Center of Gravity & Tipping

A block topples once its center of gravity passes beyond the pivot edge. Tilt the platform and watch the plumb line: it stays inside the base while θ < θc, where θc = arctan((b/2) / h). A wider base or lower CG survives a steeper tilt.

Critical tipping angle  θc = arctan((b/2)/h)
21.8°
current tilt θ = 0.0°
STABLE
plumb line falls inside the base
Base width b0.40 m
CG height h0.50 m
Platform tilt θ0.0°
Safety margin
21.8°
Plumb offset
-0.20 m
θc = arctan((b/2)/h)  ·  margin = θc − θ. Plumb offset from the pivot edge = h·tanθ − b/2 (negative = inside the base).
Tip: push the tilt just past θc and the block topples; ease it back below and it rights itself.