Tilting (AQA A Level Maths): Revision Note

Exam code: 7357

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Tilting

What does it mean if a rod is on the point of tilting?

  • A rod will tilt (rotate) about a pivot if the resultant moment about that pivot is non-zero

  • Examples of tilting:

    • A person walking a plank on a ship will get to a certain distance before the plank tilts

    • Children playing on a seesaw

    4-1-4-tilting-diagram-1

How do I solve problems involving a rod on the point of tilting?

  • If a rod is on the point of tilting about a pivot (at a support) then the reaction forces at the other supports are zero

  • The rod is still in equilibrium at the point of tilting

  • Taking moments about the pivot is the key step as it allows you to ignore the reaction force

  • The question might not use the phrase “tilting”

    • It could ask you how far along a plank that it is safe to walk (it is safe as long as the plank does not tilt)

    • It could ask you to find the maximum mass that could be hung from a rod that would keep it horizontal (as soon as it begins to tilt it is no longer horizontal)

Worked Example

A uniform rod AB of mass 9 kg and length 5 m rests on two supports at two points C and D as shown in the diagram below.

A horizontal beam AB is balanced on two triangular supports. Support C is 1.5m from A, and support D is 3m from C, with 0.5m from D to B.

A mass of 6 kg is placed at B and a mass of m kg is placed at A. Given that the rod is on the point of tilting about C, find the value of m.

_5Q5788S_4-1-4-tilting-example-solution

Examiner Tips and Tricks

  • Remember to use common sense! If a rod was supported by two supports and a mass was placed on the rod in between these supports then the rod would never tilt (in real-life it might break though).

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Dan Finlay

Author: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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