Understanding the Football Rotation Axis: A Gr. 10 Student's Explanation

[bassbreaker]

i only joined this site to post this thing... now today at school (im in gr 10 by the way) a gym teacher came up to me with a football (american) in his hand and said "bassbreaker (not really my name but we'll leave it at that) You're a smart kid, tell me how this happens." and he rotated the football on its side. Then after a couple of seconds it moved up and it was rotating on its long axis. I was like WTF?! then i said to him some bull **** excuse like, "well because of the axis the Earth spins on, taking gravity into the picture, the circumphrence of the atmospheric..." that's when he was like, ok dere, lies. But w/e i don't know how it works its probably like something to do with balance or sumthing... w/e but I've been looking all over the net n it didnt say it so please someone answer

 

[AlephZero]

A simple equation-free explanation:

The forces on the football are gravity (acting at its CG) and the reaction force against the floor.

If the football is not rotating in a perfectly symmetrical way, those forces are not lined up exactly so they apply a moment to the football. If it was spun by hand, the initial motion would not be perfectly symmetrical.

The football is effectively a gyroscope, and applying a moment turns the rotation axis in an "unexpected" direction just as with a more conventional looking gyroscope.

Once the ball is upright and rotating about the axis with the smallest moment of inertia, it is in a stable state similar to a spinning top, until it slows down (because of friction and air resistance), starts to wobble, and falls down again.

Incidentally this is a real issue when designing rotating machinery. There is a good reason why large wind turbines etc have more than two blades - if they had only two blades, they would tend to be unstable and try do the same thing as your football! With more than two blades, this can't happen.

 

[cesiumfrog]

Once the ball is upright and rotating about the axis with the smallest moment of inertia, it is in a stable state

This reason is wrong.

The more stable state is the one with minimum kinetic energy (for a given quantity of angular momentum), because that state will be approached as a spinning object internally dissipates kinetic energy as heat. Since angular momentum is proportional to angular velocity whereas kinetic energy is proportional to the square of that (and both are directly proportional to moment of inertia), kinetic energy is minimised by rotating around the axes with the greatest moment of inertia (which is how the ball begins).

[See, for example, http://einstein.stanford.edu/highlights/hl_polhode_story.html" .]

The football standing up is a completely different effect, which is complex but "well known" (http://scholar.google.com/scholar?q=spinning egg") for the case of a spinning egg, and mainly has to do with friction. Without friction, as explained above, the stability of rotational axes produces the exactly opposite result.