A gun fixed on the disk which can rotate freely,
after first shoot, the disk Angular velocity is ω, Kinetic energy is ΔE1=Iωω/2,
after second shoot, the disk Angular velocity is 2ω, Kinetic energy increases from Iωω/2 to
I2ω2ω/2, the growth ΔE2=3Iωω/2:
Why :
different bullet gunpowder does do different works?
and how about the tenth bullet?......

willem2 Posts: 1,060	After the first shot, the gun will be moving backwards, so the second bullet will move slower than the first, so there is more kinetic energy left for the gun and the disk.

different people will make different conclusion：
1，the people A sit on the disk will find the bullet has the same velocity;
2, only the people B standing by side will agree with you;
3, but another problem appears : after analysis people A will statement that
environment's tempreture is lower than people B's calculation.
E0=Chemical energy of gunpowder
E1=bullet's Kinetic energy
E2=disk's rotating Kinetic energy
E3=heat energy absorbed by environment
E0=E1+E2+E3 every bullet has the same E0
CAN WE CONCLUDE THAT:
in different frames, the temperature is relative?

Is anything wrong?
Equivalence principle?
In any energy conversion process we should put the saddle on the right horse.
Another example:
Two ship A and B move towards the moon, now ship A slow down by jetting gas forward .
In A's opinion the ship's kinetic energy decreases and converts into other kind of energy,so does the gas's internal energy;
But in B's opinion ship A is speeding up but not slowing down! Ship A's kinetic energy is increasing up. Ship A need absorb energy !
Would you like to tell me :who is the loser and who is the winner or receiver?

Willem2:

The disk isn't an inertial frame, so you can't expect that energy is conserverd. For the people on the disk, the first bullet would suddenly appear to get more energy when you fire the second bullet.

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You are brave enough.
But the first bullet has gone with the wind. Can energy be transferred through remote sensing? Like Telekinesis ?
And every moving body can entrust different porters carrying different energy share -- even uncertain value --corresponding to different observers in different frames just in order to match their relative velocity?
My God!
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mfb:

Energy can change by changing your coordinate system - which observers on the disk do (even if it is so large that the rotational motion is nearly linear for the timescales involved).

Ship B will see a high energy of the ejected gas, as it is now quicker than ship A.


Each reference system will observe different energies for different parts of the same system, and even a different total energy. That is fine. Every system will see a conservation of this energy in its own frame.

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Would you like to tell me in different frame, the temperature is relative?
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mfb:

Temperature is usually defined in a reference frame where the object does not move. Therefore, it is pointless to discuss "temperature in a different reference frame".
In addition, I do not see the relevance here. You can look at the energy content from heat - this is the same in all reference frames (at least without special relativity).

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E0=Chemical energy of gunpowder
E1=bullet's Kinetic energy
E2=disk's rotating Kinetic energy
E3=heat energy absorbed by environment
E0=E1+E2+E3 every bullet has the same E0
The problem is the linear velocity is relative and angular velocity is absolute.
If people A find E1(a) is bigger than people B's conclusion about E1(b), He can only judge that E3(a) gets less share from E0.

After n bullets were shot the angular velocity indreased from (n-1)ω to nω--according to the law of momentum conservation;
And the rotating kinetic energy increased from I(n-1)ω(n-1)ω/2 to Inωnω/2: the growth was nIωω-Iωω/2.
The gun can be controlled to fire toward 12,3,6 or 9 o'clock direction in turn!

Let's suggest there is a wooden barrel containing the disk and sharing the same center axis.
Acording to the law of momentum conservation the barrel will gain the same size angular velocity with reverse direction.
What will happen? paradox or disaster?