Tilting (Edexcel IAL Maths)

Spec point — 6.1

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.

Answer:

Exam Hint

• 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).