# Chopping Down A Tree

A perfectly symmetrical tree has a trunk in the shape of a cylinder with diameter $0.2~\mbox{m}$. Since the tree is symmetrical the center of mass is at some distance $L$ above the ground along the axis of the cylinder. A rotten lumberjack with no concept that he's cutting down the most amazing tree ever grown uses a chain saw to cut the tree down. He saws horizontally right at the base of the tree (ground level).

What is the minimum value of $L$ in meters such that the tree begins to topple over as soon once the chain saw reaches the position in the picture?

Details and assumptions

• The chain saw blade is $8~\mbox{cm}$ wide and $0.5~\mbox{cm}$ high.
• Treat the tree as a rigid body.
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