# Does a spinning disk gain relativistic mass

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I was thinking that this could be used to accelerate spaceships.

Here is the hypothisis:

If i have a closed system with a disk that moved up and down, and the disk was made to spin by a motor at the top of the system and made to stop spinning at the bottom of the system, the whole system would feel a force that would accelerate it upwards.

The system could have a similar disk that moved up and down but spun the opposite direction than the first to stop the whole system from spinning.

I have thought about how It mightn't work, such as if you spun up the disk, would it lose translational inertia?

I think no, since according to relativity, there is no preferred frame to slow down against.

I understand that there would not be much translational force produced for 'non relativistic' speeds, but sensors are quite good, so this might even be experimentally testable on earth.

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A rotating system will gain mass, using the standard definitions. Rotation represents an accelerated reference frame, so you know there is rotational motion, and the mass must be evaluated from an inertial frame.

However, I don't think your system will work, because the up and down motion of the disk must be accompanied by a down and up motion of the container, such that the center-of-mass will not change.

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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?

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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?

It would, assuming the power source (where the energy to spin the disk is coming from) was nearer the bottom.

However you need to remember that "relativistic mass" is just a way of describing energy.

What you describe seems to be equivalent to a boat with a person sitting at one end with a heavy ball in the middle of the boat. The weight of the ball represents the energy in the power source. The person pulls the ball towards them: equivalent to spinning the disk; moving the mass to one end. They then throw the ball towards the other end of the boat (equivalent to you moving the spinning disk from one end to the other.) The ball then rolls back towards the center of the boat (equivalent to spinning down the disk and returning the energy to the power source).

What will happen? The boat will move back a bit when the ball is pulled forward. It will then move forward when the ball is thrown back. Then it will move back when the ball rolls to the center of the boat. No net movement (ignoring friction/drag).

Same here: you are just moving energy around in a closed system so it can't change the overall motion of the object.

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There is the issue of the motion.

Apparent mass gain appears to observers in relative motion.

What is the relative motion of two observers at say r/2 and r from the centre of rotation?

Does their separation alter?

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the velocity of the rim of a spinning disk with the center being at rest in a inertial frame would always be more than the center of the disk.

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But that velocity is perpendicular to r so are they in relative motion?

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

does relativistic mass gain have a certain direction like length contraction?

I suppose that this is known from circular particle accelerators where the directing force and accelerating force are separate.

Edited by 514void
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yes, in any inertial frame, the outside of a spinning disk will have relative motion to its center.

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

Edited by studiot
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The mass has to be evaluated by an observer not on the disk, i.e. in an inertial frame.

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?

In principle, yes. If you compared two systems side-by-side, one with a spinning disk and one with a disk at rest, you'd see a shift in CoM.

But to ask what happens dynamically, the details are important. e.g. how do you spin up the disk without other parts of the system also spinning up in the opposite direction?

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There is the issue of the motion.

Apparent mass gain appears to observers in relative motion.

What is the relative motion of two observers at say r/2 and r from the centre of rotation?

Does their separation alter?

This is complicated (very complicated). But also irrelevant, luckily.

does relativistic mass gain have a certain direction like length contraction?

No. Mass is not a vector and so is independent of direction. (Note that many people consider the concept of "relativistic mass" to be unnecessarily confusing. It is better to just consider energy.)

I suppose that this is known from circular particle accelerators where the directing force and accelerating force are separate.

Well, it is known from theory (and confirmed by experiment and practical issues like those you mention).

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I read somewhere that relativistic mass as opposed to rest mass does have a direction.

so to make the mass gain along a vector you would need to have the axle perpendicular to the desired force.

Also you would need spinning opposing disks to cancel the net torque on the system.

So spinning twin disks faster or slower would have no net force in any direction, but would gain directional mass.

So could you control the speed of the disks while moving them in a system to gain a net force in a direction?

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I was thinking that this could be used to accelerate spaceships.

Here is the hypothisis:

If i have a closed system with a disk that moved up and down, and the disk was made to spin by a motor at the top of the system and made to stop spinning at the bottom of the system, the whole system would feel a force that would accelerate it upwards.

The system could have a similar disk that moved up and down but spun the opposite direction than the first to stop the whole system from spinning.

