Sliding Along a Rotating Rod

A \(\SI{1}{\meter}\) rod of uniform composition and total mass \(\SI{1}{\kilo\gram}\) has one end hinged at the origin. A \(\SI{1}{\kilo\gram}\) bead is placed at the other end and is free to slide along the rod (if it reaches the open end, it will separate from the rod).

The bead and rod are prepared so that the bead sits near the open end of the rod which makes an angle of \(\theta=60^\circ\) with the horizontal.

If this system is released from rest at time zero, at what time (in seconds) does the bead slide off of the rod?

Assumptions:

  • \(g = \SI[per-mode=symbol]{10}{\meter\per\second\squared}.\)
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