An object topples when the vertical line from its centre of gravity passes beyond its base — at the critical angle θc = arctan((b/2)/h). Drag the sliders below to change the base width, centre-of-gravity height and tilt, and watch the plumb line, the tipping angle and the stable/topple status respond in real time.
Whether a shape holds its ground or goes over hinges on one line: the vertical drop from its centre of gravity. While that plumb line still lands somewhere inside the footprint, the object stands; the instant it slips past the downhill edge of the base, everything rotates about that edge and over it goes. This simulator makes that line visible so you can watch it march toward the edge as you tilt.
Base width b and centre of gravity height h set the critical tipping angle θc = arctan((b/2)/h) — the ceiling on how far you can lean before it goes. The platform tilt slider then leans the ground toward that ceiling: as you crank it, the plumb line swings toward the pivot edge, and the moment the tilt reaches θc the status flips from STABLE to TOPPLE — the exact angle at which the line reaches the base's edge.
Widen b or drop h and θc grows, so the block survives a steeper lean before it goes; raise the centre of gravity or pinch the base narrower and it surrenders at a smaller angle. That is the whole reason racing cars sit low and wide while a tall, slim load tips at a nudge. Pin down the numbers with the centre of mass calculator, then tilt, topple, and rebalance other systems across our hands-on simulation collection.
When the vertical line dropped from its centre of gravity passes beyond the edge of its base of support. Up to that point it stays balanced; past it, it rotates about the edge and falls.
It is the tilt at which an object is on the verge of toppling: θc = arctan((b/2)/h), where b is the base width and h is the height of the centre of gravity. Below θc it is stable; above θc it topples.
A wider base and a lower centre of gravity. Both increase the critical tipping angle, so the object can lean further before its centre of gravity passes the edge. That is why racing cars are built low and wide.
Not directly. What matters is where the centre of gravity's vertical line falls relative to the base, not how heavy the object is — though a low, wide object keeps its centre of gravity over a broad base, which makes it hard to tip.