1.5 Moments and equilibrium

• Moment of a force; moment about one point
• Principle of moments
• Moment about two points of support
• Torque and couple
• Centre of gravity and stability
• States of equilibrium; applications of moments

• determine the moment of a force about a point
• verify the principle of moments in turning of objects
• describe torque and couple in turning objects
• determine the centre of gravity of regular and irregular objects
• identify the states of equilibrium in bodies
• appreciate the applications of moments and stability in day-to-day life

“Why is a door handle fitted as far as possible from the hinges?”

“Why is a loaded bus more likely to overturn than an empty one?”

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1. The turning effect of a force
   40 min · 2 practice tasks · quiz
   Why where you push matters as much as how hard, and the rule that keeps a see-saw level.
2. Centre of gravity and stability
   40 min · 2 practice tasks · quiz
   Where an object's weight acts, and what decides whether it stands or topples.
3. Perpendicular distance from the pivot
   40 min · 1 practice tasks · quiz
   The distance in M = F x d is at right angles to the line of action, so an angled push is weaker than a square one.
4. Clockwise and anticlockwise moments
   40 min · 1 practice tasks · quiz
   Pick a point, name the sense of each turn, add the moments that share a sense, and set the two totals equal at balance.
5. Verifying the principle of moments
   40 min · 1 practice tasks · quiz
   Balance a metre rule on a knife edge, record both sides, and test whether clockwise moments equal anticlockwise moments.
6. Finding an unknown force or distance
   40 min · 1 practice tasks · quiz
   Rearrange clockwise = anticlockwise to find a missing weight or a missing length, keeping units consistent.
7. A beam on two supports
   40 min · 1 practice tasks · quiz
   Take moments about one support so that reaction vanishes, find the other, then use the balance of forces.
8. When the beam itself has weight
   40 min · 1 practice tasks · quiz
   A uniform beam acts at its midpoint; a non-uniform beam acts at a given centre of gravity, and forgetting it always undercounts the reactions.
9. Torque on shafts and tools
   40 min · 1 practice tasks · quiz
   Torque is the moment that turns a shaft or a nut; engines, pedals and taps are quoted in newton metres.
10. Couples and pure rotation
    40 min · 1 practice tasks · quiz
    Two equal opposite forces not in one line turn a body without moving its centre of mass; moment of a couple is F times their separation.
11. Centre of gravity of regular bodies
    40 min · 1 practice tasks · quiz
    For a uniform regular shape the centre of gravity is the geometric centre, and it may sit in empty space.
12. Locating the centre of gravity of an irregular lamina
    40 min · 1 practice tasks · quiz
    Hang an irregular card from two holes, mark the plumb lines, and use a third hole to check the crossing.
13. Investigating what makes an object stable
    40 min · 1 practice tasks · quiz
    Tip blocks of different height and base, and use the rule that a body topples when the vertical through its centre of gravity leaves the base.
14. Moments in everyday tools
    40 min · 1 practice tasks · quiz
    Doors, wheelbarrows, crowbars, bottle openers and farm tools are designed so a modest force at a large distance produces a useful moment.
15. Stability around Kenya
    40 min · 1 practice tasks · quiz
    Buses, matatus, lorries on escarpments, furniture, people carrying loads and laboratory stands: apply moments and the toppling rule to places you can point at.