# 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 [closed]

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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• Tell us what you have tried so far and what concepts specifically are confusing. – tmwilson26 Oct 23 '15 at 15:19
• i have tried to conserve energy.loss in potential energy equal to gain in rotational kinetic energy + gain in potential energy – Dev Oct 23 '15 at 15:24
• Thats a good place to start to get the speed of the particle at the bottom. However, when a collision involves two objects sticking together, it is generally considered inelastic, and conservation of energy can't be used. What other conservation laws do you know that you can consider? – tmwilson26 Oct 23 '15 at 15:26
• angular momentum of the system just before and after the collision. this will give me w(omega), not deflection. – Dev Oct 23 '15 at 15:30
• Okay, I understand where the confusion comes from, I'll write a quick answer to help you (while leaving it up to you to solve the problem) – tmwilson26 Oct 23 '15 at 15:37

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.