Motion of a rod on another rod of same mass.

1. Apr 24, 2012

andrien

1. The problem statement, all variables and given/known data

A perfectly rough rod is gently placed with one end
upon another rod of equal mass and in the same vertical
plane, moving with the velocity √2gc on a smooth table. If
the initial inclination of the first rod to the horizon be α, and
its length 2a, shew that it will just rise to a vertical position
if
2a (1 -sin α) (5 + 3 cos ^2 α) = 3c sin ^2 a.

2. Relevant equations

3. The attempt at a solution- i have used the fact that moment of momentum just after putting rough rod will be zero about point of contact to determine initial angular velocity.after that I used equation of energy and conservation of momentum in horizontal direction.but i am not sure about the end condition i used that reaction will become zero in vertical position and also may be angular velocity will become zero.none of these have yielded answers.at least i want to know the end condition.so please help.source of the problem is a.s. ramsey dynamics vol.2.