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LearnYMA01WME02 · Mechanics 2Statics of rigid bodiesTilting and non-uniform rods
Statics of rigid bodies · Subtopic 2 of 2

Tilting and Non-uniform Rods

A beam on two supports is "on the point of tilting" about one support when the reaction at the other support becomes zero. A non-uniform rod's weight acts at its centre of mass, which isn't the midpoint; treat its distance as an unknown and find it from moments.

Edexcel YMA01 WME01Edexcel YMA01 WME02Edexcel 9MA0 Paper 3AQA 7357 Paper 2≈ 35 minRevision 5 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Recognise that tilting about one support means zero reaction at the other.
  • Find how far a person can walk or how heavy a load can be before tilting.
  • Find the centre of mass of a non-uniform rod.
  • Use reactions given as a ratio or in terms of each other.
Pause and think

You walk along a plank that overhangs a wall. As you pass the wall and keep going, what happens to the reaction at the plank's other support?

Section 2 of 14

Core idea

Start hereWalking the plank

A plank rests on two trestles and overhangs one. Walk out past the trestle and at some point the far end lifts. Just before that, the other trestle carries no load. That single fact solves every tilting problem.

The big idea

On the point of tilting about one support, the reaction at the other support is zero. Take moments about the tipping support.

1. On the point of tilting

A plank about to tip over the right-hand support
reaction at A = 0reaction at B150 NW childabout to lift
An 8 m plank of 150 N, supports 1 m and 5 m from the left. A child stands near the right end. At the point of tipping, RA=0R_A=0.
Worked exampleHow far can the child walk?

8 m plank, 150 N, supports at 1 m (A) and 5 m (B). 300 N child walks right.

Goal
Furthest position.
Strategy
About to tip about B: RA=0R_A=0.
  1. RA=0R_A=0
    About to lift off A.
  2. 150(5−4)=300(d−5)150(5-4)=300(d-5)
    Moments about B: plank weight at 4 m.
  3. d=5.5 md=5.5\text{ m}
    Solve.
Answer5.55.5 m from the left (0.5 m past B).
✓ CheckAt that point RB=450R_B=450: all weight on B ✓.
Worked exampleHeaviest child at the end

Same plank: heaviest child who can stand at 8 m.

Goal
WW.
Strategy
Same condition.
  1. 150(1)=W(3)150(1)=W(3)
    Moments about B.
  2. W=50 NW=50\text{ N}
    Solve.
Answer5050 N.
✓ CheckFurther out means a smaller allowed weight ✓.
Common misconceptionWrong pivot Tipping happens about the support nearest the load, not the other one.
Pause and think

Why is RA=0R_A=0 at the point of tipping?

Summary

  • About to tip: other reaction =0=0.
  • Moments about the pivot.
Key words
Tilting
About to rotate about a support.
HistoryBalancing a crown. Archimedes' work On the Equilibrium of Planes (around 250250 BC) found centres of gravity of triangles, parallelograms and parabolic segments. He used balancing and moments as a tool to find areas long before calculus.
Fun factThe leaning tower of books. Stack identical books so each overhangs the one below as much as possible without toppling. With enough books, the top one can overhang the table by more than a whole book length: each book's centre of mass just stays above the edge beneath it.
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