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Warmacblu
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If the Earth rotated faster about its axis, how would the value of gravity change?
DavidSnider said:Faster = less gravity.
Warmacblu said:How come? Is it like those theme park rides where you spin in a circle while standing and you feel like you are floating upwards?
Nabeshin said:Not quite, but something similar, yes. I like to think of it this way, in terms of inertial reference frames:
In order to be in circular motion there is a required centripetal force. In the case of us standing on the Earth the only force there is is that of gravity. For a given rotational velocity, a force mv^2/r is required to keep us in that motion. Of course, this force is provided by gravity. In a sense, the gravitational force is "split" into partly providing for your rotational motion, and partly for the normal weight component. The larger the rotational motion, the more of the force is "allocated" towards the rotational part, so the less there is to be perceived as weight (keep in mind the gravitational force is fixed).
It's not exactly a rigorous way of thinking about it, but I hope it makes sense to you.
Nabeshin said:Pop quiz: how fast does the Earth have to rotate for there to be zero gravity?
HallsofIvy said:Strictly speaking, the force of gravity is not changed by rotation. The weight of an object, which is the difference between the gravitational force on the object and the "centrifugal force" due to the rotation changes.
An object rotating at distance r and angular velocity [itex]\omega[/itex] feels a "centrifugal force" of [itex]mr\omega^2[/itex] (that is really the centripetal force necessary to keep the object in orbit). If the gravitational force is mg, there would be "zero gravity" when [itex]mr\omega^2= mg[/itex] or [itex]\omega= \sqrt{g/r}[/itex].
Actually, neither. You can't feel gravity and you can't feel centrifugal force.Warmacblu said:So the force we feel when spinning at a high angular velocity is the centrifugal force and not any change in gravity?
D H said:Actually, neither. You can't feel gravity and you can't feel centrifugal force.
You can feel the ground pushing up on you, however.
What are you referring to here? If the Earth were rotating fast enough that you felt "no gravity", then, yes, of course, you "do not feel the ground pushing up". But at any rotation less than that (as our normal rotation) you definitely feel the grouhd pushing up. That's what "weight" is.pixel01 said:I do not think you feel the ground pushing up, just like the feeling of astronauts when on board the ISS.
Wallace already replied to this, but seeing how you misrepresented what I wrote, I need to answer as well. What I wrote is correct from either a Newtonian or a GR perspective.Ich said:D H is talking about General Relativity, while HallsofIvy uses Newtonian terms.D H said:Actually, neither. You can't feel gravity and you can't feel centrifugal force.
You can feel the ground pushing up on you, however.
That is all you feel. Even though the gravitational acceleration on astronauts on board the ISS is about 90% of that on the surface of the Earth, astronauts on board the ISS feel weightless.pixel01 said:I do not think you feel the ground pushing up, just like the feeling of astronauts when on board the ISS.
I misread Warmacblu's statement, missed the "feel"-part of it.Wallace already replied to this, but seeing how you misrepresented what I wrote, I need to answer as well. What I wrote is correct from either a Newtonian or a GR perspective.
D H said:That is all you feel. Even though the gravitational acceleration on astronauts on board the ISS is about 90% of that on the surface of the Earth, astronauts on board the ISS feel weightless.
Gravity is the force that attracts objects with mass towards each other. On Earth, gravity pulls everything towards the center of the planet, creating a downward force that gives objects weight. This force also keeps the Earth and other celestial bodies in orbit around the sun.
The Earth rotates because of the angular momentum it acquired during its formation. As the planet was forming, particles and debris collided and merged, creating a spinning motion. This rotation has been maintained over time due to the conservation of angular momentum.
The Earth's rotation determines the length of a day. As the planet rotates, it completes one full rotation on its axis every 24 hours, resulting in a day. However, the length of a day can vary slightly due to factors such as the tilt of the Earth's axis and gravitational interactions with other celestial bodies.
If the Earth suddenly stopped rotating, everything on the surface would be launched eastward at high speeds due to the planet's inertia. The sudden change in speed and direction would cause catastrophic destruction. Additionally, the lack of rotation would affect the Earth's magnetic field, leading to changes in climate and weather patterns.
Yes, the Earth's rotation can change, but the changes are very gradual. Factors such as the gravitational pull of the moon and other planets, as well as changes in the Earth's internal structure, can cause slight changes in the planet's rotation. However, these changes are so small that they are not noticeable to humans.