Mass of a gyroscope when rotating or not rotating

[HansH]

TL;DR

does spinning up a gyroscope make it heavier when determining its weight ?

when spinning up a gyroscope energy is added to it as kinetic energy. as mass and energy are equivalent, does that mean that this energy is stored as extra mass than can really be measured by a balance?

 

[PAllen]

In principle, a spinning gyroscope would weigh more on a balance than one not spinning. However, it would not be possible to detect this in practice. It is similar to the idea that a charged battery weighs more than a discharged battery - true, but not detectable in practice. However, as discussed in the latter part of the following paper, the contribution to weight of the kinetic energy of electrons has been indirectly measured:

https://arxiv.org/pdf/gr-qc/9909014v1

 

[AlexB23]

In principle, a spinning gyroscope would weigh more on a balance than one not spinning. However, it would not be possible to detect this in practice. It is similar to the idea that a charged battery weighs more than a discharged battery - true, but not detectable in practice. However, as discussed in the latter part of the following paper, the contribution to weight of the kinetic energy of electrons has been indirectly measured:

https://arxiv.org/pdf/gr-qc/9909014v1

How sensitive would a scale have to be in order to detect a change in mass for a gyroscope? Say a 1 kilo disk spinning at 1000 RPM.

 

[Ibix]

How sensitive would a scale have to be in order to detect a change in mass for a gyroscope? Say a 1 kilo disk spinning at 1000 RPM.

At non-relativistic speeds the kinetic energy is $\dfrac 12I\omega^2$, which we can call $mr^2\omega^2$ for the purposes of this calculation (just ignoring the constant prefactors because they won't change anything by more than a factor of 10). As a fraction of its rest energy, that's $r^2\omega^2/c^2$, or the square of the rim velocity in units where $c=1$. So for a rim velocity of 300m/s (which is $10^{-6}c$, and roughly the speed of sound) the kinetic energy would contribute about an extra part in $10^{12}$ to the weight.

 

[AlexB23]

At non-relativistic speeds the kinetic energy is $\dfrac 12I\omega^2$, which we can call $mr^2\omega^2$ for the purposes of this calculation (just ignoring the constant prefactors because they won't change anything by more than a factor of 10). As a fraction of its rest energy, that's $r^2\omega^2/c^2$, or the square of the rim velocity in units where $c=1$. So for a rim velocity of 300m/s ($10^{-6}c$), and roughly the speed of sound) the kinetic energy would contribute about an extra part in $10^{12}$ to the mass.

So one part per trillion? So a nanogram? Dang, that is small.

It is cool you did the math.

 

[Ibix]

So one part per trillion? So a nanogram? Dang, that is small.

That's why it took 200 years to notice anything wrong with Newton.

Edit: I don't mean this specific thing, but the general fact that the error in using Newtonian mechanics instead of relativity is absurdly tiny for everyday velocities. It's only when you start doing large fractions of $c$ or studying electromagnetism that the errors start to show.

 

[AlexB23]

That's why it took 200 years to notice anything wrong with Newton.

Yeah, as relativistic changes in mass or time flow are difficult to detect without atomic clocks or lasers.

 

[Ibix]

relativistic changes in mass

Notethat the concept of relativistic mass is deprecated. Mass doesn't change, although weight can. (I did write mass by accident at the end of #4 and corrected it to weight, but after you'd read and quoted it.)

 

[AlexB23]

Notethat the concept of relativistic mass is deprecated. Mass doesn't change, although weight can. (I did write mass by accident at the end of #4 and corrected it to weight, but after you'd read and quoted it.)

Nice. When did they change this? I remember it being called mass a decade ago.

 

[PeterDonis]

Mass doesn't change

It isn't quite that simple. What we're talking about here is a contribution to the invariant mass of a system (the rotating object) from something other than the invariant masses of its constituents (the atoms). Here the contribution is from the kinetic energy of the constituents in the center of mass frame of the system--at least, that's the easiest way to describe it in ordinary language, although if you dig into the math, you'll find that we're actually not dealing with any frame-dependent quantities, everything can be expressed in terms of invariants. So this is an actual increase in the invariant mass of a rotating object, considered as a system, as compared with a non-rotating object with the same constituents.

 

[Nugatory]

Nice. When did they change this? I remember it being called mass a decade ago.

The professional relativity community was giving up on this notion in the late 1950s, but it wasn’t until the 1980s that dropping it was more widely discussed (a paper by Lev Okun precipitated the debate) and then it took a while for the consensus to form and filter down into all the textbooks and teaching materials. And judging by posts we get here, relativistic mass is still firmly embedded in the popular imagination.

Googling for “relativistic mass deprecated” will bring up much of the history, and we have some threads here: https://www.physicsforums.com/threa...-for-deprecation-of-relativistic-mass.847218/

 

[AlexB23]

The professional relativity community was giving up on this notion in the late 1950s, but it wasn’t until the 1980s that dropping it was more widely discussed (a paper by Lev Okun precipitated the debate) and then it took a while for the consensus to form and filter down into all the textbooks and teaching materials. And judging by posts we get here, relativistic mass is still firmly embedded in the popular imagination.

Googling for “relativistic mass deprecated” will bring up much of the history, and we have some threads here: https://www.physicsforums.com/threa...-for-deprecation-of-relativistic-mass.847218/

Wow, that is an interesting history. Shame that textbooks in the 2010s still used mass, same with documentaries.

 

[HansH]

perhaps good to mention some more background why I came to this topic:
someone attracted my attention with a gyroscope where he claimed the he could use it to create a kind of propulsion in space with that thing. of course that does not work everyone will say because of action and reaction not being different from what generally happens.

But then I realized that it still may work but in a completely different way;
suppose you have a long rail in space with a gyroscope on it that can be moved along that rail by a motor.

first you move it from one side to the other side of the rail while the gyroscope is at rest. this means that you let a force F working on it during a time interval deltaT so working on the mass m of the gyroscope.

then coming at the other side of the rail you let the gyroscope spin very fast (probably using 2 gyroscopes running in opposite direction the prevent the construvtion from totating) now we have the situation that due to the rotation the mass increased to m+delta_m and then you let the gyroscope move back to the original place, therby delivering more same impuls but as the mass is now larger the total construction of gyroscope+ rail has a netto speed. so repeating thet cycle you could generate an accelleration of the whole construction.

of xourse this is all very small but this is about the fundamental principle working or not.
so does this work or not?

 

[berkeman]

But then I realized that it still may work but in a completely different way;

Reactionless drives are a forbidden topic at PF (a waste of everyone's time and electrons). Thread is closed.

EMDrive and other reactionless drives
See https://www.physicsforums.com/threads/nasas-em-drive.884753/