Yet another question, Rotation and Gravity

[MagikRevolver]

I have many questions that I haven't been able to find answers for on the internet, which is why I love these forums. I keep asking questions and thus far they have all been answered, thanks. I am a very curious person. One thing I never understood was the relationship between revolution and gravity. I understand that anything with mass inevitably exerts a gravitational pull on something else. However, on Earth if you take a globe and you put a toy human on it attached to a spring, and then you spin the globe, the spring would stretch out and the toy humans distance from the surface of the globe would increase(centrifugal force, moving out away from the center of the globe). I have always heard that the Earth's rotation increases its gravity. I don't understand that, would logically deduce that it decreases the gravity because the spinning Earth is trying to fling people off at the same time its mass induced gravity would try to keep people on. A little help on this one because it quite confuses me. Thanks.

 

[Dale]

The Earth's rotation does, in fact, decrease the apparent weight of objects on the surface of the earth. If Earth were a perfect sphere the rotation would cause some water to flow away from the poles and towards the equator until the shape of the Earth was slightly distorted away from a perfect sphere.

 

[MrXow]

I have always heard that the Earth's rotation increases its gravity.

The rotation would increase the gravity due to special relativity. Since the Earth is rotating, and therefore moving, it has more mass. With more mass comes a higher gravitational attraction.

 

[MagikRevolver]

The rotation would increase the gravity due to special relativity. Since the Earth is rotating, and therefore moving, it has more mass. With more mass comes a higher gravitational attraction.

Does that go back to e=mc^2 where if your speed increases, your mass increases. I thought that was only significant if you reached speeds closer to light. And that thus would be insignificant to the centrifugal force trying to keep people off the planet. One response to my question said the rotation does decrease gravity, the other that it increases. Which one is it?

 

[MrXow]

It is only significant when you approach the speed of light, but it does go into play. Other than the mass increase, I cannot think of any way that rotation would increase gravity. The centrifugal force does not decrease gravity, but it is in the opposite direction as gravity and decreases the net force.

 

[MagikRevolver]

It is only significant when you approach the speed of light, but it does go into play. Other than the mass increase, I cannot think of any way that rotation would increase gravity. The centrifugal force does not decrease gravity, but it is in the opposite direction as gravity and decreases the net force.

The net force being our apparent weight on the surface of the earth?

 

[pmb_phy]

I have many questions that I haven't been able to find answers for on the internet, which is why I love these forums. I keep asking questions and thus far they have all been answered, thanks. I am a very curious person. One thing I never understood was the relationship between revolution and gravity. I understand that anything with mass inevitably exerts a gravitational pull on something else. However, on Earth if you take a globe and you put a toy human on it attached to a spring, and then you spin the globe, the spring would stretch out and the toy humans distance from the surface of the globe would increase(centrifugal force, moving out away from the center of the globe). I have always heard that the Earth's rotation increases its gravity. I don't understand that, would logically deduce that it decreases the gravity because the spinning Earth is trying to fling people off at the same time its mass induced gravity would try to keep people on. A little help on this one because it quite confuses me. Thanks.

I created a web page to address these particular questions. It is at
http://www.geocities.com/physics_world/gr/inertial_force.htm

I just updated it yesterday. The page now contains more substance than merely a definition and some quotes. Let me know what you think about it or if you find something worded confusingly or you just plain found an error. It would be of great help to me.

Pete

 

[MrXow]

Yes Magik

 

[Loren Booda]

The rotation would increase the gravity due to special relativity. Since the Earth is rotating, and therefore moving, it has more mass. With more mass comes a higher gravitational attraction.

Does special relativity itself ever increase gravitational attraction?

MagikRevolver

However, on Earth if you take a globe and you put a toy human on it attached to a spring, and then you spin the globe, the spring would stretch out and the toy humans distance from the surface of the globe would increase(centrifugal force, moving out away from the center of the globe).

Centrifugal force (a misinterpretation of an object's inertia, or tendency to remain in linear motion) is a fictitious force, whereas the actual, centripetal force, describes the force needed to keep an object in circular orbit.

 

[MrXow]

Does special relativity itself ever increase gravitational attraction?

No, but an object moving does have an increase in mass. The Earth is moving and increases in mass which proportionally increases its gravitational field strength

 

[MagikRevolver]

How is centrifugal force fictitious if we can feel its effects?

 

[MrXow]

I believe Booda is saying that there is no force defined as centrifugal force. It is just a word that some people use when they are talking about the force exerted on an object traveling in a circle.

 

[Loren Booda]

For a person fixed on the surface of the spinning Earth, his tendency to continue in a straight line is given by Newton's first law: with no forces acting, a moving object remains in a straight line at constant velocity. Without the centripetal restraint (gravity), the person would feel no force and follow his natural path into space.

I'd like to hear from some others about the claim that an object increases mass due to rotation. A rapidly rotating neutron star would most likely be affected if this were so.

 

[MrXow]

With special relativity mass does increase as speed increases you can check it out here

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

or ask about it in the special relativity forum.

