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Related to Perpetual motion machines and rocketry.
In my current worldbuilding project, people commonly employ enigmatic Clarkean machines called "spinners". They are two adjoined cubes, counter-rotating and effectively unstoppable. No amount of counter-torque can slow their rate of rotation. In addition, the speed at which the cubes rotate against each other can be "programmed" through a dizzying and convoluted series of mathematical instructions--a two-way mathematical dialogue via EM communication, where difficulty steps up in tandem with faster rotation. Some people have spent their entire lives unraveling and refining the rules that coax spinners up to greater and greater speeds.
Spinners are used in everything from portable heaters and electricity to vehicles and aircraft. Simple, dumb control circuitry can encourage lesser speeds from spinners, while the greatest speeds require computers of vast capability.
(In addition to speed, size may also be ordered in this way. Each cube is by default 20 cm to a side--about the span of 2 credit cards. They can be ordered to twice that in width and height and six times that in "length" parallel to the rotation axis. From two 20x20x20 cm cubes to two 40x40x120 cm rectangular "rods", and anywhere in between. It's also important to note that spinners have tensile & compressive strengths greater than any manmade material, they don't experience creep or stress deformation, and they start vaporizing at 8000 K.)

My civilization is entering an age of high-altitude and orbital flight, and I would expect the application of these magical spinners may reach far into that domain. A fully extended spinner, two rectangular bars each twice as wide/high as a hand and over a meter long, may deliver an enormous amount of torque.

Aviation is outside my familiar research. Originally, I imagined a fan-powered supersonic aircraft, but as I started to look into it I saw a lot of doubt about whether a fan motor could do any useful work with a supersonic intake. Some comments I've seen say it is impossible. Supersonic shocks on the fan blades would cut the flight short and ensure a rough landing, no known material could withstand the stresses.
My previous question asked about rocket flight and how spinners would be involved in producing thrust with fuel and out of an atmosphere. This question is somewhat the opposite: how spinners may be used in producing thrust without fuel and in an atmosphere--supersonically. Is my spinner-powered, supersonic fan motor impossible, or is that an unqualified conjecture? Is there a better hypothetical way to use spinners to achieve supersonic flight?

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    $\begingroup$ You probably try to get the cubes to rotate as slow as possible. Whatever you do with the cubes, the part where the not indestructible material is attached to the cubes shouldn't shear or be pulverised. With infinite power it doesn't matter how fast it goes. Just that it goes. With going slower you have a better chance of balancing the system to the max, so the connection points won't shatter. $\endgroup$
    – Trioxidane
    Jun 20 at 18:57
  • $\begingroup$ @Trioxidane doesn't the counter-torque translate "down" the gear train as well, though? Wouldn't it be better to attach a super-fast spinner directly to the fan blade? Have it act as the stator and rotor? $\endgroup$
    – BMF
    Jun 20 at 19:04
  • $\begingroup$ It depends a bit. I expect these things to be relatively rare, so you would want to squeeze out as much power from them as possible. In the end there is only so much material can handle. Dynamos, gears or anything else will eventually hit a limit. In a way the speed doesn't matter. There is simply a maximum of energy that leaks into the components, making heat or stress that will break the whole thing. But if you only want to turn a fan to move an airplane, a faster one is more efficient. $\endgroup$
    – Trioxidane
    Jun 20 at 19:17
  • $\begingroup$ Easy way to prove that the spinners can power the engines of a supersonic aircraft: you can always convert mechanical power into electric power with little loss, and then electric power into heat, again with little loss. So you have an inexhaustible source of heat, which can serve to power a reaction engine. $\endgroup$
    – AlexP
    Jun 20 at 19:56
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    $\begingroup$ If these spinners are unstoppable why worry about making them faster? Just add gears at a suitable ratio. $\endgroup$
    – DrMcCleod
    Jun 22 at 9:23
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Electric planes and carriers

Electric planes have been a popular concept for a long time, held back by one key factor. Gasoline and other oils are much more power dense than batteries. Electric planes have a shorter range.

Your perpetual motion machines change that. Put a generator on the plane and they can have an immensely powerful engine.

The early applications, before they finished engines, would probably be transport.

Quoting the wiki page.

While the batteries weigh more than the equivalent in fuel, electric motors weigh less than their piston-engine counterparts and in smaller aircraft used for shorter flights, can improve the disparity between electric and gasoline energy densities.

You could have extremely powerful fan motors which could transport huge amounts of goods. Massive amounts of bombs, thick shielding, or huge amounts of supplies. This would be a good route towards making a flying fortress like the helicarrier from avengers. If power is no object, you can carry a huge amount of weaponry.

Supplies and resources are the backbone of war. Your spinners let whichever side has better spinners transport massive amounts of supplies, including fuel ran jet engines, anywhere.

If electricity was a viable contender for jet engines this electrical jet engine would likely have been invented a lot earlier. You would probably start with hybrid engines, which would use the massive power reserves of electricity to empower jets, and work towards purely electrical planes.

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