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 $\theta_0=\si{0.001\ \radian}$ 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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