The distribution of mass is always relevant to rotational motion. I assume the formula you are thinking of is T=2πsqrt(L/g)
This only holds for 'simple' pendulums: Pendulums which consist of a bob hanging from a massless thread.
In general, a pendulum can be a rigid object. The more general equation for the period at low amplitudes is T=2πsqrt(I/Mgh); where I is the moment of inertia of the body, M is its mass, and h is the distance from the pivot to the center of mass of the body.
Both I and h depend on how the mass is distributed.
Also, the formulas in my previous post should be valid even for the very small angles involved in head balancing.
by James Hennigan, in response to this post 2016-03-31 21:52:08