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Rotational kinetic energy

by stevebd1
Tags: energy, kinetic, rotational
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stevebd1
#1
Mar27-08, 02:41 AM
P: 611
A quote from the 'Light-dragging effects' section from wikipedia states-

"Under general relativity, the rotation of a body gives it an additional gravitational attraction due to its kinetic energy.."

Based on this, does rotational kinetic energy contribute the gravity of an object?

[tex]E_{rotation}=\frac{1}{2}I\omega^{2}[/tex]

[tex]I=mr^{2}0.4[/tex] (0.4 for a solid sphere)

[tex]\omega= Rads/sec[/tex] or [tex]f\pi2[/tex] (f- frequency)


Rotational energy for 2 objects-


Earth-

= 1/2 x (5.9736x10^24 x 6.371x10^6^2 x 0.4) (7.29x10^-5 (rads/sec))^2

= 2.5771X10^29 joules

equivalent mass = 2.8674x10^12 kg


2 sol neutron star, 12 km radius, 1000 Hz freq-

= 1/2 x (2 x 1.9891x10^30 x 12000^2 x 0.4) (2 x pi x 1000)^2)

=4.5232x10^45 joules

equivalent mass = 5.0327x10^28 kg (which is ~2.5% of a sol mass)


While the equivalent mass for the kinetic rotational energy of the Earth is negligible compared to the Earth's overall mass, for the neutron star, it becomes significant. Technically, could it be added when calculating the gravity?

Steve
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hellfire
#2
Apr3-08, 04:39 AM
Sci Advisor
P: 1,047
The gravitational physics of rotating bodies is a very complex topic. You can read about it if you search for the Kerr solution in general relativity. I guess part of the answer to your question depends on what you understand with "gravity". In general relativity gravity is something more than newtonian attraction. The Kerr solution has some properties like frame dragging or geodetic precession that cannot be explained in terms of newtonian gravitation. So rotation actually does contribute to gravity of an object. However, I believe your question is a different one. If you assume a newtonian aproximation in the Kerr metric (you are located far away from the rotating central mass) you ask if you would measure a different central mass (that would put you on different keplerian orbit) for different rotational speeds of this central mass. I believe yes, but I cannot give you a formal proof of this.
vorcil
#3
Apr3-08, 09:45 PM
P: 394
rotational kinetic energy does not create gravity but an acceleration towards the center of mass. since gravity is acceleration towards mass, rotational kinetic energy can seem like it is creating gravity, but it isn't.

if you have done basic circular motion you will know that rotating a mass with a centripetal force, the mass is accelerating towards the centre

JUST LIKE ONE OF THOSE CARNIVAL rides, you know the one the spins around in a circle while you stand up against the walls. you can't move, this is the concept of artificial gravity in space.

try researching about rotating space stations. it's quite interesting, how mass and rotational kinetic energy work together to create "an artificial gravity of some sorts".

stevebd1
#4
Apr4-08, 06:24 AM
P: 611
Rotational kinetic energy

Thanks for the responses. I'm currently looking at Kerr metric and centripetal acceleration (if I'm not mistaken, I was under the impression that centripetal acceleration actually cancelled out gravity hence why gravity is very slightly less at the equator of the Earth than at the poles, not taking into account the equatorial bulge).

I guess what I'm trying to ask here is does the rotational kinetic energy deepen the gravity well of the neutron star or increase the event horizon radius when a rapidly rotating star collapses into a black hole? Say a neutron star which has attained a critical mass of 3 sol, rotating at about 1600 Hz and has a kinetic energy of ~2.38x10^46 joules (which is the equivalent of 2.649x10^29 kg- 13.32% of a sol mass), would this kinetic energy remain with the rotating black hole and contribute to the final calculations for the event horizon(s) and gravity well?

The way I understand gravity is that in general relativity, it is the bending of space-time and in quantum mechanics, it is the propagation of the graviton. Is it possible that both exist? While I'm still in the early stages of understanding general relativity, is it possible that gravity is a separate scalar field that normally works in conjunction with space-time but separates at the event horizon, therefore, gravitons can still propagate away from the black hole and not be dependant on the geodesics of space-time? I've also asked elsewhere in the forum about the effects of frame dragging on gravity, I did some simple calcs based on Kerr metric and found that for a rapid rotating black hole of 3 sol mass, space-time can be rotating up to 0.65c at the event horizon which is an astonishing 3,900 Hz and that's just space-time itself! I find it hard to believe that gravity would slowly make its way through these rotations and speculate that while non-relativistic matter would follow the concentric circles, ultra relativistic matter (such as the photon and the graviton) would propagate more radially.

Steve


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