A particle of mass m slides down the frictionless surface from height h and collides with the uniform vertical rod of length L and mass M. After the collision, mass m sticks to the rod. The rod is free to rotate in a vertical plane about fixed axis through O. Find maximum angular deflection from its initial position.
closed as off-topic by dmckee♦ Oct 23 '15 at 15:52
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There is probably a more clever way to do this, but here are some concepts that may help you along the way. If you have a problem in this type of situation, you need to consider all the conservation laws that are at your disposal. You mention in our discussion in the previous comments using conservation of angular momentum and conservation of energy. These are both concepts that you will need to solve this problem.
Conservation of energy can be used to find the speed of the particle, but upon an inelastic collision with the rod, you know that angular momentum will be conserved.
Knowing the angular momentum, you can then recalculate the kinetic energy of the system (by knowing $\omega$ and the moment of inertia, $I$). Now you can use conservation of energy again to calculate the maximum deflection of the rod.