Spinning Top Dancer: Moment of Inertia?

[Gerenuk]

If a dancer who balances on one leg starts spinning, is having the center of mass above the point of contact enough, or does he need to assume a special shape?
I mean is the moment of inertia important provided the point of contact (feet) are not slipping?

 

[Dr Lots-o'watts]

The center of mass has to be over the pivot point. The more the mass is concentrated near the axis, the faster the spinning for a given starting energy.

 

[Gerenuk]

So wasn't so much the question.
I already assume the the COM is above the pivot point. The question is whether this is enough for a stable rotation.
I mean in free space there are only two special axis of rotation about which a stable rotation is possible. What about a spinning top? Can it's shape be arbitrary?

 

[rcgldr]

Figure skaters are able to assume various positions while spinning, but the point of contact with the ice translates across the ice somewhat during a spin.

 

[Gerenuk]

OK, but that's also not the question. The question is whether there are positions that don't work.

 

[GRDixon]

What about a spinning top? Can it's shape be arbitrary?

Yes, I would think so, provided its spin axis passes through the center of mass.

 

[Dr Lots-o'watts]

OK, but that's also not the question. The question is whether there are positions that don't work.

1. The lower the center of gravity, the more stable it will be. The reason is that small oscillations, whether intrinsic or external will not have as much tendency to displace the center of gravity over the pivot point, if it very low. In this sense, the shape will have an effect.

2. Also, the lighter the object, the less there will be friction at the pivot point, so the less energy it will waste.

3. You could also minimize energy loss by making it aerodynamic in the relevant direction.