A revolving wheel in a vacuum and removed from Gravitational Sources

[geordief]

Suppose there is a wheel that is revolving upon its axis and we imagine that it is made up of very many electro magnets(like a leggo construction).

 

Its shape is that of a conventional wheel with perhaps 20 spokes and a circumference -all made out of the same material , these very small electro magnets which are all the same size and shape so far as is possible.

 

As the wheel turns it maintains its shape , held together by the magnetic force between its components.

 

What happens when the electricity is cut ?

 

I am wondering what shape the wheel adopts as it starts to disintegrate? Do the spokes arc in the direction of the previous (before the power was cut) revolution or is it the other way round? Do they also elongate (as I imagine they do?

 

Might there be an animation somewhere that shows what happens(or something similar) ?

 

If this wheel is removed from gravitational sources , does its own distributed mass have a bearing if the speed of revolution is not too great?

Edited December 8, 2016 by geordief

[swansont]

Each part will move in a straight line with the velocity it had when the power was cut (ignoring any transient effects in the magnets)

[Bender]

The spokes will seemingly rotate in the same direction, but slow down. They will never stop, but will never quite reach a 90° rotation with respect to the position they had when the magnets were released.

The spokes will continue to elongate at a slightly increasing rate [math]r=\sqrt{r_0^2+(\omega t r_0)^2}[/math]

 

(not sure what this has to do with relativity, though)

Edited December 15, 2016 by Bender

[Sriman Dutta]

As the wheel rotates, it has centrifugal force which the throws away the material.

[swansont]

As the wheel rotates, it has centrifugal force which the throws away the material.

No, it doesn't. There is no force directed outward. The material will go in a tangential straight line when the force holding it together is removed.

[Sriman Dutta]

No, it doesn't. There is no force directed outward. The material will go in a tangential straight line when the force holding it together is removed.

Why? Centrifugal force?

[Klaynos]

Why? Centrifugal force?

Inertia.

[Sriman Dutta]

Inertia of motion according to Newton's First Law of Motion.

[Klaynos]

The force holding them is removed, there is no force so they go straight as Swansont stated. Inertia.

[Bender]

If it turns so slow that the parts approach the escape velocity of the combined mass of the parts closer to the centre, they would start spiralling noticeably. If below the escape velocity, they'll approach a circular orbit.

[geordief]

 

 

(not sure what this has to do with relativity, though)

I was ruminating on time dilation caused by acceleration/gravity and this scenario came to my mind.

 

As I was unable to work out what would happen , I asked for help.

 

The "spokes" turn into nautilus like shaped spirals,don't they?

[Bender]

I was ruminating on time dilation caused by acceleration/gravity and this scenario came to my mind.

 

As I was unable to work out what would happen , I asked for help.

 

The "spokes" turn into nautilus like shaped spirals,don't they?

Not at normal speeds and masses typically associated with magnets and lego. The spokes will remain straight (at least within realistic measurement accuracy), unless they are moving very, very, very slowly.

[geordief]

Not at normal speeds and masses typically associated with magnets and lego. The spokes will remain straight (at least within realistic measurement accuracy), unless they are moving very, very, very slowly.

thanks.

[swansont]

Not at normal speeds and masses typically associated with magnets and lego. The spokes will remain straight (at least within realistic measurement accuracy), unless they are moving very, very, very slowly.

 

You mean fast?

[Bender]

Let's estimate the escape velocity

[math]v_e = \sqrt{\frac{2GM}{r}}[/math]

Let's say the mass is 10 kg and the radius is 10 cm, then the escape velocity is [math]10^{-4}[/math] m/s, which for that radius is [math]2 \cdot 10^{-4}[/math] revolutions/s or roughly one revolution every hour. (I must admit that this is higher than what my intuition told me)

 

Several orders of magnitude faster than that, and the effect of gravity is hardly going to be noticeable. (until you get to relativistic speeds perhaps)

 

This calculation holds for the parts at the outer rim. For those closer to the centre, it depends on the mass distribution. If most of the mass is concentrated in the hub, and the speed is below the escape velocity, you will indeed get a spiral, somewhat like the milky way.

