Does a spinning disk gain relativistic mass

[imatfaal]

wait, 1 person says it slows down and 1 person says it doesn't

 

If the disc is rotating at x rad/s and increases to x+1 rad/s then there must be an external torque - and angular momentum in the system of the disc will not be conserved. If the increase in speed of rotation is enough to start thinking about relativistic effects then you just need a bigger torque.

 

The fact that posters can say the exact opposite is the problem with text based physics - the unwritten assumptions of different posters can be different. When we deal with equations, force diagrams, and frames of reference we have no room for confusion

[514void]

so if I did relativistic maths, it would say that spinning up disks would keep their velocity, but if I did conservation of momentum maths it would say that it would slow down. (velocity as opposed to angular velocity)

I'm not sure what maths I should do.

Edited March 3, 2014 by 514void

[imatfaal]

so if I did relativistic maths, it would say that spinning up disks would keep their velocity, but if I did conservation of momentum maths it would say that it would slow down. (velocity as opposed to angular velocity)

I'm not sure what maths I should do.

 

 

No - quite the opposite. You get the same answers which ever way you do it if you are correct - if you can generate different answers then you have an internal contradiction and a big problem. SR and newtonian mechanics are mathematically internally consistent - that is to say no thought experiment nor set of calculations can cause a self-contradiction. Because when you do the maths you know what you have set as constant, what your frame of reference is, and what underlying assumptions are; all models that correctly use SR will be consistent in their answers.

 

You need to engage with the equations - otherwise it is like saying you understand motor-mechanics because you once watched Nascar

[514void]

is newtonian mechanics and SR consistent with each other?

If not, then is conservation of momentum only applicable to newtonian mechanics?

[studiot]

 

If the disk was fixed at the top of the container, and it was spun up, would the center of mass move closer to the disk?

 

 

What is the centre of mass in a relativistic system?

[514void]

 

What is the centre of mass in a relativistic system?

I had a look for it:

http://en.wikipedia.org/wiki/Center_of_mass_(relativistic)

It seem like it is unresolved.

[swansont]

I had a look for it:

http://en.wikipedia.org/wiki/Center_of_mass_(relativistic)

It seem like it is unresolved.

 

Unresolved for your example? Please show how this is.

[514void]

 

Unresolved for your example? Please show how this is.

unresolved as its isn't a clearly defined equation, so I could use it inappropriately.

[swansont]

unresolved as its isn't a clearly defined equation, so I could use it inappropriately.

 

I think the issue is that there are situations where it's not clearly defined. Is this one of those situations?

[studiot]

Your problem is that your object (a disc) has components that possess differential tangential velocities with relastivistic implications, particularly for the mass summations needed to evaluate a 'centre of mass'.

 

You did not answer my question about relative velocity, which should help you answer this,as should an appeal to symmetry.

[514void]

relative velocity of what?

[studiot]

 

514void

yes, in any inertial frame, the outside of a spinning disk will have relative motion to its center.

 

 

Studiot

If two objects are in relative motion does not the separation change, unless that relative motion is zero?

 

[514void]

this is only true in only one reference frame.

the reference frame would be spinning around the center of the disk, at the same angular velocity of the disk.

spinning reference frames are sort of silly, since if the frame extends past a certain radius, it would be going FTL.

 

Unless you propose some sort of spiral reference frame that has angular velocity that goes at the speed of light at infinity radius.

This sounds sort of cool.

Edited March 5, 2014 by 514void

[studiot]

What I am trying to get you to consider is the distribution of mass gain as a function of radial distance along with its implications, with both my earlier and more recent comments.

 

Perhaps I haven't expressed myself very well, if so I'm sorry.

[514void]

Ok, That makes me think that if relativistic mass is directional, then there would be no relativistic mass force on the center of the disk when it isn't accelerating.

this sort of makes sense since if relativistic mass isn't directional, then a spinning disk would slow down and eventually stop spinning.

If relativistic mass is directional, then is slowing an object easier than speeding it?

[studiot]

I don't see mass as having a direction.

 

What must vary is the apparent density, from point to point within a spinning relativistic system.

Edited March 5, 2014 by studiot

[514void]

I'm not so sure what happens.

But I think that there is a warning against considering a change in any sort of structure of the object due to relativistic mass.

Edited March 5, 2014 by 514void

[514void]

but yes, there would be a velocity gain as a linear function of the radius regardless of relativistic mass direction.

Relativistic mass increases exponentially with velocity.

 

So it would be beneficial to have the rest mass mostly near the edge of the disks.

 

Is there anything else I should consider?

Edited March 5, 2014 by 514void

[studiot]

 

Is there anything else I should consider?

 

 

 

You might like to look at Ehrenfest's Paradox.

 

http://en.wikipedia.org/wiki/Ehrenfest_paradox