 

[Loren Booda]

A person fixed on an idealized (rigid, nonaccelerating, etc.) Earth's surface observes that its rotation does not cause any other point on the planet to move relative to her, just to her cosmic background (planets, stars, dust, galaxies, gas, etc.) [see Mach's principle]. I believe that the Baez article mention of mass increase due to special relativity is for nonzero, linear velocities. With the cosmic background, nonzero, rotational velocities would require general relativity.

 

[rl.bhat]

Rotation and Gravity Reply to Thread

I have many questions that I haven't been able to find answers for on the internet, which is why I love these forums. I keep asking questions and thus far they have all been answered, thanks. I am a very curious person. One thing I never understood was the relationship between revolution and gravity. I understand that anything with mass inevitably exerts a gravitational pull on something else. However, on Earth if you take a globe and you put a toy human on it attached to a spring, and then you spin the globe, the spring would stretch out and the toy humans distance from the surface of the globe would increase(centrifugal force, moving out away from the center of the globe). I have always heard that the Earth's rotation increases its gravity. I don't understand that, would logically deduce that it decreases the gravity because the spinning Earth is trying to fling people off at the same time its mass induced gravity would try to keep people on. A little help on this one because it quite confuses me. Thanks.

Reply: The Earth's rotation does not increase its gravity. Ther expression for the rotational gravity is given in the attachment.

 

[rl.bhat]

Rotation and Gravity Reply to Thread

I have many questions that I haven't been able to find answers for on the internet, which is why I love these forums. I keep asking questions and thus far they have all been answered, thanks. I am a very curious person. One thing I never understood was the relationship between revolution and gravity. I understand that anything with mass inevitably exerts a gravitational pull on something else. However, on Earth if you take a globe and you put a toy human on it attached to a spring, and then you spin the globe, the spring would stretch out and the toy humans distance from the surface of the globe would increase(centrifugal force, moving out away from the center of the globe). I have always heard that the Earth's rotation increases its gravity. I don't understand that, would logically deduce that it decreases the gravity because the spinning Earth is trying to fling people off at the same time its mass induced gravity would try to keep people on. A little help on this one because it quite confuses me. Thanks.

Comparative change in gravity due to reativity and rotation is given in the attachment.

 

[MrXow]

Yes, the general relativistic mass increase is commonly known as the gravitational potential energy PE= mgh, but that would be present in all gravitational fields regardless of rotation.

 

[MagikRevolver]

Okay, so if the Earth stopped spinning, would it theoretically increase or decrease our apparent weight if all other factors stayed the same. Like for example if my little globe and toy analogy was taken into deep space (no forces acting on it by other bodies) would the toy spin off away from the center of the globe, or increase the gravity induced by the globe? Also can gravity be 9.88m/sec^2 in many scenarios as a constant while apparent weight changes?

 

[Dale]

Okay, so if the Earth stopped spinning, would it theoretically increase or decrease our apparent weight if all other factors stayed the same. Like for example if my little globe and toy analogy was taken into deep space (no forces acting on it by other bodies) would the toy spin off away from the center of the globe, or increase the gravity induced by the globe? Also can gravity be 9.88m/sec^2 in many scenarios as a constant while apparent weight changes?

The centripetal acceleration is a much greater effect than any relativistic concerns. If you stayed on a scale and stopped the Earth your scale would report a higher number, and the difference between the stopped and rotating measurements would be greatest at the equator.

 

[MrXow]

The centripetal acceleration is a much greater effect than any relativistic concerns. If you stayed on a scale and stopped the Earth your scale would report a higher number, and the difference between the stopped and rotating measurements would be greatest at the equator.

Exactly.

 

[MagikRevolver]

Alright, I see. Thanks much

 

[sullyhet]

hi all

i am sorry about this but i need to clear something up...

"cetrifugal force" force fleeing the center...

the correct term for say, an object on the end of a string being swung in a circle...

centripetal FORCE

i can elaborate, when you cut said string or in the case of Earth's rotation, the object moves in tangent to the path it was following because, the string or gravity was, pulling it towards the center, not force fleeing the center but force seeking the center, the Earth's rotation would only decrease the attractive force of gravity if the Earth suddenly stopped spinning and then it would be in a direction tangental to the Earth's rotation

and centripetal FORCE would actually (i think) add too Earth's force of gravity

i could be wrong, but...

 

[Dale]

Hi sullyhet, this is a pretty old thread, if you have questions about centrifugal and centripetal forces you are probably better off opening a new thread.

 

[russ_watters]

the correct term for say, an object on the end of a string being swung in a circle...

centripetal FORCE

i can elaborate, when you cut said string or in the case of Earth's rotation, the object moves in tangent to the path it was following because, the string or gravity was, pulling it towards the center, not force fleeing the center but force seeking the center, the Earth's rotation would only decrease the attractive force of gravity if the Earth suddenly stopped spinning and then it would be in a direction tangental to the Earth's rotation

and centripetal FORCE would actually (i think) add too Earth's force of gravity

i could be wrong, but...

Gravity provides the force in place of the string. If the rotation wasn't there, that little bit of gravity that keeps you from flying off in a tangent wouldn't be subtracted from the total gravitational force.

Or maybe this is easier: the object on the string is trying to pull itself away from the string just like your motion with the Earth's rotation is trying to pull you away from the earth.