Balancing Stacked Coins: Understanding the Physics

[Katopanishad]

when we place a coin on top of a table it is balanced because the line connecting the centre of mass and the ground pass though the point which is within the base of the coin.But if start stacking the same type of coins beyond a point it is unstable and this depends on the diameter of the coin.My doubt here is when we stack similar coins the combined centre of mass shd still be on the same initial line.Then why shd the stack of coins collapse beyond a particular no of coins stacked?

 

[Naty1]

Hi Kato...
The higher the center of gravity the less stable the object(s)...there is a greater potential "righting" (really tipping) moment which can topple the pile of coins and it becomes easier to move the higher stack off center...

for example it's tough to topple one coin lying flat, real easy when you have them stacked, say, 50 high...a small horizontal (lateral) displacement does not change the COG of one coin but does when stacked high...different ways of saying the same thing...

Also many coins have a raised edge and this would also tend to make the stack a bit irregular and it might also contribute to the instability.

A search of wiki did not reveal "righting moment" details but the metacentric height of a ship is a roughly analogous concept...

See here for one interesting pictorial description of the center of rotation and center of mass: http://en.wikipedia.org/wiki/Center_of_gravity#Rotation_and_centers_of_mass