u/BreakerChap

Suppose we have two perfectly rigid solid objects in uniform gravity, with no air resistance. The lower object is fixed to a flat ground plane, and the upper object may be placed in any orientation on top of it. Friction between the two objects is zero or negligible, but the ground has enough friction that the lower object does not move.

Is it always possible to place the upper object so that it is in static equilibrium on the lower object?

I am allowing equilibrium at a single point of contact, even if it is unstable, as long as such a configuration exists. For example, balancing one sphere on another at a single point would count.

Does the answer change if there are multiple objects stacked together? That is, once some collection of objects is balanced, can it be treated as a new rigid “foundation” shape for the next object?

Intuitively, I think this should this should be true. I can't imagine two objects that couldn't balance atop one another, but I would love to be proved wrong (ideally with an illustration). Is there a general theorem or counterexample?

Why is =RIGHT(PI()) 9?

Can you balance any object on another?