The reason why the rotating coin does not fall down is that the gyro effect is produced when the coin rotates. The role of gyro effect is to keep the direction of the rotating central axis of the rotating object unchanged. Therefore, if there is a gyro effect, the central axis of rotation of the coin will always be perpendicular to the desktop and will not fall off. There seems to be a flaw in your question, which is the thickness here. If the thickness of the coin is changed to 1 cm, I'm afraid that as long as you put it casually and don't rotate, the coin will stand up. I know LZ didn't mean to ask that. Then let's start with his rotation and standing! As mentioned earlier, his standing while rotating is related to the "gyro" effect. You should play top. The top will stand on the ground when it rotates. If the "top effect" is not enough to make the coin stand, it will fall. In other words, if the rotation speed is too low, the gyro effect it produces will be very small and coins will fall to the ground. Then as long as we can make the coin turn, it can stand longer. Let's talk about thickness first. You mentioned that increasing the thickness means increasing the area, but the increase of the area does not affect the friction force, which is only related to the friction coefficient and pressure. Now let's look at increasing the outer diameter and inner diameter. Increasing the inner diameter and outer diameter can spread the mass of coins on a larger rotating circumference, which will help to increase the throughput during rotation and make coins rotate for a longer time. However, there is a contradiction that the increase of inner and outer diameters will definitely increase the air resistance during rotation, and the rotation time will not be long at that time. Therefore, it is not the larger the inner diameter and the outer diameter. Only by reaching that intermediate value, the moment of inertia is increased, and the air resistance is not increased too much. The longer the coin rotates, the longer it can stand. Of course, with the increase of inner diameter and outer diameter, the center of gravity of the coin is also higher, which is also unfavorable for the standing of the coin.