A thin uniform rod is rotating at an angular velocity of 5.18rad/s about an axis
ID: 1722886 • Letter: A
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 66A 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/sRelated Questions
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