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Does a ball resting on the Earth's ground have acceleration caused by gravity?

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    $\begingroup$ By acceleration, do you mean proper or coordinate acceleration? $\endgroup$ Dec 31, 2014 at 1:39
  • $\begingroup$ I mean in the axis pointing to the center of the earth $\endgroup$ Dec 31, 2014 at 1:41
  • $\begingroup$ That doesn't answer the question. See: en.wikipedia.org/wiki/Proper_acceleration $\endgroup$ Dec 31, 2014 at 1:44
  • $\begingroup$ So the value of the balls acceleration is 1g? $\endgroup$ Dec 31, 2014 at 1:48
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    $\begingroup$ OK I don't understand anything.when I placed my mobile phone on the ground, its accelerometer shows nine point something m/s^2. So is that the value of its acceleration? $\endgroup$ Dec 31, 2014 at 2:03

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OK I don't understand anything.when I placed my mobile phone on the ground, its accelerometer shows nine point something m/s^2. So is that the value of its acceleration?

That is the value of the phone's proper acceleration. From the Wikipedia article "Proper acceleration":

proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object.

In the (non-inertial) coordinate system of the ground, the phone has no coordinate acceleration.

The proper acceleration of the phone is not due to gravity but, rather, the fact that the ground is preventing the phone from falling freely towards the center of the Earth. That is to say, the phone has an accelerated world line.

In summary, the phone has a proper acceleration of $g$ and a coordinate acceleration, in the coordinate system of the ground, of zero.

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  • $\begingroup$ Ok. With my friend we had a bet. I said that when a marble is at the floor the value of its acceleration is equal to g. He said that this value is 0 because we cannot see any change in the value of speed (constantly 0). Who won the bet? $\endgroup$ Dec 31, 2014 at 2:49
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    $\begingroup$ You both won and you both lost? One is simply living in inertial land and the other one isn't. The observer in inertial land will say that the ball is accelerating. The one in non-inertial land will say that the ball is standing still. So you are living in inertial land and your friend likes non-inertial land better, I guess. $\endgroup$
    – CuriousOne
    Dec 31, 2014 at 2:54
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    $\begingroup$ @ChrisMitsis One thing about the word "Proper" in contexts like these: I always found the terminology a bit weird until I lived in France, when I found that that one of the main meanings of the adjective "propre" is "intrinsic" or "its own". So I'm guessing that this meaning (which seems only to arise in English in this kind of scientific setting) came from mediaeval latin in scientific communications, and I always find it helpful to recall the etymology when I hear things like "proper velocity of galaxies" and so forth. It means something that can be measured within the thing's own being, ... $\endgroup$ Dec 31, 2014 at 3:25
  • $\begingroup$ @ChrisMitsis ... without reference to other, outside "not-its-own" things. So a proper acceleration is what something carrying its own, self contained instruments can measure. $\endgroup$ Dec 31, 2014 at 3:26
  • $\begingroup$ @WetSavannaAnimal aka Rod Vance - I agree that 'proper' normally means intrinsic as with proper time and proper acceleration, both of which can be measured by devices carried by the object without reference to any particular choice of reference frame. But 'proper velocity' has always seemed to me like an unfortunate choice of terminology, since it does depend on a choice of reference frame and thus is not 'intrinsic' in the same way, being defined as (distance traveled in the chosen frame)/(proper time). $\endgroup$
    – Hypnosifl
    Dec 31, 2014 at 5:57

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