How to calculate the angle at which a cylinder topples?

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SUMMARY

The angle at which a cylinder topples is determined by the position of its center of mass relative to its base. The critical angle is defined as the angle between the vertical and the line connecting the center of mass to the edge of the base. The mass of the cylinder does not directly affect this angle; instead, it is the geometry and distribution of mass that play a crucial role. Understanding these principles is essential for accurately calculating the toppling angle in practical applications.

PREREQUISITES
  • Understanding of center of mass concepts
  • Basic principles of static equilibrium
  • Knowledge of geometry related to cylinders
  • Familiarity with critical angles in physics
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  • Research how to calculate the center of mass for various shapes
  • Study static equilibrium conditions for rigid bodies
  • Learn about the effects of mass distribution on stability
  • Explore practical applications of toppling angles in engineering
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Students in physics, engineers working on stability analysis, and hobbyists involved in projects requiring an understanding of toppling mechanics.

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I know the mass, length, and width of a cylinder. How do I calculate the angle at which the cylinder topples over? A quick Google search tells me that I need to find the cylinder's center of mass, which should be the actual center of the cylinder.


This is for a personal project and not homework related. I was unable to reply to Mark44's private message so I'm stating it here.
 
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What do think you should do with the center of mass? Where's it going to be to not topple, or to topple?
 
Bystander said:
What do think you should do with the center of mass? Where's it going to be to not topple, or to topple?
Don't know...
Does the mass of the cylinder affect it's "toppling angle"?
 
In general, the critical angle, or the angle at which an object is about to topple is the angle between the vertical/horizontal and the line passing through the centre of mass and the edge over which the object is about to topple.
 

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