Spinning Footballs


Why when a M & M or a football is spun on its minor axis does it, as it decelerates, rotate up about it's major axis? That is, why does the football begin to spin on its pointed side?


Let's imagine a football spun about its long axis and placed on the ground with that axis at an angle to the vertical. Then gravity acting downward on the football's center of gravity and the ground acting upward on the end of the football will produce a torque tending to increase the long axis angle from the vertical. This torque interacting with the angular velocity of the football's rotation will cause the long axis to precess, that is rotate horizontally about the vertical line through the ball's point of contact with the ground. See gyro theory for more detail on this.

Both the initial spin and this precession have kinetic energy associated with them. Also there is potential energy associated with the ball's center of gravity being elevated due to the long axis not being horizontal. When the ball's angular velocity about the long axis is large, the lowest energy configuration is with the long axis vertical and no precession. As the spin velocity decreases due to friction losses, the lowest energy configuration shifts to include some precession, some spin and somewhat less potential energy of elevation. As the ball continues to slow, the potential energy seeks its minimum value, the spin if manifest as rolling and the precession degenerates into rotation about a short axis. Ultimately the ball comes to rest with its center of gravity as low as possible and no spin or precession.

The observed behavior of the football then is nothing more than Mother Nature's tendency to be a lazy dame, always driving systems to their lowest available energy configuration. The mathematical determination of the minimum energy combination of spin, precession and elevation of center of gravity, as a function of spin velocity is pretty much a mess.