A thin uniform rod is rotating at an angular velocity of 5.18rad/s about an axis

Question

A thin uniform rod is rotating at an angular velocity of 5.18rad/s about an axis that is perpendicular to the rod at its center.As the figure indicates, the rod is hinged at two places,one-quarter of the length from each end. Without the aid ofexternal torques, the rod suddenly assumes a "u" shape, with thearms of the "u" parallel to the rotation axis. What is the angularvelocity of the rotating "u"?

Chapter 9, Problem 66

A thin uniform rod is rotating at an angular velocity of 5.18rad/s about an axis that is perpendicular to the rod at its center.As the figure indicates, the rod is hinged at two places,one-quarter of the length from each end. Without the aid ofexternal torques, the rod suddenly assumes a "u" shape, with thearms of the "u" parallel to the rotation axis. What is the angularvelocity of the rotating "u"?

Explanation / Answer

given intial angular velocity = 0 =5.18rad/s since the change occurs without the aid ofexternal torques the angular momentum of the system isconserved If f = I00 f = 0 (I0/If ) where for a rod of mass M and length L then I0 = 1/12 ML2 to determine If we will treat y the arms ofthe u as point masses with mass M/4 a distance L/4 fromthe rotation axis If = (1/12 ( M/2) (L/2)2 ) + 2(M/4 (L/4)2 = 1/24 ML2 f = 0(1/12ML2/ 1/24 Ml2 ) = 5.18 rad/s *2 = 10.36rad/s f = 0(1/12ML2/ 1/24 Ml2 ) = 5.18 rad/s *2 = 10.36rad/s

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