Mini Physics
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Stability and toppling

Use the line of action of the weight to decide whether a tilted body falls back or topples, and calculate the angle at which a block just topples.

  • A-Level H2 Physics topic extensions

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Tilt a box slightly and let go, and it falls back flat. Tilt it far enough and it falls over. Where the change happens follows from moments and the centre of gravity.

Stable, unstable and neutral equilibrium

Give a body in equilibrium a small push and watch what happens next:

  • stable equilibrium: a moment acts to return it to where it was;
  • unstable equilibrium: a moment acts to move it further away;
  • neutral equilibrium: it stays in its new position, because that is also an equilibrium position.

A ball in a bowl, a ball on top of an upturned bowl and a ball on a flat table are the standard three examples.

Follow the line of the weight

Take a rigid block on a level floor and tilt it slowly about one bottom edge, without it slipping. Only the weight has a moment about that edge.

  • If the vertical line through the centre of gravity falls inside the edge, the weight’s moment turns the block back onto its base.
  • If it falls outside the edge, the weight’s moment turns the block further over, and it topples.
  • At the boundary the line passes through the edge, so the weight has no moment about it.
The weight line at the boundary of topplingA uniform block is 0.40 metres wide and 0.80 metres high. Initially its downward weight line is inside the base. When tilted about its lower-right edge by 26.6 degrees from upright, its centre of gravity is vertically above the pivot edge. The weight then has zero moment about the edge; a further tilt would put its line of action outside the base.When does the weight line reach the edge?Upright: weight line inside baseBoundary: weight line through edgeWWPivot edge26.6°0.40 m0.80 m
Scroll across the figure to read all labels.
For slow tilting without slipping, the boundary occurs when the vertical weight line passes through the pivot edge. This geometry assumes a uniform rigid block and no extra supports. The angle is drawn to scale; force-arrow lengths are schematic.

This test is for a block tilted slowly and released from rest. A push, a fixing or the block’s own rotation as it moves can change the result.

Try it yourself 1

The angle at which a block topples

Minimal support

Problem

A uniform rectangular block is 0.40 m wide and 0.80 m high. It is tilted slowly about one bottom edge without slipping. Find the angle from upright at which it is just about to topple.

Find the angle

Unit: °

Hints

Hint 1: where the centre is

Before tilting, the centre of gravity is half the width in from the edge and half the height up.

Show solution step by step

  1. The condition

    Method

    Tilt until the centre of gravity is directly above the edge.

    Reason

    Any further tilt and the weight’s moment turns the block over.

    Working

    The line from the edge to the centre of gravity is then vertical.

  2. Geometry

    Reason

    The centre of a uniform block is at its middle.

    Working

    From the edge, the centre is 0.20 m across and 0.40 m up. The tilt needed to bring it vertically above the edge is the angle that this line makes with the vertical.

  3. Angle

    Working

    tan θ = 0.20/0.40 = 0.50, so θ = 26.6°.

A lower centre of gravity

For a uniform block of width w and height h, the same geometry gives

tan θ_critical = (w/2)/(h/2) = w/h

A wider base or a lower centre of gravity increases the critical angle, so the body is harder to topple. This is why racing cars are low and wide, and why heavy items go on the bottom shelf.

Check your understanding 1: A lower block

A uniform block has the same 0.40 m width as in the example but is only 0.40 m high. Find its critical angle and explain why it is larger.

Show answer

tan θ = 0.40/0.40 = 1, so θ = 45°. Its centre of gravity is lower, so it must be tilted further before the line of the weight reaches the edge.

Common mistakes

  • Taking moments about the centre of the base instead of the edge the body tilts about.
  • Using the full width and height instead of the half-width and half-height to the centre of gravity.
  • Thinking a body topples once its top passes the edge; what matters is the centre of gravity.
Syllabus and review details

No official syllabus alignment is listed for this lesson.