# Does object gain mass when spinning?

1. Oct 8, 2014

### 1832vin

everyone knows, E= MC^2 + PC^2
but does that apply to spinning objects?
when i was small, i always was under an impression that you can create more gravity when you spin the object(well, not classical physics fast)
i mean, the displacement is 0, so wouldn't the velocity= 0
and if really gets that fast, wouldn't the center be moving in time at a much more slower pace?

sorry, i have alot of questions, answering any would do or even just pointing me to the right google search!
thankyou

oh, and just how much mass do you gain when you go to close to C? and porportional to that, how much gravity would you be making just by spining?

2. Oct 8, 2014

### Staff: Mentor

Yes.
Not the center, the outer parts would have time slowed down (for them, as seen by us) due to their velocity.
Nothing, as mass is measured in the center of mass frame. You gain a lot of energy, given by the formula above (but it is easier to calculate the Lorentz factor and subtract your rest energy).
If you spin so fast your outer parts move with a significant fraction of the speed of light, then this could become notable.

3. Oct 8, 2014

### 1832vin

so does that mean that even if i somehow managed to spin something at 0.9C on the outside, there will be NO gravity changes?
and by the way... when you say "center of mass frame", is it just mathematically? or in real life?
sorry for having so much questions, i'm just very curious

4. Oct 8, 2014

### PAllen

I think Mfb may have misunderstood that your intent was that the statement about moving near c was still in reference to the spinning body. For the spinning body, he already answer 'yes you gain mass'. An in general relativity (the relevant theory of gravity for such a problem) you would indeed find additional 'gravity' due to the spinning. It can get quite large. For a material body, the affect is far more complex than 'integrating a gamma factor'.

5. Oct 8, 2014

### 1832vin

thankyou for answering me, you seems like you are familiar with gravitational theories, and such.
do you have a book commendation or some sort that explains gravity, and all the relevant topics and the contemporary theories of it.
i don't mind it being 5000 pages

6. Oct 8, 2014

### PAllen

See:

https://www.physicsforums.com/forums/physics-astro-textbook-listings.224/?prefix_id=32 [Broken]

Last edited by a moderator: May 7, 2017
7. Oct 8, 2014

### pervect

Staff Emeritus
The effects of spin on mass and gravity have already been answered well by Pallen, there's not much more to be said. But there's a bit more to be said about some of the other questions I think.

As far as the gravitational effects of a moving object, I would suggest the paper "Measuring the active gravitational mass of a moving object", by Olson and Guarino. One can find a link to the paper on google scholar, however while the paper is good, the provenance of the website that turns up in google scholar which hosts the paper is - err - not so good, unfortunately. Thus I won't provide the link, interested parties such as the original poster can find the full text of the paper online through google scholar however. A search through the forum will also find quite a bit of discussion of this topic and frequent mentions of this paper.

Note that "active gravitational mass" the way that Olson and Guarino define it, is NOT the same as _either_ of the sorts of mass one may be familiar with from special relativity, invariant mass (the E^2 - p^2 sort mentioned by the original poster ), or relativistic mass (which is just another name for energy). Also, the term "active gravitaational mass" is not used much in the literature or textbooks outside Olson and Guarino. (with the possible exception of Schutz). The paper itself will mention a few other defintions of mass as well.

The most straightforrwards way in my opinion to explain things is to point out that it is only in Newtonian gravity that "mass" causes gravity. In general relativity, it is the stress-energy tensor that causes gravity and not "mass". The stress-energy a lot of different components, which can be basically classified as energy, momentum, and pressure. If you think of energy, momentum, and pressure as all causing gravity, you'll be on the right tract.

As far as introductory papers on gravity, I'd suggest Baez' "The Meaning of Eintein's Equation", available at http://math.ucr.edu/home/baez/einstein/einstein.pdf. There's also a HTML version available. Baez's paper considers things from the center of momentum frame, so it won't tell the reader much about the effects of motion (Olson & Guarino is better for that). But it will give the reader more info about the stress-energy tensor, and about how pressure causes gravity, a useful bibliography, and a good intermediate overview and a place to start further reading.