Calculating equatorial velocity

  • Context: Undergrad 
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Discussion Overview

The discussion revolves around the calculation of Earth's equatorial velocity, exploring the discrepancies in results obtained using different equations. Participants examine the application of centripetal acceleration and gravitational acceleration in this context.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant calculates Earth's equatorial velocity as ~465 m/s using the equation Rω = v, but finds a conflicting result of ~8000 m/s using g = a_{c} = v²/R.
  • Another participant asserts that the second calculation is incorrect, suggesting that it represents the speed required for an object in orbit just above Earth's surface, where centripetal force is provided by gravitational weight.
  • A third participant mentions that Earth's motion includes both rectilinear and rotational components, implying that the assumption of using a = v²/r is flawed.
  • A fourth participant questions the use of g in the equation, noting that gravitational acceleration is not constant across Earth's surface.

Areas of Agreement / Disagreement

Participants express disagreement regarding the appropriateness of the equations used for calculating equatorial velocity, with no consensus reached on the correct approach or interpretation of gravitational acceleration.

Contextual Notes

Limitations include the assumption that gravitational acceleration is uniform and the potential misunderstanding of the relationship between centripetal and gravitational forces in this scenario.

awygle
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I'm confused about some results I've been getting. I tried calculating the equatorial velocity of Earth by the equation R\varpi=v, and I got ~465 m/s. According to various resources, this is correct. But then I tried to calculate it again, using g=a_{c}=\frac{v^{2}}{R}, and I got ~8000 m/s.

Obviously, the second is wrong. My question is why? My only guess is that maybe g doesn't work as a_{c} in this case due to the normal force from the Earth or something of the sort, but that seems a weak explanation...
 
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It's wrong because the equation is not the correct one to use.
You have calculated the speed an object would have to travel in orbit around the Earth if its path was literally just above the surface. In other words, its centripetal force was provided by its weight.
 
earth has both rectilinear and rotatory motion.but you take a=v^2/r.so your assumption is wrong.
 
hi,friend in your equation how we have take a=g.that is for surface on Earth and although 'g' is not constant at all.
 

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