Genius Insect!

Classical Mechanics Level 5

A Thin rod of length \(l\) is hinged at the center. An insect falls on it from a height \(h\). The distance of the impact point is \(l/4\) from the center.
Apparently, the insect is a Genius. To avoid much dizziness, it devices a method to make the rod rotate at constant angular velocity. The insect starts crawling towards the outer edge of the rod.

Find the height \(h\) from which the insect drops, such that by the time the rod becomes vertical, the insect reaches the outer edge.

Details and Assumptions:

  • \(l = 5m\)
  • \(g=9.8m/s^2\)
  • The mass of the insect is equal to the mass of the rod
  • Neglect air resistance and friction due to the rod.

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