# Yet another question, Rotation and Gravity

1. Oct 21, 2007

### 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 earths 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.

2. Oct 21, 2007

### Staff: Mentor

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.

3. Oct 21, 2007

### MrXow

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.

4. Oct 21, 2007

### MagikRevolver

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?

5. Oct 21, 2007

### 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.

6. Oct 21, 2007

### MagikRevolver

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

7. Oct 21, 2007

### pmb_phy

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

8. Oct 21, 2007

### MrXow

Yes Magik

9. Oct 21, 2007

### Loren Booda

Does special relativity itself ever increase gravitational attraction?

MagikRevolver
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.

10. Oct 21, 2007

### MrXow

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

11. Oct 21, 2007

### MagikRevolver

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

12. Oct 21, 2007

### 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.

13. Oct 21, 2007

### 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.

14. Oct 21, 2007

### MrXow

15. Oct 22, 2007

### 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.

16. Oct 22, 2007

### rl.bhat

Rotation and Gravity Reply to Thread

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

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17. Oct 22, 2007

### rl.bhat

Rotation and Gravity Reply to Thread

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

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18. Oct 22, 2007

### 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.

19. Oct 22, 2007

### MagikRevolver

Okay, so if the earth stopped spinning, would it theoretically increase or decrease our aparent 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 aparrent weight changes?

20. Oct 22, 2007

### Staff: Mentor

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.

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