Actually, the force that the pole exerts upon the guy sliding down is not referred to as 'Coriolis force'.

Rather, it's like this: if you would release an object to free fall, right alongside the sliding pole, then onboard the cartwheel space station you would see the object deviate from falling straight down. That deviation from moving in a straight line with respect to the space station is attributed to 'fictitious force'.

That is why it's insisted that you can't measure 'fictitious force' with an accelerometer.

Cleonis

 

[Cleonis]

I mean inertia as described by the second law: in order to accelerate an object a force is required.

That is usually called force, not inertia.

That which causes the acceleration is called force.
It's essential to maintain rigorous distinction between force and inertia.

The definition of force is that it occurs as a Third Law force pair. To have a force being exerted you must have two objects, exerting a force upon each other, accelerating each other.

Inertia is not a force.
Inertia is the fact that force is required to cause acceleration with respect to the inertial coordinate system.

Cleonis

 

[D H]

That which causes the acceleration is called force.
It's essential to maintain rigorous distinction between force and inertia.

I see what you are talking about now. Why don't we just call it linear momentum? That is the standard name. Inertia is a bit (more than a bit) archaic.

The definition of force is that it occurs as a Third Law force pair. To have a force being exerted you must have two objects, exerting a force upon each other, accelerating each other.

Precisely! Fictitious forces such as centrifugal force and coriolis force do not have a third law pair. Instead of arising from some interaction, they arise purely from the geometry of the reference frame.

 

[YellowTaxi]

The Coriolis force is not measurable from the perspective of a windowless elevator car. From the perspective of an inertial observer, this thing that you are calling coriolis force can always be attributed to plain old linear momentum.

If the guy sliding down the pole is replaced by your windowless elevator, the guy will be thrown sideways against the wall.

He may even break through the side-wall of your windowless elevator if the construction can't handle the magnitude of the coriolis force. So the force is real enough for anyone inside such an elevator. People could measure it just for fun as it goes up and down inside the spacestation. They may throw-up because of it. But don't worry DH, it doesn't exist , right ?

 

[Cleonis]

That which causes the acceleration is called force.
It's essential to maintain rigorous distinction between force and inertia.

I see what you are talking about now. Why don't we just call it linear momentum? That is the standard name. Inertia is a bit (more than a bit) archaic.

Well, whether the word 'inertia' is perceived as archaic probably varies from country to country. Where I was taught physics it was standard.

Linear momentum is a vector quantity. Linear momentum is assigned after the choice of inertial coordinate system has been made. You attribute a velocity and then you attribute a linear momentum.

The concept of Inertia is more general, it doesn't refer to velocity, instead it refers to change of velocity. It embodies that deceleration and acceleration are the same thing, given the principle of relativity of inertial motion.

The common factor of linear momentum and kinetic energy is inertial mass, another illustration that inertia is a more general concept than linear momentum.

You get my drift: I want to keep using the word inertia, I need to.

I have to say: it hadn't even occurred to me that in some parts of the world the word 'inertia' could have faded from the physics vocabulary.

Cleonis

 

[D H]

If the guy sliding down the pole is replaced by your windowless elevator, the guy will be thrown sideways against the wall.

The only real interaction here is that the pole is making the elevator car accelerate. The interaction between the pole and the car is a real force, the electromagnetic force. The force that the pole exerts on the car is equal but opposite to the force that the car exerts on the pole. There is zero real reason to invoke coriolis force here.

Scientists use fictitious forces as a convenience, not a necessity. There is always a frame of reference in which those inertial forces vanish. Those inertial forces are a mental construct. In comparison, the contact force between the pole and the car is very real. It doesn't vanish in any frame.

At times, using a rotating frame to explain what is going on is very convenient indeed. Explaining the behavior of the Earth's atmosphere from the perspective of a rotating frame is very hard. Properly modeling the Earth's atmosphere has been one of the driving forces for making supercomputers. Hard as this task is, modeling the behavior of the Earth's atmosphere from the perspective of a non-rotating frame would be utterly insane.

 

[Cleonis]

If the guy sliding down the pole is replaced by your windowless elevator, the guy will be thrown sideways against the wall.

I'm reminded of the joke: "Falling down doesn't hurt at all - not until you hit the ground."

Yes, in the cartwheel space station the guy in the fast elevator will be thrown against the wall. But as long as he hasn't hit that wall yet an accelerometer that he's carrying will read zero sideways acceleration (unless he's swept of his feet and is thrown on the floor).

Once he's up against the wall the accelerometer he's carrying will read an acceleration, and that will be the acceleration due to the force that the elevator wall is exerting upon that guy.

Cleonis

 

[YellowTaxi]

There is zero real reason to invoke coriolis force here..

People who lived in such a spacestation probably would have to, their lives may depend on it. If the elevataor moves too fast people could get hurt because their bodies will be trying to follow a 'coriolis path' instead of just sitting in the middle of the elevator.

There could be warnings posted on the walls -
"Please be aware of the sideways push this elevator exerts.
In the event of accident call the coriolis engineer: DH76523."

 

[Cleonis]

Properly modeling the Earth's atmosphere has been one of the driving forces for making supercomputers. Hard as this task is, modeling the behavior of the Earth's atmosphere from the perspective of a non-rotating frame would be utterly insane.

Well, let's take a look at a 'what if' scenario.

What if a group sets out make a supercomputer numbercrunch the equations of motion for the Earth centered inertial coordinate system? For one thing, they'd have to set that up only once. Once working algorithms are in place they will remain in service.

The input of the atmospheric models is the combined dataset: data from wheather stations, data from wheather satellites etc. Data such as temperature carry over directly, only the wind direction and velocity data must be transformed to velocity relative to the inertial coordinate system. Arrays of processors can do that in parallel, so it can be done very fast.

The numbercrunching will be about the same computational load. The equations of motion will have a simpler form, no need to include any fictitious force in the computation!

To convert to usable output a second coordinate transformation transforms wind directions and velocities to motion relative to the co-rotating coordinate system. Again, that can be done very fast.

For meteorological insitutions working with supercomputers there is no need to switch to using the equations of motion for the inertial coordinate system, but if they would switch it would require just a small, temporary investment in manpower.

The supercomputers are just numbercrunching, the form of the equations of motion doesn't matter much. The user interface of the software will accept input and present output as velocities and directions relative to the co-rotating coordinate system.

Cleonis