Increasing speed by decreasing intertia?

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Allen Dowe
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Just curious, explanation if youre going to answer please!

2 horizontal disks stacked on one another spinning at constant v, (about a frictionless axis perpendicular to their center), both have mass.

Okay, so let's say its possible to instantaneously remove the top disk. So would that make the other spin faster?
 
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It would not. Each disk has its own velocity, momentum, inertia, etc. Removing one does not change the other. We don't even need to magically remove one of the disks. We can just assume there is some mechanism that pushes the top disk off of the bottom disk and off of the axle connecting the two.