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## Main Question or Discussion Point

Two identical discs, one of which is rotating about its center, the other, stationary.

Suddenly they're locked / fused / meshed together (by whatever means - at 1:1 ratio).

The angular momentum is thus shared equally between them - one is accelerated, by the same amount the other is decelerated.

We still have all of our momentum, but each disc now only has a quarter the original energy, for a net total of half the original... the other half seems to have been factored out of existence by the spontaneous doubling of the MoI. If we began with 10 J of RKE on one disc, we now have 2.5 on each, and 5 J 'destroyed'.

Successive divisions will likewise eliminate another 50% total system energy per step. All of the momentum remains conserved, but its energy value keeps halving.

We can 'undissipate' the momentum, by adding a rotary spring that is wound up by one disc, braking it to a halt, then transferring this loaded spring over to the second disc, unloading into and thus further accelerating it. But this only causes the energy to sum - so we could add the 2.5 J from one disc back onto the other for a 5 J total. But the other 5 J we're missing doesn't spontaneously re-appear - so this loss mechanism isn't time-symmetrical, merely consolidating the remaining energy. Is this a manifestation of the 2nd law, or what? I understand where the energy's 'gone', and each disc always has the right KE for its given momentum, so i can see

This appears to be a time-dependent input / output asymmetry, from a simple collision?

And it gets worse - suppose both discs had equal opposite angular momentum!? All momentum and KE destroyed!?

Or consider that one disc is simply spinning twice as fast as the other, but in the same direction - again, they're suddenly locked together, and again, all system momentum fully conserved (example: one is spinning 200°/s CW, the other 100°/s CW, after locking together each now has 150°/s CW), and yet some energy is still apparently 'obviated' out of existence.

Final example, reverse the sign of the above 200°/s disc, relative to the other one, and upon locking together, the CW and CCW momentums equalise to just 50°/s velocity on each disc - again, seemingly destroying momentum and energy.

Obviously, in a real collision some dissipative loss is inevitable but here i'm disregarding friction etc. precisely to focus on the apparent non-dissipative losses.

So is my interpretation / conclusions correct (and thus trivial, if surprising to me), or am i missing something?

I'll try posting up some examples from WM2D in a sec..

Suddenly they're locked / fused / meshed together (by whatever means - at 1:1 ratio).

The angular momentum is thus shared equally between them - one is accelerated, by the same amount the other is decelerated.

We still have all of our momentum, but each disc now only has a quarter the original energy, for a net total of half the original... the other half seems to have been factored out of existence by the spontaneous doubling of the MoI. If we began with 10 J of RKE on one disc, we now have 2.5 on each, and 5 J 'destroyed'.

Successive divisions will likewise eliminate another 50% total system energy per step. All of the momentum remains conserved, but its energy value keeps halving.

We can 'undissipate' the momentum, by adding a rotary spring that is wound up by one disc, braking it to a halt, then transferring this loaded spring over to the second disc, unloading into and thus further accelerating it. But this only causes the energy to sum - so we could add the 2.5 J from one disc back onto the other for a 5 J total. But the other 5 J we're missing doesn't spontaneously re-appear - so this loss mechanism isn't time-symmetrical, merely consolidating the remaining energy. Is this a manifestation of the 2nd law, or what? I understand where the energy's 'gone', and each disc always has the right KE for its given momentum, so i can see

*why*we can't recover the original system KE, even though we can re-unify all of the momentum back into a single disc, from any number of discs it's been divided into. But i usually only encounter the 2nd law with regards to entropic losses, whereas here, the loss mechanism is non-thermal.This appears to be a time-dependent input / output asymmetry, from a simple collision?

And it gets worse - suppose both discs had equal opposite angular momentum!? All momentum and KE destroyed!?

Or consider that one disc is simply spinning twice as fast as the other, but in the same direction - again, they're suddenly locked together, and again, all system momentum fully conserved (example: one is spinning 200°/s CW, the other 100°/s CW, after locking together each now has 150°/s CW), and yet some energy is still apparently 'obviated' out of existence.

Final example, reverse the sign of the above 200°/s disc, relative to the other one, and upon locking together, the CW and CCW momentums equalise to just 50°/s velocity on each disc - again, seemingly destroying momentum and energy.

Obviously, in a real collision some dissipative loss is inevitable but here i'm disregarding friction etc. precisely to focus on the apparent non-dissipative losses.

So is my interpretation / conclusions correct (and thus trivial, if surprising to me), or am i missing something?

I'll try posting up some examples from WM2D in a sec..