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8.3Rotational Motion

Equilibrium and Centre of Mass — American System Physics Revision Notes & Topical Questions

10 min read 7 parts Lesson 5 of 5 1 quiz

📚 American System Physics Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

Describe how to find the centre of mass of a flat irregular object experimentally.Equilibrium condition 1resultant force = 0: ΣF = 0 (N).Equilibrium condition 2resultant torque about any axis = 0: Στ = 0 (N·m).Principle of momentssum of clockwise moments = sum of anticlockwise mo…

  • Weight acts through the centre of mass
  • For a beam on supports
  • Centre of gravity
  • Translational equilibrium
  • Rotational equilibrium
  • Static equilibrium

Section 1 of 7Equilibrium and Centre of Mass

Essential knowledge
8.3 Equilibrium and Centre of Mass concept map: Equilibrium condition 1, Equilibrium condition 2, Principle of moments, Weight acts through the centr, For a beam on supports
Visual guide to the key ideas explained in this lesson.
The centre of mass of a symmetrical uniform object is at its geometric centre; for an irregular lamina it can be found with a plumb line, because a freely hanging object comes to rest with its centre of mass directly below the pivot.
The centre of mass need not be inside the object – for a ring or a boomerang it lies in empty space.
When thrown, an object may spin, but its centre of mass follows a smooth parabolic path, just like a point particle.
An object is in equilibrium when BOTH the resultant force is zero and the resultant moment is zero; it is then at rest or moving with constant velocity and constant angular velocity.
For a beam on supports
For a beam on supports use ΣF = 0 (upward forces = downward forces) and take moments about one support to remove that unknown force from the equation.
A uniform beam's weight is treated as acting at its midpoint when calculating moments.
If an object is tilted, its weight acting through the centre of mass gives a moment about the edge of the base. While the line of action is inside the base, the moment pulls it back; once outside, the moment tips it over.
Racing cars, buses and table lamps are designed with low centres of mass and wide bases to increase stability; people bend and spread their feet for the same reason.
In a rotating frame (e.g. a car turning a corner), passengers feel pushed outward. This 'centrifugal force' is apparent: really, their inertia tends to keep them moving in a straight line while the car turns under them.
The Coriolis effect is an apparent deflection of objects moving over the rotating Earth; it causes large-scale winds and hurricanes to rotate (counterclockwise in the Northern Hemisphere).

Section 2 of 7Process & sequence

1
Hang the irregular lamina (flat card) freely from a pin through a small hole near its edge.
2
Hang a plumb line from the same pin and let both settle.
3
Mark the line of the plumb line on the card.
4
Repeat from a second (and third) hole well away from the first.
5
The point where the lines cross is the centre of mass.
6
Check by balancing the card on a pencil tip at that point; repeat marking with a third hole to reduce error.

Why a tilted object toppleswrite these steps in this order; each step is a marking point.

1
The object is tilted about one edge of its base.
2
Its weight still acts vertically down through the centre of mass.
3
If this line lies inside the base, the weight's moment turns it back.
4
If the line moves outside the base, the moment turns it further over.
5
The object topples; a lower centre of mass or wider base delays this.

Section 3 of 7Compare

Types of equilibrium
TypeSmall push makes the centre of mass...ResultExample
StableriseReturns to original positionCone on its base; pendulum at rest
UnstablefallTopples furtherCone balanced on its tip
Neutralstay at same heightStays in new positionBall on flat floor; cone on its side
Conditions for equilibrium
ConditionEquationMeaning
First conditionΣF = 0No linear acceleration
Second conditionΣτ = 0 about ANY pointNo angular acceleration

Both must hold for full equilibrium.

Section 4 of 7Worked examples

250 N
A uniform 4.0 m plank weighing 200 N rests on supports at each end. A 600 N person stands 1.0 m from the left end. Find the force from each support.
  • Moments about left support (clockwise = counterclockwise):
    600 × 1.0 + 200 × 2.0 = FR × 4.0 → 1000 = 4.0FR → FR = 250 N
    ΣF = 0: FL + 250 = 800 → FL = 550 N.
95 cm mark
A metre rule is pivoted at its 50 cm mark. A 3.0 N weight hangs at 20 cm. Where must a 2.0 N weight hang to balance?
  • Distance of 3.0 N from pivot = 30 cm.
    • Moment = 3.0 × 0.30 = 0.90 N·m.
      2.0 × d = 0.90 → d = 0.45 m, so hang it at the 95 cm mark.

Section 5 of 7Key terms

Section 6 of 7Command terms

Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Section 7 of 7Exam technique

Keywords the mark scheme looks for in this lesson

Keywords the mark scheme looks for in this lesson
Centre of mass · Centre of gravity · Equilibrium · Translational equilibrium · Rotational equilibrium · Static equilibrium · Stability · Stable equilibrium · Unstable equilibrium · Neutral equilibrium · Base (of support) · Centrifugal 'force' · Coriolis effect
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary, never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

1
the object is in equilibrium because it is not movingthe resultant force and the resultant moment on it are both zero
2
the centre of mass is always in the middleit is at the geometric centre only for uniform symmetrical objects
3
it falls over because it is top heavyit topples when the line of action of its weight passes outside its base
4
centrifugal force pushes you outwardyour inertia tends to keep you moving in a straight line while the car turns
5
a wide base makes it heavier so it is stablea wide base means it must tilt further before the centre of mass passes outside the base

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3 & IGCSE —

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