0
$\begingroup$

Body A is sitting on a chair at sea level. Body B is sitting on a chair on a tall mountain. Body A mass = Body B mass

Not sure how to ask this question - but I want to know, given all of the movements they both would experience: the earth rotating about its axis, the earth revolving around the sun, the solar system revolving around the center of the galaxy, etc., which Body would be accelerating more? A more than B, B more than A, or equal? I don't think the usual formulas regarding acceleration can answer this, but again I'm not sure.

Thanks for your time!

Improve this question
$\endgroup$

2 Answers 2

Reset to default
1
$\begingroup$

Given the fact you're talking about rotation, you'd be asking about centripetal acceleration.

The person on the mountain is further away, so for that person their distance from earth's center is greater. But the person on the mountain would also have a greater tangential speed since they move a greater distance in the same amount of time.

But note that centripetal acceleration is given by $$a=\frac {v^2}{r}$$ which means that although the acceleration drops off as $\frac 1r$, it also increases as the square of the velocity. This means that the centripetal acceleration for the person on the mountain is greater. Now as for your question regarding the sun, solar system, galaxy etc., given that both observers are in the same frame of reference about these bodies (earth's surface), the amount they accelerate about these bodies is the same.

Ignoring rotation, since they are both in a stationary frame of reference (earth’s surface), neither of them are accelerating from the point of view of someone on earth’s surface, nor are they moving with respect to each other.

Improve this answer
$\endgroup$
6
  • $\begingroup$ I think that the statement "given that both observers are in the same frame of reference about these bodies (earth's surface)," within errors, as in the first part of the answer you consider the different surfaces they trace out. After all distance from sun modulates the tides oceanservice.noaa.gov/education/tutorial_tides/… $\endgroup$
    – anna v
    Commented Mar 5, 2022 at 7:17
  • $\begingroup$ You think that they have different accelerations around the e.g, the sun, even though they are both on the same rigid body? Is the acceleration of earth around the sun different at different points on earth? How so? And what of the tides? How does that come into the subject? $\endgroup$
    – joseph h
    Commented Mar 5, 2022 at 7:30
  • $\begingroup$ The tides are rotational acceleration of the given bodies. There would be no effect from the sun on tides if the rotational acceleration were not affected. You discuss rotational acceleration. $\endgroup$
    – anna v
    Commented Mar 5, 2022 at 9:29
  • $\begingroup$ No. Not rotational acceleration. Centripetal acceleration. Big difference. Given tidal forces have a small effect, no point complicating things and confusing the OP. $\endgroup$
    – joseph h
    Commented Mar 5, 2022 at 9:50
  • $\begingroup$ I appreciate your responses (guess I have to learn how to add comments!). I keep thinking that if you could stand outside the universe and look down (no I'm not taking about creation!) and view everything and how it moves (I keep thinking accelerate in this case), and you could see Body A and Body B that you would conclude that Body B is accelerating more since it is higher up the Earth's atmosphere. But then I think that this couldn't be the case since they are both stationary on the earth (which is what I believe you are saying in your last response). So I guess that's it then. $\endgroup$
    – Bernie
    Commented Mar 8, 2022 at 0:51
0
$\begingroup$

enter image description here

The centrifugal force is proportional to $\omega^2\,r$ where r is the earth radius . The earth radius is 6371 [km] . Thus $\frac{r_B-r_A}{r_A}$ is very small, this means that the centrifugal force at point B and point A is approx. the same.

Improve this answer
$\endgroup$
2
  • $\begingroup$ So if I could just ask about this one point: "Now as for your question regarding the sun, solar system, galaxy etc., given that both observers are in the same frame of reference about these bodies (earth's surface), the amount they accelerate about these bodies is the same." - I've read where physicists have said we can predict all the way back to a time a billionth of a billionth (etc many times...)second after the big bang. Given that sort of infinitesimal granularity - could your first statement that the person on the mountain top is accelerating more (universally?) still be true? Thanks $\endgroup$
    – Bernie
    Commented Mar 6, 2022 at 22:51
  • $\begingroup$ I’m sure you meant that question for me even though it posted it under another answer. When you talk about motion, you always need to specify relative to who or what. There is no absolute frame of reference (unless you count the CMBR). Whenever a physics problem is posed, like what is the velocity of the car where the author does not state a frame of reference, one assumes that the frame of reference is the stationary earth. To answer your question, no. Two points on a rigid body are stationary relative to each other, by definition. Even in the frame of the expanding universe. $\endgroup$
    – joseph h
    Commented Mar 7, 2022 at 0:44

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.