Why don't we feel the Earth's rotation?

[CrazyNeutrino]

Pardon me if this seems like an incredibly naive question. Perhaps the question could also be rephrased as such: "Why do the laws of classical mechanics hold true with Earth as a frame of reference?"

A quick google search turned up the usual answer: the Earth rotates at a constant speed. Regardless of what speed the Earth is rotating at doesn't the fact that it is rotating/changing velocity mean that objects on the surface of the Earth are constantly accelerating? If so then why don't we feel the Earth's rotation and why is Newton's second law valid? Isn't it no longer an inertial frame of reference if the Earth is accelerating.

 

[Ibix]

You don't notice it because the non-inertial effects are very small on an "across the room" kind of scale. But go up in scale and you will notice that the Earth's surface frame isn't inertial. You may wish to look up the Coriolis effect - a non-inertial-frame effect, the standard example of which is the way storm systems rotate.

 

[CrazyNeutrino]

You don't notice it because the non-inertial effects are very small on an "across the room" kind of scale. But go up in scale and you will notice that the Earth's surface frame isn't inertial. You may wish to look up the Coriolis effect - a non-inertial-frame effect, the standard example of which is the way storm systems rotate.

So are Newtons laws an approximation on earth?

 

[Ibix]

In the frame attached to the Earth's surface, yes. It's a rotating frame. I gather that long range artillery fire will miss if you don't account for that fact, and I've already mentioned the weather. But you'll need to be an extremely careful experimentalist to spot the errors in the lab.

That said, you can always pick an inertial frame and work in that; Newton's laws will be exact (up to relativistic corrections, anyway). But the Earth's surface is not stationary in such a frame.

Edit: Actually, I think it depends what you mean by Newton's Laws. In some senses they apply in any frame; they just don't take the familiar simple form in a non-inertial frame. You'll still find that momentum and energy are conserved and things like that. It's just that what you (in your rotating frame) are calling a straight line is not what an inertial frame calls a straight line. Inertial forces (like the Coriolis force) drop out of the maths to explain why things don't follow what you want to call a straight line.

Edit 2: xkcd: https://xkcd.com/123/

 

[Dale]

f so then why don't we feel the Earth's rotation and why is Newton's second law valid?

Sufficiently sensitive experiments do feel the Earth's rotation. Our inner ear and other proprioceptive organs are just not sensitive enough.

 

[CWatters]

A quick google search turned up the usual answer: the Earth rotates at a constant speed. Regardless of what speed the Earth is rotating at doesn't the fact that it is rotating/changing velocity mean that objects on the surface of the Earth are constantly accelerating? If so then why don't we feel the Earth's rotation and why is Newton's second law valid? Isn't it no longer an inertial frame of reference if the Earth is accelerating.

Perhaps I misunderstand but..

Accurate weighing scales have to be calibrated according to the latitude where they will be used. As I recall the apparent weigh of an object is 0.3% less at the equator due to the Earth's rotation. Not enough for us to feel it.

There is also this effect if you are moving but the variation is even less significant..
https://en.wikipedia.org/wiki/Eötvös_effect

 

[Drakkith]

I gather that long range artillery fire will miss if you don't account for that fact

Absolutely. I recently saw an old manual on the targeting of battleship cannons and they had to take the Earth's rotation into account in order to accurately fire at long ranges. When your shell has a flight time of around a minute and a half and goes around 20 miles, you start to approach the scale at which the Earth's rotation has an appreciable effect.

 

[jbriggs444]

Absolutely. I recently saw an old manual on the targeting of battleship cannons and they had to take the Earth's rotation into account in order to accurately fire at long ranges. When your shell has a flight time of around a minute and a half and goes around 20 miles, you start to approach the scale at which the Earth's rotation has an appreciable effect.

Are you thinking of this thread? https://www.physicsforums.com/threads/coriolis-effect-on-ballistics-and-old-chart.917776/

 

[Drakkith]

Are you thinking of this thread? https://www.physicsforums.com/threads/coriolis-effect-on-ballistics-and-old-chart.917776/

Yes, that's the one. I believe I also managed to find the entire manual online somewhere.