AQA A Level Maths: Mechanics复习笔记4.1.4 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)

   

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