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4.5MechanicsStretch

Tilting

When a beam on two supports is about to tilt, it is on the point of rotating about one support — and the reaction at the other support becomes zero. This key idea unlocks tilting problems.

24 min Moments
Edexcel A Level Maths: 4.5 Tilting (Moments, Resultant Force)Curated by Kepler, not produced by us. Watch it before the notes below.
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What you'll be able to do

  • Recognise the condition for tilting
  • Set a support reaction to zero
  • Take moments about the pivot support
  • Find limiting loads or positions
1

On the point of tilting

When a beam is about to tilt about a support, the reaction at the other\textbf{other} support is zero. Set that reaction to 00 and take moments about the pivot support to find the limiting case.

Rother support=0 at the point of tiltingR_{\text{other support}} = 0 \ \text{at the point of tilting}
The far reaction vanishes.
Example 1A beam about to tilt about support B. What is the reaction at A?
1On the point of tilting about B, the beam lifts off A.
2So RA=0R_A = 0.
Answer
RA=0R_A = 0.

Tip — About to tilt about one support ⇒ the reaction at the OTHER support is zero.

Formula recap

Rfar support=0R_{\text{far support}} = 0
Condition for tilting.
∑Mpivot=0\sum M_{\text{pivot}} = 0
Take moments about the pivot.

Common mistakes to avoid

Setting the pivot support’s reaction to zero.
It is the OTHER (far) support whose reaction is zero.
Forgetting which support the beam tilts about.
Identify the pivot, then zero the far reaction.

Key takeaways

  • On the point of tilting, the far support’s reaction is zero.
  • Take moments about the pivot support.
  • Use this to find limiting loads or positions.

Test yourself

Answer a few questions, then review anything you missed.

Prefer paper? Open the written self-check

Answer each question before opening its answer. This self-check does not record a quiz score.

  1. When a beam is about to tilt about a support, the OTHER support’s reaction is:

    • zero
    • maximum
    • equal to the weight
    • negative
    Show answer and explanation

    Answer: zero

    Beam lifts off it.

  2. About to tilt about B means R_A is:

    • 00
    • maximum
    • half the weight
    • unknown
    Show answer and explanation

    Answer: 00

    Far reaction vanishes.

  3. You then take moments about:

    • the pivot support
    • the far support
    • the centre
    • either end
    Show answer and explanation

    Answer: the pivot support

    Eliminates its reaction.

  4. Tilting problems find the:

    • limiting load or position
    • mass density
    • speed
    • acceleration
    Show answer and explanation

    Answer: limiting load or position

    The critical case.

  5. At the point of tilting the beam is about to:

    • rotate about a support
    • fall straight down
    • slide
    • stretch
    Show answer and explanation

    Answer: rotate about a support

    Rotational motion.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

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Put the methods into practice: see how A-Level maths duels work. An account is required to play; the overview and sample are public.