Why does a spinning hemisphere right itself?

[joelio36]

I noticed this intriguing phenomena whilst messing about in work with a perfect glass hemisphere the other day:

Place the hemisphere on a surface, with the flat surface facing upwards. (Looks like a 'D' rotated 90 degrees clockwise).

When I spin the hemisphere fast enough, it will spin until it is spinning on it's side (Looks like a 'D' rotating around the straight line in the 'D' )

Then it will 'tip' over the edge, and by the time it stops moving, the flat surface is facing down ('D' rotated 90 degrees anti-clockwise)

It appears any force which I exert which is not purely rotational about the primary rotation axis grows until the 'wobble' is enough to topple the hemisphere.

The only possible explanation I can come up with myself is that the friction force with the surface is influencing the motion.

If someone could shed some light on this I would appreciate it!

 

[.Scott]

As long as it is perfectly horizontal, it will continue spinning that way.
But as soon as it tilts even slightly in any direction, it will upright itself.

Here's how:
We'll make Z the vertical axis - with the rotation initially about X=0, Y=0.
Let's say that it wobbles slightly so that +X is now low. So the point in contact with the surface is now moving along the Y axis. The resistance will cause a force to be applied in the opposite direction - either +Y or -Y depending on the direction of spin.

Since the hemisphere is acting like a gyroscope, the actual rotation that occurs with this force will be to force +X to go further down. The fact that you are no longer supporting it along the center of gravity will also cause it to precess.

 

[.Scott]

My description above is a bit off. It's the fact that the hemisphere is being supported off its center of gravity that causes it to right itself. So even if there was no friction, given enough spin, it would still stand up.