Why Does a Spinning Coin Wobble Faster Just Before It Stops?

Spin a coin on its edge and it gradually leans over, ending with a rapidly rising rattle. It can look as though the coin is “spinning faster”, but two motions need to be separated. Rotation about the coin's own axis is slowing overall. Meanwhile, its tilted axis and point of contact circle around the vertical direction; this is precession. It is the precession that speeds up near the end.

When the coin is more upright, its centre of mass is higher and each cycle of its lean covers a larger spatial path. As friction and slipping remove energy, the coin settles closer to the table, lowering its centre of mass and shrinking the circle traced by the contact point. The torque due to gravity can then carry the coin through one circuit along a shorter path and at a smaller inclination, so the precession frequency rises. The accelerating hum is produced by increasingly frequent contact and tiny impacts.

This does not violate conservation of energy. A higher frequency does not mean greater total kinetic energy: the amplitude is shrinking, while mechanical energy continues to become heat, sound and minute vibrations of the surface. Experiments indicate that rolling or sliding friction is the main loss mechanism on typical tested surfaces, although the relative role of air drag depends on the stage and model. Eventually smooth rolling gives way to slipping, bouncing and material deformation, and the coin abruptly lies flat. It has not gained a final burst of energy; it is moving more frequently through an ever smaller range.

https://www.nature.com/articles/35009017
https://link.aps.org/doi/10.1103/PhysRevE.66.045102