Tilting (AQA A Level Maths): Revision Note
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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
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 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.
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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