Stability & States of Equilibrium

1. Definition

A. Stability

Stability is the ability of an object to return to its original position after a small displacement.

2. Key Ideas

• Stable equilibrium: returns to its original position after a small displacement.
• Unstable equilibrium: moves further away from its original position (usually topples) after a small displacement.
• Neutral equilibrium: stays in its new position after a small displacement.
• An object topples when the line of action of weight falls outside its base.
• Stability is increased by a lower centre of gravity and a wider base.

Data table

Fixed base width
Centre of gravity height, h (m)	Critical tilt angle (°)
0.1	63
0.2	45
0.3	34
0.4	27
0.5	22
0.6	18

3. Detailed Explanations

A. States of equilibrium

B. When does an object topple?

An object topples when the line of action of its weight no longer passes through its base of support.

How to check stability (exam workflow):

1. Draw the base (the contact area with the ground).
2. Mark the centre of gravity.
3. Draw a vertical line down from the centre of gravity (line of action of weight).

• If the line falls within the base, it tends to stay upright.
• If the line passes through the edge of the base, it is about to topple.
• If the line falls outside the base, it topples about the edge.

C. Why a low centre of gravity increases stability (qualitative)

If an object’s centre of gravity is lower, it must be tilted through a larger angle before the line of action of weight falls outside the base.

So it is more stable.

D. Why a wide base increases stability (qualitative)

A wider base means the line of action of weight can move more before it reaches the edge.

So the object can be tilted more without toppling.

4. Common Mistakes

• Mixing up the definitions of stable, unstable and neutral equilibrium.
• Thinking an object topples when the centre of gravity is outside the object (it can be outside and still be stable).
• Forgetting the “tipping rule”: check the line of action of weight against the base.
• Saying “more friction” as the main reason for better stability when the question is about toppling (use centre of gravity and base).

5. Exam Tips

• Use the key phrase: “An object topples when the line of action of its weight falls outside the base.”
• When asked “how to increase stability”, state two clear methods: lower the centre of gravity, and widen the base.
• Link your explanation to moments: once the line of action is outside the base, the weight produces a turning effect about the edge (see Moment Of A Force).

6. Worked Examples

Example 1: Identify the state of equilibriumCore

State whether each is in stable, unstable or neutral equilibrium:

1. a ball in a bowl
2. a ball on top of a hill
3. a cylinder lying on a flat surface

Show Answer

1. stable
2. unstable
3. neutral

Example 2: Why is a double-decker bus easier to topple than a sports car?Core

Explain your answer using centre of gravity.

Show Answer

A double-decker bus has a higher centre of gravity.

So the line of action of its weight reaches the edge of the base with a smaller tilt, and it topples more easily.

Example 3: When does an object topple?Core

An object is pushed sideways but does not slide.

Explain when it will topple.

Show Answer

It topples when the vertical line through its centre of gravity (line of action of weight) falls outside its base.

At that point, the weight produces a turning effect about the edge and the object rotates over.

Example 4: Same object, different orientationCore

A rectangular block is placed on a table in two ways:

• (A) standing upright on a small base
• (B) lying on its side with a wider base

Which position is more stable against toppling? Explain using centre of gravity and base width.

Show Answer

(B) is more stable.

Lying on its side gives:

• a lower centre of gravity, and
• a wider base

So it must be tilted more before the line of action of weight falls outside the base.

Example 5: Why do racing cars have wide wheels and a low body?Core

Explain why these design features increase stability.

Show Answer

Wide wheels give a wider base of support, so the line of action of weight can move more before reaching the edge.

A low body gives a lower centre of gravity, so a larger tilt is needed before the line of action falls outside the base.

7. Mind Stretchers

Mind stretcher 1: Design a more stable objectExtension

A tall, narrow object keeps toppling easily.

Suggest two design changes and explain why each change helps.

Show Answer

1. Lower the centre of gravity (e.g. add mass near the bottom): it must be tilted more before the line of action of weight falls outside the base.
2. Widen the base: the line of action of weight can move more before reaching the edge of the base.

Mind stretcher 2: Sliding vs toppling (which happens first?)Extension

A tall cupboard is pushed sideways on the floor.

Explain what determines whether it is more likely to slide or topple first.

Show Answer

Toppling depends mainly on whether the line of action of weight falls outside the base (centre of gravity height and base width).

Sliding depends mainly on how large the frictional force can be compared to the pushing force.

So a cupboard with a high centre of gravity and narrow base tends to topple more easily, while a cupboard with high friction (good grip) tends to slide less easily.

8. Practice, Quiz and Next Step

Close your notes and use Stability & States of Equilibrium in the supplied context below. This requires a constructed explanation or working, not recognition of an option.

Fresh context: Two blocks have the same mass and base width, but block A is twice as tall as block B; each is slowly tilted.

1. Retrieve: define centre of gravity, base and toppling in your own words, including units, sign or conditions where relevant.
2. Represent: Sketch both blocks with centre-of-gravity weight lines and the edge of the base at the tipping point.
3. Apply: Predict which topples first and explain using the line of action rather than the vague claim that one is heavier.

Check the response before looking back

• The body under analysis is named and only forces on that body are combined.
• Directions, line of action and perpendicular distance are explicit where relevant.
• The conclusion follows from the resultant force or moment, not from motion alone.

If one check fails, name that exact gap, revisit the matching explanation or worked example, and redo the task with different values or a different situation. Then use theO-Level topic checks orpractice browser for an independent re-test.