# Falling Pencil

Estimate the time it takes for a pencil of length $$l=\si{10\ \centi\meter}$$ to fall if the pencil starts from rest at the angle $$\theta_0=\si{0.001\ \radian\square}$$ with the vertical.

Give your answer to 3 significant digits.

Details and assumptions

• Assume that the pencil is a thin rod with uniform mass distribution along its length.
• Assume the pencil tip does not slip.
• Take the gravitational acceleration to be $$g=\SI{10}{\meter\per\second\squared}$$.
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