At what angle θ will the cylinder of height h and radius r will tumble?

AI Thread Summary
The discussion centers on determining the angle θ at which a cylinder of height h and radius r will begin to tumble when tilted. The key point is that the cylinder will tumble when its center of gravity (cog) moves beyond the supporting edge. The relationship established is that tan(θ) equals the ratio of the cylinder's width (2r) to its height (h). This geometric approach effectively calculates the critical angle for the cylinder's stability. Understanding this concept is crucial for applications involving cylindrical objects in physics and engineering.
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1. [One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r will tumble?]


3. The Attempt at a Solution [I know that the angle at which it tilts is when the cog moves beyond the supporting edge. Also, I know that length = h and width = 2r. How do I find that angle with this?]
 
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Draw vertical lines from cog when it is straight and tilted. In the second case this vertical line must pass through the supporting edge. Angle between these vertical lines is the required angle.
 
Does that leave us with tan(theta) = (2r/ h)?
 
That is right.
 
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