I have thought about how It mightn't work, such as if you spun up the disk, would it lose translational inertia?

I think no, since according to relativity, there is no preferred frame to slow down against.

I understand that there would not be much translational force produced for 'non relativistic' speeds, but sensors are quite good, so this might even be experimentally testable on earth.

Here's an alternative version:

A battery is loaded, then the loaded battery is thrown, then the flying battery is drained, then the empty battery is stopped.

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I don't see how that wouldn't work, nice one.

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I don't see how that wouldn't work, nice one.

It is exactly the same as yours: you add energy to an object, move it from one place to another, remove the energy, then move it back again. Again, no net change in momentum.

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I read somewhere that relativistic mass as opposed to rest mass does have a direction.

so to make the mass gain along a vector you would need to have the axle perpendicular to the desired force.

Also you would need spinning opposing disks to cancel the net torque on the system.

So spinning twin disks faster or slower would have no net force in any direction, but would gain directional mass.

So could you control the speed of the disks while moving them in a system to gain a net force in a direction?

Relativistic mass is indeed velocity dependent, as opposed to simply being speed dependent, as viewed from the perspective of Newton's second law.

But the spinning disk can be analyzed without resorting to relativistic mass. A spinning disk has more mass than one that's not spinning, just as an atom that has absorbed a photon has more mass than one in the ground state.

Where does the energy come from to get the disk(s) up to speed?

Let's say you have a battery that runs a motor. If the battery is within the system, then the system's mass won't change, since the total energy (ignoring losses) will be the same. If the energy source is outside, then you are changing the mass elsewhere, and you have to account for that, too, in analyzing the problem.

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It is exactly the same as yours: you add energy to an object, move it from one place to another, remove the energy, then move it back again. Again, no net change in momentum.

A battery is loaded -> it becomes more massive.

Then battery is pushed so that it slides along a surface.

On the surface there are metal strips that short circuit the battery.

Then the drained battery, which is less massive than the battery that was pushed, is stopped.

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A more effective means of propulsion might be to use the energy to expel some sort of exhaust material in the direction opposite to that in which you want to travel. We need a catchy name for such a system; maybe "rocket"?

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A battery is loaded -> it becomes more massive.

Then battery is pushed so that it slides along a surface.

On the surface there are metal strips that short circuit the battery.

Then the drained battery, which is less massive than the battery that was pushed, is stopped.

Where does the energy come from that loads the battery, and where does the energy go that comes from the battery? These will affect the mass distribution as well. You can't ignore these steps.

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the energy would be transferred to the container, which would gain mass and the battery wouldn't transfer as much 'negative' momentum as it is slowed and returned to the start. win, win.

Edited by 514void
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the energy would be transferred to the container, which would gain mass and the battery wouldn't transfer as much 'negative' momentum as it is slowed and returned to the start. win, win.

It's easy to state such a thing; it's part of almost all perpetual motion claims. This is why rigor is needed. Show the calculation.

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Moving energy backwards and forwards is not different from moving mass backwards and forwards.

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It is interesting. I think if you are displacing energy wrt the centre of mass/energy in a closed system, there should be an equal and opposite displacement of mass or energy such that the centre of mass energy cannot change.

So where at each stage is there an equal but opposite effect?

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Two spiral cords are connected to the terminals ot the moving battery. Now the moving battery can be easily drained to a static battery.

So what will happen:

When the batteries move away from each other: We try to remove energy from the battery but what happens is that some electro-chemical energy turns into kinetic energy. A reduced amount of energy arrives to the static battery.

When the batteries move towards each other: We want to remove the electro-hemical energy from the battery but some kinetic energy turns into electro-chemical energy. an increased amount of energy arrives to the static battery.

In both cases the cord tries to move away from the moving battery ... like a toy that consists of a whistle and a rolled paper tube ... what is that called?

(You see, the battery is blowing energy into a curly hose, and the energy is redshifted or blueshifted)

Edited by Toffo
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Does previous post sound a little bit like a joke?

Here's yet another way to transfer energy from a moving battery: Laser device attachet to the battery. With this energy transfer method it's clear that there exist a thrust effect and redshifft effect.

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