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If an object is rotated on its axis near the speed of light would its mass increase?

Normally if the object was moving (in relationship to the Earth for example) I would agree that its mass would increase. I think, when rotating that it won't increase mass, but I can't prove it.

In the other hand if $E=mc^2$ and $E$ is the energy of motion, does that mean that rotation has energy of motion?

Qmechanic
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J_Strauton
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    Related: http://physics.stackexchange.com/q/76835/ – dmckee --- ex-moderator kitten Nov 14 '14 at 23:11
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    Short, short version: the mass of a system can be either more or less than the mass of the components. – dmckee --- ex-moderator kitten Nov 14 '14 at 23:13
  • @dmckee Although that post is somewhat related, I am talking about rotating at the speed of light or close to it. I appreciate it though, it was a good read, but I still have this burning question. I think they solved the question by concentrating on forces while I am interested in mass. – J_Strauton Nov 15 '14 at 00:33
  • If you read Mark Eichenlaub's answer carefully, you'll that he casually states that the lawnmower's "mass" increases due to $E = mc^2$. The question is - which "mass"? It's the "relativistic mass", which is really not a good concept, as it is not invariant under change of reference frames (in a comoving frame, the "mass" increase is gone again!). Just stick to rest masses. – ACuriousMind Nov 15 '14 at 00:56
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    @ACuriousMind: We are referring to rest mass. Rest mass isn't additive and depends on the motion of the objects comprising the system. –  Nov 15 '14 at 01:20
  • @BenCrowell: Hm...I'll defer to you there. It seems I need to reexamine my understanding of mass in relativity, then. – ACuriousMind Nov 15 '14 at 01:26
  • related: http://physics.stackexchange.com/questions/94921/mass-in-terms-of-special-relativity –  Nov 17 '14 at 23:49

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Yes, this is certainly true. Mass is defined by $m^2=E^2-p^2$ (in units with $c=1$), where $(E,p)$ is the momentum four-vector built out of the mass-energy and momentum. (This defines what's known as invariant mass, as opposed to "relativistic mass.") Mass as defined in this way is not additive, and depends on the motion of the particles within a system.

As a simple example, say we have two masses $m$ at the ends of a massless stick. When the stick is at rest and not rotating, the momentum four-vectors are both $(m,0)$, the sum is $(2m,0)$, and the mass of the system is $2m$.

Now let the stick rotate end over end. The momentum vectors are now $(m\gamma,m\gamma v)$ and $(m\gamma,-m\gamma v)$. The total momentum four-vector is $(2m\gamma,0)$, which means the mass of the system is $2m\gamma$.