Why the speed of the coin rotating in a table increases when it begins to stop ?
Here is how I think it works.
It's all about angular momentum. As the coin begins to spin it's spinning straight up and down, around an axis which is also spinning straight up and down. The sides of the coin are rotating around the coin's central axis. The energy begins being rotated around the central axis, which has a very small diameter. This sets the angular momentum's base rate.
As the coin slows down, the coin eventually falls onto either side, but the angular momentum continues to cause the perimeter of the coin to roll on its edges. The diameter, however, has now increased from a relatively thin vertical axis of rotation, to what is now the entire diameter of the coin.
Thus, in order to achieve the same amount of angular momentum, the energy has to travel a greater distance. Not just the inside axis of rotation, but now it has to travel around the coin's entire diameter. This causes what you see as faster spin, to cover a greater distance, in a shorter time.
The coin does not rotate faster when it begins to stop. It precession rate increases. That happens because as it loses energy due to friction, its axis of rotation tips closer to the ground, and the force of gravity produces a greater torque, which causes the axis to precess faster.
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