I was writing about the illusion that the earth stays still and the sun appears to move and I got interested in the question of why we don't notice the earth spinning. Many sites will tell you that at the equator an object on the surface is moving at about 1600 km/h or about 450 m/s. That is about mach 1.5 or three times faster than the cruising speed of a 747. You'd think we'd notice this. But we don't.
But in looking at the answers on various "science" websites they all get it seemed to get the basic physics wrong. They all tell us that going in a circle at a constant rate is not acceleration so we don't notice we are moving. But to move in a circle is to be under constant acceleration!
This is because velocity is a vector, i.e. it has both magnitude and direction. A change in direction is also an acceleration even if the magnitude doesn't change. As we go around a corner in a car, we feel a push away from the centre of the curve, which we call centrifugal force. Technically this is our bodies trying to go in a straight-line (because of inertia) and being pushed in a new direction by the seat and door of the car. Sometimes even simple physics is counter-intuitive!
Now, we humans have different ways of sensing acceleration, such as noticing muscle tension in our bodies or feeling our internal organs pushing on the inside of our belly (also inertia). But one of the main ways we register movement and acceleration is the inner ear. It has three fluid filled loops aligned roughly with the three directions in space relative to our body (our head is up). Bodily movement makes the fluids slosh (inertia again) and we register this as movement.
For some reason spinning motions cause trouble for our inner-ears and for many of us this in turn tends to cause nausea. That's why if you put me on a roundabout and spin me round I will throw up despite being in the same inertial frame as the round about (and even if I cannot see the world). We are not really designed for spinning around, though some weirdos enjoy the sensation.
The complete answer to why we don't feel the earth spinning has two parts.
Firstly, yes, we are in the same inertial frame as the earth and air and everything is moving at the same speed, so visually you perceive this as being stationary. So as we pivot away from the sun on the turning earth it looks like the sun is moving. But why do we not feel the spinning?
This is because secondly, we also perceive acceleration through our inner ear. And despite the high speed of rotation, the distance to the axis of rotation is much greater, so the acceleration we experience as a result of going quite fast around in a very large circle is actually tiny. We do not feel the earth spinning because the acceleration because of it is below the threshold of our detector (the inner ear). It is also very much smaller than gravity.
The atmosphere does feel it though and it creates the coriolis effect and affects weather patterns. The ocean also feels it and it creates large scale currents.
And incidentally this is one reason why rotating a spacecraft to simulate gravity won't work. Apart from the enormous expense of building the mechanism and keeping it going against inevitable friction, the people inside with experience a sideways coriolis force that induces nausea. To get 1g in a human sized space craft with would have to be very large not to have an nausea inducing coriolis effect. According to one source a ring with a diameter of 224 m would have to rotate once every 30 s to produce 1g and no appreciable coriolis effect. That's about 26 km/h at the outer surface. The energy involved in getting a structure that large to rotate smoothly at that speed would be enormous.
As to why some quite serious science websites get the basic physics wrong, it's a mystery. It's physics I remember from high-school 35 years ago, so you'd think it would be obvious to those more up to date!