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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