Rotational kinetic energy and gravity

In summary, the conversation discusses the concept of rotational kinetic energy and its contribution to the gravity of an object. It is mentioned that rotation does contribute to gravity, but it is a complex topic and is more than just Newtonian attraction. The conversation also touches on the concept of artificial gravity in space and how it relates to rotating space stations. There is a question posed about whether rotational kinetic energy deepens the gravity well of a neutron star or contributes to the calculations for the event horizon and gravity well of a rotating black hole. There is also discussion about the nature of gravity in general relativity and quantum mechanics, and the possible effects of frame dragging on gravity.
  • #1
stevebd1
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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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  • #2
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.
 
  • #3
mhmm

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".
 
  • #4
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 canceled 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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FAQ: Rotational kinetic energy and gravity

What is rotational kinetic energy?

Rotational kinetic energy is the energy an object possesses due to its rotation around a fixed axis. It is calculated by multiplying the moment of inertia of the object by the square of its angular velocity.

How is rotational kinetic energy related to gravity?

Rotational kinetic energy is affected by gravity as it determines the magnitude of the moment of inertia. The closer an object is to the center of gravity, the smaller its moment of inertia and therefore, the higher its rotational kinetic energy.

What is the formula for calculating rotational kinetic energy?

The formula for rotational kinetic energy is E = 1/2 * I * ω^2, where E is the rotational kinetic energy, I is the moment of inertia, and ω is the angular velocity.

Can rotational kinetic energy be converted into other forms of energy?

Yes, rotational kinetic energy can be converted into other forms of energy such as mechanical energy, thermal energy, and electromagnetic energy through various processes such as friction, collisions, and electromagnetic induction.

How does rotational kinetic energy impact the motion of objects?

Rotational kinetic energy plays a crucial role in the motion of objects, especially those in rotational motion. It determines the speed and direction of rotation and is also involved in the conservation of energy and momentum in rotational systems.

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