K323 / 2027
Turning effects of forces overview

Topic 4 of 4

Stability and toppling

To decide whether a tilted object tends to return or topple, compare the vertical line of its weight with the edge it could turn about.

The weight acts downwards through the centre of gravity. Its moment depends on which side of the pivot its line of action lies.

Imagine gently tilting a box clockwise about its bottom-right edge, then releasing it. Assume it does not slide. The edge is the possible toppling pivot; gravity still acts vertically downwards while the box tilts.

  • If the weight's line of action lies to the left of that edge, weight produces an anticlockwise, restoring moment. The box tends to return towards its original position.
  • If the line passes through the edge, weight has zero moment about the edge at that instant. This is the boundary between the two cases.
  • If the line lies to the right of the edge, weight produces a clockwise moment and promotes further toppling.

Same shape and base, different centre-of-gravity heights

Both bodies are tilted 30 degrees about the right-hand edge, without sliding. The dimensions and weight are unchanged; the load is placed lower or higher.

Lower centre of gravity

Anticlockwise: restoring moment from weightA body 0.60 metres wide and 1.0 metre high is tilted clockwise by 30 degrees about its bottom-right edge. Before tilting, its centre of gravity was at mid-width and 0.2 metres above its base. Weight still acts vertically downwards from G. Its vertical line of action falls to the left of the toppling edge, producing an anticlockwise restoring moment. Only weight is shown; the contact force acts at the edge and has no moment about it. The blue curved arrow indicates turning tendency, not an extra force.GWToppling edge

Anticlockwise: restoring. The weight line is left of the toppling edge.

Higher centre of gravity

Clockwise: toppling moment from weightA body 0.60 metres wide and 1.0 metre high is tilted clockwise by 30 degrees about its bottom-right edge. Before tilting, its centre of gravity was at mid-width and 0.8 metres above its base. Weight still acts vertically downwards from G. Its vertical line of action falls to the right of the toppling edge, producing a clockwise moment that promotes toppling. Only weight is shown; the contact force acts at the edge and has no moment about it. The blue curved arrow indicates turning tendency, not an extra force.GWToppling edge

Clockwise: toppling. The weight line is right of the toppling edge.

Red straight arrows show equal weights. Dashed lines extend their lines of action; blue curved arrows show turning tendency. Only weight is shown.

Both bodies have the same base width and are tilted 30° clockwise about their bottom-right edges without sliding. With G lower in the body, the weight line remains on the restoring side. With G higher, it has passed to the toppling side.

A lower centre of gravity allows more tilt

The illustrated bodies are each 0.60 m wide and 1.0 m high. When upright, G is at mid-width and either 0.20 m or 0.80 m above the base. Their different mass distributions place G at different heights.

At the same tilt, the lower G has not moved far enough sideways for its weight line to pass the edge. The higher G has. For otherwise comparable objects, lowering G allows a greater tilt before the weight starts to promote toppling.

A wider base can increase stability

Keeping the height of G unchanged, a wider base in the direction of the tilt places the toppling edge farther from the upright weight line. More tilt is then needed before that line passes beyond the edge.

For example, placing a heavy load low in a vehicle can lower its overall G. Increasing the support width can also help resist toppling. In each case, explain what happens to the position of G or the edge, rather than only saying the object is "more stable".

Greater weight alone does not determine the toppling boundary. With the same geometry and G position, a larger weight changes the size of its moment, but not which side of the edge its line acts on. The line-of-action argument here assumes the object does not slide.

Optional check Viewed from the front, a box is tilted clockwise about its bottom-right edge without sliding. The vertical line through its centre of gravity now falls to the right of that edge. What does its weight tend to do?
Viewed from the front, a box is tilted clockwise about its bottom-right edge without sliding. The vertical line through its centre of gravity now falls to the right of that edge. What does its weight tend to do?