The physics
A body that hangs on a wire twists to and fro. The wire pushes back with a torque −κθ, like a spring.
T = 2π √(I / κ)
I is the moment of inertia about the wire. A disc has I = ½MR². Mass far from the axis makes I big.
A body that swings about a pivot is a physical pendulum. Gravity pulls at its centre of mass, a distance d from the pivot.
T = 2π √(I / m g d) rod about an end: I = m L² / 3, d = L / 2
On a flat, smooth table gravity gives no torque about a hinge. A spring at a distance d gives a torque −kd²θ.
ω = d √(k / I)
A twist stores energy ½κθ². At the middle of the swing it is all spin energy, ½Iω².