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I have read this question:

Why can't we feel the Earth turning?

My question is different, because that question does not talk about (only the comments) the fact (that I think matters most) that the Earth's rotation (or the person on the surface) is an accelerated frame. The answers (and comments) to that question talk about comparing the feeling to traveling in a ship with constant speed. That is an inertial frame of reference. My question is about why we do not feel being accelerated in the (non-inertial) frame of reference on the surface of Earth rotating?

Where Wouter says:

I know it's very late in the game for this question, but this is partly a biology question. We don't feel the rotation of the earth because our brains are biased, they evolved that way. It's not useful to experience/be aware of this rotation day by day, in the same way it isn't useful to be aware of gravity.

And where Dan says

Because the rotation of the earth is very smooth and doesn't change, the centripetal acceleration we feel is very nearly constant. This means that the (small) centrifugal force from the rotation gets added to gravity to make up the "background force" we don't notice.

And this:

https://www.sciencealert.com/here-s-why-we-don-t-feel-earth-s-rotation-according-to-science

Where it says:

So why can't we all feel it? The answer lies in the nature of Earth's movement. Think of being on an aeroplane when it's smoothly travelling at a constant speed and constant altitude. You've unbuckled your seatbelt to go on a walk down the aisle, but you can't feel the movement of the plane. The reason is simple: you, the plane, and everything else inside it is travelling at the same speed. In order to perceive the movement of the plane, you have to glance at the clouds outside.

So this one is saying that we don't feel it because like in an aeroplane, we move with the plane, so this is our inertial frame of reference.

But the plane is moving with a constant speed in this example. I believe it is not OK to compare it to the rotation of the Earth, because the Earth's spin is an angular momentum, and though the angular momentum itself is constant, this is considered acceleration, so any point (or person) on the surface of the Earth is accelerating.

Now one answer says that we do not feel it because our brain is used to the acceleration. The other one says it is because the angular momentum of the Earth is constant.

Which one is right? I do not understand, is it because there is no change in the acceleration, or is it because our brain is used to it, or is it because the centripetal force is so little compared to gravity?

Question:

  1. Why do we really not feel the angular momentum of the Earth, is it because there is no change in the acceleration, or is it because our brain is used to it, or is it because the centripetal force is so little compared to gravity?

  2. Even if the acceleration is not changing, the person on the surface is in a non-inertial reference frame. How can't we feel this acceleration? The equivalence principle only goes for gravity and the acceleration and as per GR we would not know the difference between them. But we would still feel it.

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  • $\begingroup$ You mean rotation of earth around the sun, or rotation around its own axis? $\endgroup$ – Hugo V Oct 13 '18 at 18:04
  • $\begingroup$ Spin, so own axis. $\endgroup$ – Árpád Szendrei Oct 13 '18 at 18:05
  • $\begingroup$ You are aware of jet streams? $\endgroup$ – marmot Oct 13 '18 at 18:11
  • $\begingroup$ I can imagine sensitive instruments can feel it, but our biological sensors are probably not precise enough. $\endgroup$ – B.fox Oct 13 '18 at 18:15
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I would imagine the reason is to do with the fact that the centripetal acceleration as a result is actually pretty small. The velocity of the Earth at its surface can be calculated by noting it takes $1 \text{ day} = 86400 \text{ s}$ to rotate a full $2\pi$ radians, so

$$v=\frac{2\pi R_\text{Earth}}{T_\text{day}}\sim\frac{2\pi\times6400\times10^3\text{ m}}{86400\text{ s}}\sim470\text{ m s}^{-1}$$

The centripetal acceleration is then

$$a=\frac{v^2}{R_\text{Earth}}\sim\frac{(470\text{ m s}^{-1})^2}{6400\times10^3\text{ m}}\sim0.035\text{ m s}^{-2}\ll9.8\text{ m s}^{-2}$$

So gravity would definitely swamp this extra acceleration, and we would not notice it.

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although humans have sensitive rotation detectors in our inner ears, the reason we can't detect the earth's rotation with them is that it is too slow for those detectors (the semicircular canals) to sense. they work well when your head is rotating at a angular velocity of order ~1 revolution per second but at ~1 revolution per minute, they produce no signal- and the rate of the earth's rotation is one revolution per 24 hours.

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  • $\begingroup$ I agree with you that the answer is both physical and biological. There is no evolutionary advantage to sense the rotation of the Earth -- in fact, it would interfere with more immediate needs to sense rotation -- which drives the evolution of rotation detection to be as you describe in this answer. $\endgroup$ – DrSheldon Oct 14 '18 at 2:16
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Why do we really not feel the angular momentum of the Earth, is it because there is no change in the acceleration, or is it because our brain is used to it, or is it because the centripetal force is so little compared to gravity?

You don't feel the centrifugal force (not centripetal) because it is exactly cancelled out by the local gravity: the geoid has already shifted in order to accommodate this effect, and no local experiment can differentiate between the two.

The effect which does count is the Coriolis force, and you can experience its effects on a human time-scale by building a Foucault pendulum. However, the magnitude of this acceleration is too low for human senses to detect.

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  • $\begingroup$ What is meant by "the geoid has already shifted in order to accommodate this effect"?? $\endgroup$ – user45664 Oct 14 '18 at 16:52
  • $\begingroup$ The Earth is, to a suitable level of approximation, an oblate spheroid, and at almost all latitudes the radius vector (pointing to the point at the surface from the center of the Earth) is not orthogonal to the local plane of the surface. The reason you don't "fall sideways" in such gravity is because of the centrifugal force produced by the rotation. $\endgroup$ – Emilio Pisanty Oct 14 '18 at 17:32
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Wikipedia says

Jet streams are the product of two factors: the atmospheric heating by solar radiation that produces the large scale Polar, Ferrel, and Hadley circulation cells, and the action of the Coriolis force acting on those moving masses. The Coriolis force is caused by the planet's rotation on its axis. On other planets, internal heat rather than solar heating drives their jet streams. The Polar jet stream forms near the interface of the Polar and Ferrel circulation cells; the subtropical jet forms near the boundary of the Ferrel and Hadley circulation cells.[2]

So jet streams originate in part from the rotation on earth, and have a profound impact on us. Apart from explaining why on the northern hemisphere west coasts have a more moderate climate than east coasts, thy also explain why trips from Europe to the US take longer than the other direction.

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