The increase in rotation speed of a coin on a table as it begins to stop is primarily due to angular momentum. Initially, the coin spins around a narrow vertical axis, but as it slows down, it tips onto its side, increasing the diameter of its axis of rotation. This change requires the energy to travel a greater distance to maintain the same angular momentum, resulting in a faster spin. Additionally, as friction reduces the coin's energy, its axis tilts closer to the ground, leading to increased torque from gravity and a higher precession rate. Ultimately, the observed faster spin is a result of these physical dynamics rather than an actual increase in rotational speed.