How Do We Determine Proper Inertial Frames of Reference?

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Determining a proper inertial frame of reference hinges on the absence of acceleration. While the Earth is not an inertial frame due to its rotation and orbital motion, a car is also not an inertial frame because its acceleration can be felt by passengers. The inability to feel the Earth's rotation stems from its constant presence and the lack of a comparative reference point. Modern physics, particularly general relativity, suggests that local distinctions between force and acceleration are indistinguishable. Tools like accelerometers or a Foucault Pendulum can detect rotation, revealing that while we experience slight variations in weight due to Earth's rotation, these changes are often too subtle to notice.
daveed
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how do you determine if something is a proper inertial frame of reference? the Earth is but a car isnt? you can feel a car accelerate, even though you are in it, but you can't feel the Earth accelerate as it changes directions in its orbit.. is there a poitn after which you don't feel accelerations much? but this is just Newtonion, what's the modern view on this?
 
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An inertial frame of reference is one that is not accelerating. Just because you can't feel it doesn't mean it's not accelerating. Sitting here on the surface of the Earth we are NOT in an inertial frame since the planet is rotating and we're rotating right along with it (rotation is a form of acceleration!).
 
Newton's first law is true in inertial frames!
 
then you can't say anything is a proper frame.

why wouldn't we be able to feel the Earth's rotation?
 
Use an accelerometer... a cube containing a mass supported by springs. If the mass is centered, then its "reference frame" is not accelerating. To detect rotation, you might need an array of accelerometers.

(A Foucault Pendulum can detect rotation.)
 
daveed said:
then you can't say anything is a proper frame.

why wouldn't we be able to feel the Earth's rotation?

True. In a sense, the general theory of relativity is based on the concept that you can't (locally) distinguish between a force and an acceleration.

The Earth's rotation has the effect of making you a little lighter than you would be if the Earth were not rotating. You don't "feel" the Earth's rotation for two reasons: First, it is with you all the time so you have nothing to compare it to. Second, if you were to go from the north or south pole to the equator, you would become slightly lighter but the effect would probably be too small to measure.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...

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