I think the hula-hoop example seems about right. Heavier, larger diameter hoops can hold their spin longer as they have greater moments of inertia and can develop more torque. If Moment of inertia is related not only to total mass but also the distance each bit of mass is offset from the axis of spin, a hoop would seem to be a shape/form that nearly maximizes the possible moment of inertia for some given mass.
Are spinning hoops in turn more easily kept upright because these factors also maximize the spinning hoops g-scopic stability? I'm sure there is more to it--did I get it nearly right?
That whip top looks less interesting than those big ones from the frozen lake photo.