Edited December 16, 2016 by Bender

[swansont]

Let's estimate the escape velocity

[math]v_e = \sqrt{\frac{2GM}{r}}[/math]

Let's say the mass is 10 kg and the radius is 10 cm, then the escape velocity is [math]10^{-4}[/math] m/s, which for that radius is [math]2 \cdot 10^{-4}[/math] revolutions/s or roughly one revolution every hour. (I must admit that this is higher than what my intuition told me)

 

Several orders of magnitude faster than that, and the effect of gravity is hardly going to be noticeable. (until you get to relativistic speeds perhaps)

 

This calculation holds for the parts at the outer rim. For those closer to the centre, it depends on the mass distribution. If most of the mass is concentrated in the hub, and the speed is below the escape velocity, you will indeed get a spiral, somewhat like the milky way.

What gravity? The system is held together by magnets.

[Janus]

The top image shows what would happen to 1 spoke, after the magnets release as viewed from the non-rotating frame. The thickness (along the line of sight) will not change, while the spokes expand outward away from the axis of rotation. The spokes will also become less and less dense as the individual components spread out.

The straight-up spoke is represents the moment the magnets release and each of the others is the same spoke at different moments in time. The thin lines represent the center-line of the spoke if it had continued to rotate around the axis.

The bottom image shows the same scenario but from a frame that was rotating with the station. If you plot the position of the end of the spoke over time, you get a spiral-like arc.( though the spokes themselves remain straight.)

 

 

[Bender]

What gravity? The system is held together by magnets.

Not after the magnets are switched off. The magnets don't really matter in this thought experiment.

[geordief]

The top image shows what would happen to 1 spoke, after the magnets release as viewed from the non-rotating frame. The thickness (along the line of sight) will not change, while the spokes expand outward away from the axis of rotation. The spokes will also become less and less dense as the individual components spread out.

The straight-up spoke is represents the moment the magnets release and each of the others is the same spoke at different moments in time. The thin lines represent the center-line of the spoke if it had continued to rotate around the axis.

The bottom image shows the same scenario but from a frame that was rotating with the station. If you plot the position of the end of the spoke over time, you get a spiral-like arc.( though the spokes themselves remain straight.)

 

 

spokes2.jpg

Is the original circle elongated in the direction of the original rotation? (an ellipsoid?)

 

What about from the two frames of reference , the evolving c.o.g ** of the system and the original one? Do they differ?

 

 

** centre of gravity

Edited December 17, 2016 by geordief

[swansont]

Not after the magnets are switched off. The magnets don't really matter in this thought experiment.

 

 

The OP says gravity is not an issue. So the opposite of what you claim.

[Janus]

Is the original circle elongated in the direction of the original rotation? (an ellipsoid?)

 

What about from the two frames of reference , the evolving c.o.g ** of the system and the original one? Do they differ?

 

 

** centre of gravity

The wheel simply expands equally in all directions perpendicular to the axis of rotation as shown in the two images below. The top is as seen from the non-rotating frame. The red arrows show the paths of the ends of the spokes after the release of the magnets.

I'm not sure what you mean by the evolving CoG, as the center of gravity never changes (always at the center of the Wheel) do you mean according to the changing angular velocity of the expanding structure? In that case you get the bottom image, just a expanding wheel(no rotation relative to you.)

 

 

 

 

From the original frame of rotation, you get this for the four spokes.

 

The apparent spiral path comes from viewing linear motion from a rotating frame.

[geordief]

I'm not sure what you mean by the evolving CoG, as the center of gravity never changes (always at the center of the Wheel) do you mean according to the changing angular velocity of the expanding structure? In that case you get the bottom image, just a expanding wheel(no rotation relative to you.)

 

 

Not quite sure what I was thinking . I wasn't sure that the CoG would stay the same as I was imagining the circumference of the wheel transforming into a non spherical shape .

 

Thanks.

[Bender]

 

 

The OP says gravity is not an issue. So the opposite of what you claim.

I interpreted this as there not being sources of gravity outside the wheel. Since it was suggested the wheel would spiral, I elaborated how it could, and where that idea might come from.

[geordief]

I interpreted this as there not being sources of gravity outside the wheel. Since it was suggested the wheel would spiral, I elaborated how it could, and where that idea might come from.

I did have both scenarios in mind . The wheel can be arbitrarily massive and the original speed of rotation can also vary from barely observable to relativistic(if that is possible).

 

So a few parameters there,I think.

 

Is the circular shape of the (circumference of the ) wheel changed under some of those initial conditions ?

Edited December 18, 2016 by geordief

[Bender]

I cannot think of a way the circular symmetry could be broken, unless the wheel itself starts asymmetrical.